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## Material Information- Title:
- Design of an Integral Thermal Protection System for Future Space Vehicles
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- BAPANAPALLI, SATISH KUMAR (
*Author, Primary*) - Copyright Date:
- 2008
## Subjects- Subjects / Keywords:
- Approximation ( jstor )
Boundary conditions ( jstor ) Buckling ( jstor ) Design analysis ( jstor ) Design optimization ( jstor ) Heat transfer ( jstor ) Insulation ( jstor ) Reentry ( jstor ) Structural deflection ( jstor ) Surface temperature ( jstor )
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- 5/31/2008
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- 659814587 ( OCLC )
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PAGE 1 1 DESIGN OF AN INTEGRAL THERMAL PRO TECTION SYSTEM FOR FUTURE SPACE VEHICLES By SATISH KUMAR BAPANAPALLI A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLOR IDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2007 PAGE 2 2 Â© 2007 Satish Kumar Bapanapalli PAGE 3 3 To my loving wife Debamitra, my parents Na gasurya and Adinarayana Bapanapalli, brother Gopi Krishna and sister Lavanya PAGE 4 4 ACKNOWLEDGMENTS I would like to express my sincere gratitude to my advisor and mentor Dr. Bhavani Sankar for his constant support (financial and otherwise) and motivation throughout my PhD studies. He allowed me to work with freedom, was always supportive of my ideas and provided constant motivation for my research work, which helped me grow into a mature and confident researcher under his tutelage. I also thank my committee co-chair Dr. Rafi Haft ka for his invaluable inputs and guidance, which have been instrumental for my research work. I am also grateful to him for getting my interest into the field of Structur al Optimization, which I hope would be a huge part of all my future research endeavors. I am also thankful to Dr. Max Blosser (NASA Langley) for his crucial inputs in my research work, which ke pt us on track with the expectations of NASA. I sincerely thank my dissertation committ ee members Dr. Ashok Kumar and Dr. Gary Consolazio for evaluating my research work a nd my candidature for the PhD degree. I also would like to acknowledge Dr. Peter Ifju and Dr. Nam-Ho Kim for their useful inputs and comments. I am thankful to NASA, for their fi nancial support through the CUIP Project, and the program manager Claudia Meyer. Thanks also go to all the past and current members of Center of Advanced Composites: Ryan, Jongyoon, Huadong, Oscar, Jianlong, Thi, Sujith and Ben, and other graduate students in the department: Christian, Tushar, Vijay, and Palani. PAGE 5 5 TABLE OF CONTENTS page ACKNOWLEDGMENTS...............................................................................................................4 LIST OF TABLES................................................................................................................. ..........7 LIST OF FIGURES................................................................................................................ .........9 ABSTRACT....................................................................................................................... ............11 CHAPTER 1 INTRODUCTION AND OBJECTIVES.............................................................................13 1.1 Introduction............................................................................................................... ........13 1.2 Requirements of a Thermal Protection System................................................................16 1.3 Objectives................................................................................................................. ........19 1.4 Approach................................................................................................................... ........20 1.4.1 The Optimization Problem.....................................................................................20 1.4.2 Geometry and Design Variables.............................................................................21 1.4.3 Analysis: Finite Element Methods.........................................................................21 1.4.4 Loads and Boundary Conditions............................................................................22 1.4.5 Formulation of Constraints.....................................................................................22 1.4.6 Optimized Designs.................................................................................................23 2 BACKGROUND..................................................................................................................24 2.1 Approaches to Thermal Protection...................................................................................24 2.1.1 Active TPS..............................................................................................................2 4 2.1.2 Semi-passive TPS...................................................................................................25 2.1.3 Passive TPS............................................................................................................25 2.2 TPS and NASA............................................................................................................... ..27 2.3 Need for a load-bearing TPS: ITPS..................................................................................36 2.4 ITPS Design Challenges...................................................................................................38 2.5 Choice of Constraints...................................................................................................... .41 2.6 Background on Corrugated-Core and Truss-Core Sandwich Structures..........................43 2.7 Background on Multi-Disciplinary Optimization and Response Surface Approximation Techniques.................................................................................................45 3 FINITE ELEMENT MOD ELS AND ANALYSES.............................................................49 3.1 Finite Element Analysis for Heat Transfer.......................................................................49 3.1.1 Incident Heat Flux and Radiation Equilibrium Temperature.................................49 3.1.2 Loads, Boundary Conditions and Assumptions.....................................................52 3.1.3 One-Dimensional and Two-Dimensional FE Models............................................55 3.1.4 Temperature vs. Reentry Time and Temperature Distribution..............................58 PAGE 6 6 3.1.5 Obtaining Temperature Data from the FE Analysis...............................................61 3.2 Finite Element Buckling Analysis....................................................................................62 3.3 Stress and Deflection Analysis.........................................................................................68 4 RESPONSE SURFACE APPROXIMA TIONS AND OPTIMIZATION PROCEDURE...................................................................................................................... 69 4.1 Response Surface Approximations...................................................................................69 4.1.1 Response Surface Approximations for Maximum Bottom Face Sheet Temperature.................................................................................................................70 4.1.2 Response Surface Approximations for Buckling...................................................70 4.1.3 Response Surface Approximations for Stress and Deflection................................71 4.2 Procedure for Generation of Response Surfaces Approximations...................................71 4.3 Optimization Procedure....................................................................................................7 5 5 ITPS DESIGNS................................................................................................................... .76 5.1 Selection of Loads, Boundary Conditions and Other Input Parameters...........................76 5.2 Corrugated-Core Designs.................................................................................................80 5.2.1 Accuracy of Response Surface Approximations....................................................83 5.2.2 Optimized Corrugated-Core Panel Designs...........................................................86 5.2.3 Buckling Eigen Values, Deflections and Stresses at Different Reentry Times......90 5.2.4 Optimized Designs with Changed Boundary Conditions.......................................97 5.3 Truss-Core Structures for ITPS........................................................................................98 6 EFFECT OF INPUT PARAME TERS ON THE ITPS DESIGN.......................................104 6.1 Sensitivity of ITPS Designs to Heat Transfer Parameters..............................................105 6.1.1 Changing the Emissivity of the Top Surface of ITPS..........................................105 6.1.2 Allowing Heat Loss from the Bottom Face Sheet................................................106 6.1.3 Increasing the initial temp erature of the structure................................................107 6.2 Sensitivity of ITPS Designs to Loads and Boundary Conditions...................................109 6.2.1 Effect of Boundary Conditions.............................................................................109 6.2.2 Increasing the Pressure Load on the Top Surface................................................109 6.2.3 Increasing the In-Plane Load................................................................................110 7 CONCLUSIONS AND FUTURE WORK........................................................................111 7.1 Conclusions................................................................................................................ .....111 7.2 Future Work................................................................................................................ ....113 APPENDIX: MATERIAL PROPERTIES USED FOR THE RESEARCH WORK..................116 LIST OF REFERENCES............................................................................................................. 120 BIOGRAPHICAL SKETCH.......................................................................................................126 PAGE 7 7 LIST OF TABLES Table page 3-1 Peak radiation equilibrium temp eratures for reentr y heat fluxes...........................................51 3-2 Load steps in the FE heat transfer analysis.............................................................................54 5-1 Summary of mechanical loads applie d on the ITPS panel fo r buckling and stress analysis cases................................................................................................................. ....79 5-2 Ranges of the 7 design variable s for corrugated-core ITPS panels........................................82 5-3 Accuracy of the res ponse surface approximations for peak bottom face sheet temperature and top face sheet deflections........................................................................84 5-4 Accuracy of the respons e surface approximations for top face sheet and web buckling eigenvalues.................................................................................................................... .....84 5-5 Table showing the accuracy of the respon se surface approximations for stresses in the ITPS panel..................................................................................................................... .....86 5-6 Table listing the optimized de signs for corrugated-core panels.............................................88 5-7 Table listing the optimized designs for corrugated-core panels with relaxed boundary conditions on the bottom face sheet...................................................................................98 5-8 Comparison of values predicted by res ponse surface approximations and finite element analysis for Designs I and IV.............................................................................................98 5-9 Comparison of the stresses in beam model and shell model................................................102 6-1 Changes in ITPS design due to d ecrease in emissivity value to 0.7.....................................105 6-2 Changes in ITPS design due to loss of h eat from the bottom face sheet corresponding to a bottom face sheet emissivity value of 0.2.....................................................................108 6-3 ITPS designs with increase in initial temperature to 395 K. Initial temperature in the baseline model was 295 K...............................................................................................108 6-4 ITPS designs with increase in pr essure load to 2 atmospheres............................................110 6-5 ITPS designs with increase in in-plane load to 150,000 N/m..............................................110 A-1 Temperature dependent mate rial properties of Ti-6Al-4V..................................................116 A-2 Temperature dependent materi al properties of Inconel-718................................................117 A-3 Temperature dependent materi al properties of Beryllium alloy..........................................118 PAGE 8 8 A-4 Temperature dependent ma terial properties of SAFFILÂ®....................................................119 PAGE 9 9 LIST OF FIGURES Figure page 1-1 A unit cell of the corrugated-core ITPS design......................................................................22 2-1 Pictures of the space capsules............................................................................................ .....29 2-2 Apollo heat shield structure.............................................................................................. ......29 2-3 Distribution of TPS on the Space Shuttle Orbiter..................................................................30 2-5 ARMOR TPS construction. ................................................................................................. .34 2-6 Prepackaged superalloy honeycomb panel.............................................................................35 2-7 Corrugated-core sandwich structur e construction for ITPS applications...............................38 3-1 Heating profiles of a Shuttle-like vehicle...............................................................................5 1 3-2 Typical heating profile used for the ITPS design...................................................................52 3-3 Schematic of loading and boundary condi tions for the heat transfer problem.......................53 3-4 Typical mesh for 2-d heat transfer problem............................................................................56 3-5 Schematic representation of 1-D heat transfer model............................................................57 3-6 Comparison of 1-d and 2d heat transfer analyses.................................................................60 3-7 Temperature variation vs. reentry times for top and bottom surfaces and web mid-point obtained from 1-d heat transfer analysis............................................................................60 3-8 Temperature distribution through the thickn ess of the ITPS panel at different reentry times.......................................................................................................................... .........61 3-9 Typical FE shell element mesh for buckling analysis............................................................63 3-10 Typical ITPS panel illustrating the manner in which the webs are partitioned into 10 regions to impose approximate temperat ure dependent material properties.....................67 3-11 Typical buckling modes of the ITPS panel. .......................................................................68 4-1 Flowchart illustrating the proce dure followed by the ITPS Optimizer..................................72 5-1 Heat flux input used for the de sign of corrugated-core structures.........................................77 5-2 Aerodynamic pressure load on the TPS for a Space Shuttle-like design...............................79 PAGE 10 10 5-3 A unit cell of a corrugated-core ITPS panel illustrating the 6 design variables.....................81 5-4 A typical FE contour plot illustrating the stresses at the panel edges at the junction between the face sheets and the webs................................................................................87 5-5 Buckling modes for optimized designs..................................................................................89 5-6 Typical web deformation tendency due to the temperature gradient in the panel..................90 5-7 Von Mises stress distributi on in the ITPS panel, Design 1, tmax T. .......................................90 5-7 ITPS panel behavior with resp ect to reentry time for Design 1.............................................94 5-8 ITPS panel behavior with resp ect to reentry time for Design 2.............................................96 5-9 Stress singular ity at beam-plate junction points...................................................................101 5-10 FE experiment to compare beam mode l to a more realistic shell model. .........................102 5-11 Truss-core model with only shell elements. .....................................................................103 6-1 Heat flux entering the ITPS through the top surface for two different emissivity values imposed on Design I........................................................................................................107 PAGE 11 11 Abstract of Dissertation Pres ented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy DESIGN OF AN INTEGRAL THERMAL PRO TECTION SYSTEM FOR FUTURE SPACE VEHICLES By Satish Kumar Bapanapalli May 2007 Chair: Bhavani V. Sankar Cochair: Raphael T. Haftka Major: Mechanical Engineering Thermal protection systems (TPS) are the featur es incorporated into a spacecraftÂ’s design to protect it from severe aerodynamic heating during high-speed trav el through planetary atmospheres. The ablative TPS on the space capsul e Apollo and ceramic tiles and blankets on the Space Shuttle Orbiter were designed as add-ons to the main load-bearing structure of the vehicles. They are usually incompatible with th e structure due to mismatch in coefficient of thermal expansion and as a result the robustness of the external surface of the spacecraft is compromised. This could potentially lead to catastrophic consequences because the TPS forms the external surface of the vehicle and is s ubjected to numerous other loads like aerodynamic pressure loads, small object high-speed impact s and handling damages during maintenance. In order to make the spacecraft external surface robust, an Inte gral Thermal Protection System (ITPS) concept has been proposed in this resear ch in which the load-bearing structure and the TPS are combined into one single structure. The design of an ITPS is a formidable task because the requirement of a load-bearing structure and a TPS are often contradictory to one another. The design process has been formulated as an optimization problem with mass per unit area of the ITPS as the objective PAGE 12 12 function and the various functions of the ITPS were formulated as constraints. This is a multidisciplinary design optimization pr oblem involving heat transfer a nd structural analysis fields. The constraints were expressed as response surface approximations obtained from a large number of finite element analyses, which were ca rried out with combinations of design variables obtained from an optimized Latin-H ypercube sampling scheme. A MATLABÂ® code has been developed to carry out these FE analyses automatically in conjunction with ABAQUSÂ®. Corrugated-core structures were designed fo r ITPS applications with loads and boundary conditions similar to that of a Space Shuttle-like vehicle. Temp erature, buckling, deflection and stress constraints were considered for the de sign process. An optimized mass ranging between 3.5Â–5 lb/ft2 was achieved by the design. This is cons iderably heavier when compared to conventional TPS designs. However, the ITPS ca n withstand substantia lly large mechanical loads when compared to the conventional TPS. Truss-core geometries used for ITPS design in this research were found to be unsuitable as th ey could not withstand large thermal gradients frequently encountered in ITPS applications. The corrugated-core design was used for furthe r studying the influence of the various input parameters on the final design weight of the IT PS. It was observed that boundary conditions not only significantly influence the IT PS design but also have a major im pact on the effect of various input parameters. It was found that even a sm all amount of heat loss from bottom face sheet leads to significant reduction in ITPS weight. Aluminum and Beryllium are the most suitable materials for bottom face sheet with Beryllium ha ving considerable advantag es in terms of heat capacity, stiffness and density. Although ceram ic matrix composites have many superior properties when compared to metal alloys (Tit anium alloys and Inconel), their low tensile strength presents difficulties in ITPS applications. PAGE 13 13 CHAPTER 1 INTRODUCTION AND OBJECTIVES 1.1 Introduction One of the most important goals of the space industry in the new century is to reduce the cost of access to space. Large amount of money is being invested into launching satellites for various civilian and military purposes, building the International Space Station and planning future missions to Moon and Mars. According to estimates [1], the cost of delivering a pound of payload into space in the period 1990 to 2000 varied from $4000 to $20,000. There has been no significant improvement over this period in the form of development of a new vehicle or implementation of new concepts for space launch. Th erefore, it can be assumed that the cost of launching a pound of payload has in creased considerably. One of the long-standing goals of National Aeronautics and Space Administration (NAS A) has been to reduce the launch cost by an order of magnitude (t o about $1000 per pound [2]). Today, the least expensive means of delivering payloads into space is by using expendable rocket launch vehicles like the United StatesÂ’ De lta, EuropeÂ’s Ariane, RussiaÂ’s Proton, ChinaÂ’s Long March and IndiaÂ’s Geosynchronous Sate llite Launch Vehicle (GSLV). The biggest disadvantage of these vehicles is that they ar e for one time use and have to be rebuilt for each launch. NASA built the Space Shuttle Orbiter as a part ially reusable vehicle with the capabilities to deliver and bring back men and materials from sp ace. It can also be used as a short-term space laboratory, deliver payloads to lo w earth orbit, and repair and re trieve malfunctioning satellites. However, it amounts to enormous cost to refurbis h the solid rocket boosters, build a new external fuel tank and maintain the Shuttle between f lights. In order to overcome the challenges These estimates are for Â“WesternÂ” launch vehicles and the variations in cost of payloads are due to different vehicles and different orbits into which the payloads are delivered. PAGE 14 14 associated with the Space Shuttle, NASA along w ith US industry aimed at developing a fully reusable single-stage-to-orbit (SSTO) vehicle, the VentureS tar. However, this vehicle development has been stopped due to various budgetary and technolog ical constraints. In 1993, NASA made a study Â“Access to SpaceÂ” [2], which concluded that an SSTO reusable launch vehicle (RLV) can bring down the cost of access to space by an order of magnitude. Thus, despite enormous challenges a nd setbacks, reusable or partially reusable launch vehicles are still somethi ng to strive for in future, at least for manned missions to the space, Moon and Mars. When a spacecraft enters any planetary atmosphe re, it usually does so at hypersonic speeds of over Mach 20 and up to Mach 40. High ener gy, high velocity fli ghts through planetary atmospheres lead to extremely severe aer odynamic heating and pressures on the vehicle exteriors. The vehicle structure needs to be prot ected from damage due to this heating. Design features incorporated into a ve hicle to withstand this aerodyna mic heating and protect it from damage are known as Thermal Protection Systems or TPS. Early thermal protection systems used on lunar vehicles, like Mercur y, Gemini and Apollo, were single-use ablators, in which material on th e surface ablates by absorbing the heat and thus prevents the heat from enteri ng the capsule [3Â–9]. This concept is still in use on the Soyuz capsules used by Russia for manned missions. The Space Shuttle Orbiter uses thermal protection systems made of high-temperatur e-resistant ceramic tiles and blankets [10,11], which primarily function as insulators and prevent heat from reach ing the vehicle interiors. These tiles make the Space Shuttle exterior very brittle and susceptible to damage even due to small impact loads. In order to overcome these difficulties, scientists at NASA developed a fully metallic ARMOR TPS [12Â–16] for the VentureStar program. The ARMOR TPS uses metallic honeycomb sandwich PAGE 15 15 panels as the outer surface, to withstand pressure loads, and high efficiency fibrous insulation materials to prevent heat from reaching the vehicle interior. However, the load-bearing capabilities of this TPS are limited, and large loads like in-plane inertial loads cannot be accommodated under this design and are taken by the structure of the vehicle. TPS occupies a huge acreage on the vehicle exte riors and forms a majo r part of the launch weight. Therefore, it is imperative that apart fr om making the TPS suitable for thermal protection purposes, it should also be made li ghtweight in order to keep the launch costs down. TPS is also required to present a robust external surface fo r the vehicle. One approach proposed towards achieving this goal it to combine the functions of load-bearing and thermal protection into one structure. Efforts are on to develop a robus t load-bearing TPS structure called Integral Thermal Protection System , ITPS. The ITPS has both the thermal pr otection and load-bearing capabilities integrated into one structure. This is unlike the Space Shuttle TPS in which thermal protection and load-bearing functions are performed by co mpletely different members. The biggest challenge of an ITPS is that the requirement s of a load-bearing member and a TPS are contradictory to one another. A TPS is requ ired to have low conductivity and high service temperatures. Materials satisfying these conditions are ceramic materials, which are also plagued by poor structural properties like low impact re sistance, low tensile st rength and low fracture toughness. On the other hand, a robust load-bearing structure needs to have high tensile strength and fracture toughness and good impact resistance. Materials that sa tisfy these requirements are metals and metallic alloys, which have relativel y high conductivity and low service temperatures. A structure with good load-bearing properties is usually a dense structure. A dense structure presents a larger heat conduction path between th e outer surface and vehi cle interiors. On the PAGE 16 16 contrary, a good TPS is usually made of low-de nsity material. The challenge is to develop a structure that can combine these two functions into one single structure an d this is the objective of the current research effort. 1.2 Requirements of a Thermal Protection System TPS forms the external surface of a vehicle a nd is exposed to a variety of environmental conditions at different times duri ng its flight. The specific times and nature of these conditions differ for different missions and vehicle type. For example, the Space Shuttle TPS encounters different types of environments during both launch and reentry, while space capsules like Apollo and Soyuz encounter severe environments only dur ing reentry, as they are well shielded during launch. The aerodynamic heating and pressures expe rienced by a TPS are also dependent on the vehicle shape and the trajectories taken by the vehi cle. A set of general re quirements of a TPS is presented in this section. Heat Load. The primary function of a TPS is to re gulate the heat flow to and from the vehicle. In most cases, the major design driver for TPS is the aerodynamic heating during vehicle reentry into EarthÂ’s atmosphere . Depending on the vehicle design, the TPS may be subjected to considerable plume heating. Plume heating is the heating of the TPS due to the combustion process of propellants that gene rate considerable heat upon exiti ng the rocket nozzles. In some case like the VentureStar, the TPS may act as in sulation to the cryogenic tanks. In this case, the function of a TPS is to prevent the formation of liquid oxygen or ice on th e vehicle exteriors as well as to limit the amount of cryogenic fuel lost to boil-off. Solar heatin g and radiative heat loss from the outer surface to space may be factors in design of TPS for vehicles that spend considerable amount of time in space. Apart from regulating the heat flow, the materials used for TPS should be able to withstand the high temp eratures without substantial degradation in material properties. PAGE 17 17 Mechanical Loads. Mechanical loads on the TPS include transverse aerodynamic pressure loads, in-plane inertial loads, and acoustic and dynamic loads. These loads vary widely depending on the vehicle shape and the position of the TPS on the vehicle. In the Space Shuttle, the nose cone, and wing and tail leading e dges experience tremendous aerodynamic pressure. Aerodynamic pressure loads are also very high for windward side of a space capsule. In contrast, the leeward side of a space cap sule and most other areas on th e Space Shuttle are subjected to slight negative aerodynamic pressure loads, whic h may not be major design drivers. In-plane inertial loads on a vehicle are extremely high fo r TPS on the rear part of the vehicle than compared to the front portion. In addition, ther e may be acoustic and dynamic loads on the TPS, usually generated by the propulsion system. TPS must be able to withstan d these loads without failure in the form of yi elding, buckling or fracture. Deflection Limits. TPS forms the external surface of the vehicle and, ther efore, dictates the aerodynamic profile presented by the vehicle. Thermal and m echanical loads could lead to considerable amount of deflection of the top surface. It is required that the top surface deflections of the TPS be below certain limit in order to maintain the smooth aer odynamic profile of the vehicle. Excessive local deflection, such as a top surface dimpling, can le ad to severe local aerodynamic heating [12,13], which may lead to catastr ophic failures. Impact Loads. Good impact resistance is another desi rable property of a TPS, which can be subjected to various types of impact. Duri ng installation and maintenance, the TPS can be subjected to various handling damages and low speed impacts like accidental dropping of the panels on a hard surface or accidentally dropping of tools on the TPS. During launch and landing, it may be subjected to im pact from runway debris. During flight, it may encounter small object impact like hail, bird-str ike, rain, snow, and dust. In th e space, it may be subjected to PAGE 18 18 high-speed impact from space debris and meteorite s. A TPS should be able to withstand these small-object-high-velocity impact loads so that th ey do not lead to a catastrophic failure. Impact resistance of TPS is beyond the scope of this research work. Chemical Deterioration. During reentry the high temperatures on the top surface may make the TPS susceptible to chemical attack su ch as oxidation. TPS properties may be altered due to water absorption and spills of various su bstances during maintenance. TPS should be able to resist these chemical attacks. Chemical stabilit y of TPS is not considered in the this research effort. Low Cost Operability. Apart from initial fabrication and installation costs, the life cycle cost of a TPS also includes its maintenance th roughout its life. TPS that is robust and operable leads to low maintenance costs. A robust TPS is one that is not easily damaged by its design environment and can withstand damage to a cert ain extent without requiring immediate repair. An operable TPS is one that can be inspected and maintained easily, removed, replaced or repaired, if necessary. Light Weight. TPS occupies a huge acreage on space vehicles and constitutes a major portion of the launch weight. Increase in launch lo ads could lead to increased fuel requirements and/or decrease in the payload mass. Therefor e, TPS should be designed for minimum mass to perform its various functions. The large number of often-contradictory re quirements makes the TPS design a formidable task. It requires a good unders tanding of many tec hnical disciplines. TPS design involves transient heat transfer analysis, stress and deflection analysis, and mechanical and thermal buckling analysis. In this researc h, the heat load on a TPS is assume d to be available. Calculation of aerodynamic heating and pressures is out of the scope of this research, as it requires a large PAGE 19 19 amount of information like vehicle shape, trajec tory and velocity at di fferent times during its flight. ITPS design can be considered to be an ex tension of the ARMOR TPS design. It is aimed at including design features to carry large in-plane loads (typical of Space Shuttle) and substantially higher pressure load s, apart from providing the insula tion properties similar to that of the ARMOR TPS. Previous ITPS attempts lik e multi-wall TPS (details in Section 2.2) faced difficulties like manufacturability and evacu ation of the gaps in between the walls. Manufacturability can be a potential concern for the current ITPS design as well; however, addressing this concern is beyond the scope of th is research work. The use of high-efficiency insulation materials, like SAFFIL, is considered to be the major improvement over multi-wall TPS, as the insulation material blocks the ra diation from the top surface and decreases the thermal conductivity of the structure substantia lly. Some of the demonstrated manufacturing capabilities for the ARMOR TPS can be potential ly exploited for ITPS fabrication as well. 1.3 Objectives The objective of this research work is to develop a multidisciplinary design optimization procedure to design an Integral Thermal Protection System by reconciling the various conflicting requirements of a TPS and a load-bearing member into one single structure. The goal is to demonstrate the feasibility of such a desi gn concept by comparing it to the other TPS performance and weight. Another objective is to study th e influence of variation of input parameters on the ITPS weight. Some of the parameters studied are surfac e emissivity, heat loss from ITPS to the vehicle interiors, initial temperature of the structure be fore reentry, thermomechanical properties of the materials used for the ITPS, different displacement/rotation boundary conditions on the panels PAGE 20 20 and the magnitude of pressure loads and in-plane loads. These would help formulate a general set of guidelines for ITPS design. 1.4 Approach 1.4.1 The Optimization Problem Various conflicting requirements of a TPS a nd a load-bearing structure need to be reconciled to find a feasible solu tion. This is possible by formul ating the design process as an optimization problem. The objective of the process is to make the structure as light as possible while fulfilling all the functions required of an ITPS. Theref ore, the obvious choice for an objective function would be mass pe r unit area of the ITPS panel, M . Various functions of the panel were formulated in the form of constr aints for the optimizati on problem. Thus, the optimization problem can be stated as Â“minimize mass per unit area of the panel while satisfying all the constraintsÂ” such as temperatures, stress es and deflections limits in various parts of the structure, and withsta nd global/local buckling. Critical functions of an ITPS that have a poten tial influence on the design were taken into account [12,13]. The following are th e four critical constraints ta ken into account for the design (see Section 2.5 for more details): 1. Maximum temperature of the bottom surface of the panel must be below certain limit. 2. Panel must be able to withstand global/lo cal buckling due to mechanical and thermal forces. 3. Maximum stresses in the various members of the panel must be within allowable limits. 4. Maximum deflection of the top surface of the panel must be below acceptable limit. The mathematical statement for the optimization problems is as follows Minimize M ({ v }) subject to the constraints allowable B BT v T PAGE 21 21 Lv B allowablev allowable T Tu v u where { v } represents the design variables, TB is the peak bottom face sheet temperature, TBallowable is the maximum allowable bott om face sheet temperature, { B } is an array containing the buckling eigenvalues, L is the minimum allowabl e buckling eigenvalue, { } is a vector containing the maximum stresses in the panel, allowable is the maximum allowable stress in the panel, uT is the maximum deflection of the top f ace sheet in the thickness direction, and uT-allowable is the maximum allowable deflection of the top face sheet. 1.4.2 Geometry and Design Variables The geometry of the ITPS structure with co rrugated-core design is shown in Figure 1-1. This geometry can be completely described using the following 6 geometric variables: 1. Thickness of top face sheet, tT, 2. Thickness of webs, tW, 3. Thickness of bottom face sheet, tB, 4. Angle of corrugations, , 5. Height of the sandwich pane l (center-to-center distance between top and bottom face sheets), h , 6. Length of a unit-cell of the panel, 2 p . 1.4.3 Analysis: Finite Element Methods Heat transfer, buckling and stress analyses ha ve to be carried out on the ITPS structure in order to formulate the temperatur e and other structural constraint s. In this research, all the analyses were carried out by finite element (FE) methods using ABAQUSÂ® finite element package. Heat transfer finite element analyses were carried out to determine the maximum bottom face sheet temperatures and temperature distribu tions in the ITPS, buckling FE analyses were PAGE 22 22 carried out to determine the smallest buckling ei genvalues, and stress anal yses were carried out to determine the maximum stresses in the ITPS an d the maximum deflection of the top surface. Details of these analyses, and load and boundary conditions used are presented in Chapter 3. Figure 1-1. A unit cell of the co rrugated-core ITPS design. The six variables describing the geometry are illustrated. Directions y and z of the global coordinate system of the ITPS panel are also shown ( x -axis comes out perpendicular to the plane of the paper). 1.4.4 Loads and Boundary Conditions The ITPS can be considered an extension of or improvement over the ARMOR TPS design [12Â–14]. Therefore, in the desi gn process the aerodynamic heat lo ad and the mechanical loads from a VentureStar RLV design were used [12,13] . The design performance and weights are also compared with those of the ARMOR TPS, in orde r to gain a perspective on the ITPS design with respect to the current designs. The material selection for the designs was also similar to that of the ARMOR TPS. Details have been presented in Chapter 5. 1.4.5 Formulation of Constraints The relation between the geometric design variab les and the constraints was established in the form of response surface approximations. Hundr eds of FE analyses were conducted at design points in a suitably chosen design space. The desi gn points were obtained with the help of an optimized Latin-Hypercube Sampling technique. Results from FE analyses were used to fit tT tW h 2p z y tB PAGE 23 23 quadratic polynomials called re sponse surface approximations. For each constraint, one or more response surface approximation was obtained in the form of a complete quadratic polynomial in terms of the design variables. The response su rface approximations can approximately predict the value of a constraint, given an arbitrary co mbination of design variables. The process for obtaining these approximations has been described in Chapter 4. Generation of response surface approximati ons requires a large number of function evaluations, or in this ca se a large number of FE analyses. It is not possible to carry out these FE analyses manually. Therefore, a MATLAB code called ITPS Optimizer was developed for this process, which has the capability to automati cally carry out hundreds of FE analyses in conjunction with ABAQUS FE package. 1.4.6 Optimized Designs The response surface approximations were generated from the data obtained from the ITPS Optimizer using least squares approximation method. These response surface approximations were then used for the optimization proce ss, which was carried out using the Matlab optimizer subroutine fmincon ( ). PAGE 24 24 CHAPTER 2 BACKGROUND This chapter presents background relevant to this research work. First a discussion on the general types of TPS used on space vehicles is presented followed by a summary of the history of TPS and NASA. Then a discussion on the need for an ITPS and the various challenges related to ITPS design is presented. As the ITPS panel geom etry is similar to co rrugated-core or trusscore sandwich structures, a brief summary of the research work related to these sandwich structures is presented. Finall y, literature on multidisciplinary optimization (MDO) and response surface approximations technique is presented. 2.1 Approaches to Thermal Protection Type of TPS and specific designs can depend on the magnitude and duration of aerodynamic heating. Even on the same vehicle several different TPS may be used, as the heating varies over the vehicle surface. TPS a pproaches can be broadl y classified into 3 categories: active , semi-passive , and passive [11: p.24]. 2.1.1 Active TPS Active TPS have an external system that supplie s coolant to continually remove heat or to block the heat from reaching the structure. There are three commonly discussed active TPS concepts [11: p.28]: transpiration, film and convec tive cooling. In transpir ation and film cooling a fluid is ejected from the vehicle surface, which flows along the surface and evaporates by absorbing the aerodynamically-generated heat, t hus, preventing the heat from reaching the surface of the vehicle. Convective cooling is a mo re practical TPS concept and has been studied for use in the airframe structure of National Aerospace Plane [11: p.28]. In this concept, a coolant is circulated through passa ges in the airframe to remove heat that has been absorbed from aerodynamic heating. In all these cases, an exte rnal pumping system is required to bring the PAGE 25 25 fluid from a coolant reservoir to the surface. The weight of the coolant is added to the launch weight along with the weight of the pumping sy stem. Further, the design of these active coolant components is very complicated and may lead to high maintenance costs. 2.1.2 Semi-passive TPS Semi-passive TPS use a working fluid to remove heat from the TPS but require no external system to circulate the fluid. Two of the most frequently discussed semi-passive TPS concepts are heat pipes and ablators. Heat pipes are su itable for regions where there is extremely high, localized heating close to a cooler region. Heat pipes embedded in carbon-carbon TPS have been studied for the wing leading edge of the National Aerospace Plane [17]. In this concept, heat is absorbed by the working fluid in the hotter area . This heat vaporizes the fluid and the vapor flows into the cooler regions where it condenses by giving up heat to the cooler structure. The coolant is then brought back to the hotter regions by the cap illary action of a wick. Ablators are very practical and attractive concepts for thermal protection and were extensively used on space capsules like Apollo and Soyuz. Ablators undergo chemical changes by absorbing the aerodynamic heat and generate gases, thus, bloc king the majority of the heat from reaching the vehicle surface. Apollo us ed a phenolic epoxy resin ablator for thermal protection [5,6]. While ablation has been successfully used for small areas for thermal protection, it is not a viable concept for large vehicl e surfaces like the Space Shuttle Orbiter. 2.1.3 Passive TPS Passive TPS radiate the heat from top surface an d/or absorb heat into the structure during high heating periods and dissipate it after the heating subsides. Passive TPS have no working fluids to remove or dissipate heat. Passive syst ems have the simplest designs and are suitable for low heat loads. For high heat loads the weight of the passive TPS becomes prohibitively high. PAGE 26 26 Three different types of passive TPS are discu ssed here: heat sink, hot structure and insulated structure. Heat Sink. In this concept, a major portion of the incident heat load on the TPS is absorbed into the TPS structure. The amount of h eat that can be absorbed is determined by the specific heat capacity and maxi mum service temperature of the TPS material, and initial temperature of the TPS structure. For higher heat load, higher amount of T PS material has to be added. But the structure weight could become larg e for high heat loads. Th e biggest advantage of heat sink concept is that it leads to a simple and reliable design. Heat sink approach has been implemented on early ICBMs and the afterbodies of the Mercury and Gemini reentry vehicles [4,11: p.25]. Hot Structure. The temperature of a hot structure is allowed to increase close to the radiation equilibrium temperature, so that a major portion of the heat is radiated out of the TPS. Radiation equilibrium temperature is the temp erature of the surface at which the heat flux radiated out is equal to the incident heat flux. The radiati on equilibrium temperature is determined by the emissivity of the top su rface of the TPS. The radiation equilibrium temperature for heat fluxes on the Space Shuttle Orbiter could be as high as 3000 F [10]. Thus, materials used for a hot structure TPS need to have extremely high service temperatures. Insulated Structure. This structure has features of both hot structure and heat sink. The outer surface of the TPS is in sulated from the underlying struct ure using insulation materials. Since the insulation material conducts only a fracti on of the total incident heat, the temperature of the top surface increases close to radiation equ ilibrium temperature and radiates away most of the heat. The structure also acts as a heat si nk and stores the heat th at has been absorbed. PAGE 27 27 Insulation TPS are usually not designed to with stand significant mechanical loads. They are made of thin gauge material and low-density insulation materials. Most of the active and semi-passive TPS concep ts have the capacity to accommodate large heat fluxes for long periods of time. However, these TPS require overcoming a number of technological challenges and still may have a co mplicated design and high operating costs in the form of maintenance and additional launch co sts for coolant and pumping systems. The prohibitive technological challenges and operating costs limit the use of these TPS to small areas where there is severe aerodynami c heating. For most part of th e vehicle surfaces, passive TPS concepts are used. The ITPS is based on the passive TPS concept. 2.2 TPS and NASA Since its conception in 1958, NASA has been he avily involved in research related to manned-space flight. Of the numerous technical cha llenges for manned flights, TPS is one of the most critical. The history of TPS in NASAÂ’s ma nned space flights can be described using details from three vehicles: a) Apollo, b) Space Shuttle Orbiter, c) X33/VentureStar. The Apollo program ran from 1963 to 1972. . It had two predecessors capable of human space flight: Mercury (1959Â–1963) and Gemini ( 1963Â–1966), from which the technologies were derived to develop TPS forApollo [4,5] (See Fi gure 2-1). It was designed to land men on the Moon and bring them back safely to the Earth. The spacecraft was launched into space and propelled towards the Moon using a three-stage rocket, Saturn V. After completing the lunar mission, the only component that came back to the Earth was the Apollo Command Module, which carried the astronauts. The Command Module was designed for a ballistic reentry to Earth, in other words, it just fell to the Earth from the space, and the reentry speeds were as high as 35,000 km/hr [5]. This resulted in severe aerodynam ic heating on the front face and relatively lower heating on the afterbody. The high heating rates necessitated the use of ablative TPS on PAGE 28 28 these capsules. From among a large number of ab lators developed for this program [6], a lowdensity ablation material, AVC OAT 5026-39/HC-GP was used [6]. The Apollo heat shield structure is shown in Figure 2-2. In order to increase the ablator tensile strength, it was injected into a fiberglass reinforced-nyl on-phenolic honeycomb structure, which was bonded to a brazed stainless steel honeycomb structur e. The functions of the stainl ess steel honeycom b substructure were to hold the ablator in place and to tr ansfer the aerodynamic loads to the aluminum honeycomb panel at the bottom, which was the prim ary load bearing structure. The differential thermal expansions between the stainless stee l and aluminum honeycombs were accommodated by using a slip-stringer strain-isolation system [5]. The ablator was designed to maintain the temperature at the ablator-sta inless steel honeycomb interface below 600 F. The space capsules were for one time use only. None of the parts were reused for the next missions. The Space Shuttle Orbiter was a drastically di fferent manned space flight concept than the space capsules. Development of the orbiter bega n in the late 1960s and the first successful manned launch was in 1981. The OrbiterÂ’s shape is similar to commercial airplanes. It is a vertical-take-off-horizontal-landing vehicle. During reentry, the Space Shuttle navigates through the atmosphere similar to airplanes, except that it flies at hypersonic speeds of over Mach 20 during early stages of reentry. Th e Space Shuttle reentry phase is much longer than that of the space capsules because the Shuttle has a much longer reentry trajectory unlike the ballistic reentry of the capsules. The Space Shuttle Orbi ter is much larger and has a complicated aerodynamic profile when compared to space ca psules. As a result, the aerodynamic heating rates and the integrated heat loads vary consid erably over the surface. The large surface area ruled out the use of non-reusable ablative heat shields. Therefore, mo st of the Space Shuttle PAGE 29 29 surface is covered with passive reusable ceramic TPS materials, which have excellent insulation and high temperature resistance properties. A B C D Figure 2-1. Pictures of the space capsules. A) Mercury. B) Gemini. C) Apollo. and D) Thickness of ablative material at diffe rent locations on the Apollo capsule. Figure 2-2. Apollo heat shield struct ure. (Obtained from Reference [5]). Ablator in n y lonp henolic hone y comb Stainless Steel hone y comb Insulation Aluminum hone y comb Sli p -strin g er strain-isolation s y ste m PAGE 30 30 Different insulation materials originally used on the Space Shuttle include reinforced carbon-carbon (RCC), two types of ceramic reusable surface insulation (R SI) tiles, and a limited amount of non-reusable ablative material [10]. RCC has a reuse temperature of 2900 F [10] and is used at the stagnation regions such as nose cap, wing and tail leading edges, where the heating rates are extremely high. The ceramic RSI tiles c over a major portion of the Shuttles and are of two varieties high and low temperature reusable surface insulation (HRSI, LRSI). In a few areas the HRSI tiles have later been replaced by st ronger fibrous refractor y composite insulation (FRCI) [11: p.30]. Most of the LRSI tiles on the leeward side were also replaced by an advanced flexible reusable surface insu lation, AFRSI [11: p.31]. Figure 23 shows the TPS distribution on the Space Shuttle Orbiter. Figure 2-3. Distribution of T PS on the Space Shuttle Orbiter. (Obtained from Reference [11]) PAGE 31 31 The biggest disadvantage of RSI tiles is that they are highly brittle [10]. They cannot withstand even the slightest of im pact loads and also have a very low strain to failure. Therefore, they cannot be used as structural elements. The tiles are bonded to a sub-structure made of aluminum alloys. The aluminum substructure be ars all the mechanical loads. The ceramic tiles also have a low coefficient of thermal expansi on when compared to aluminum. If the tiles were bonded directly to aluminum, any thermal or mech anical strains in the substructure may cause considerable tensile strain in th e tiles, which could lead to cracki ng. In order to avoid this, strain isolation pads (SIPs), which have a very low shea r and extensional modulli, are used to separate the tiles from the aluminum substructure, Figur e 2-4. Further, the tiles are also made of dimensions 6 inches or less in length and width [10]. Gaps are le ft between tile edges to allow for relative motion when the aluminum skin expa nds or contracts, Figure 2-4. The tiles also require silicon polymer water proofing before ev ery flight. Thus, even though the Space Shuttle TPS provides excellent thermal protection for th e vehicle, it is not robust and is highly susceptible to catastrophic damage. Tile mainte nance between flights requires approximately 40,000 man-hours [11: p.2] and this has increased the turnaround times considerably when compared to the original estimates [10]. These factors have contributed to the enormous launch costs of Space Shuttle flights besides ma king it structurally not very robust. The X33 was an experimental vehicle aimed at developing a comple tely reusable launch vehicle (RLV), the VentureStar RLV. The progr am began in mid 1990s and was cancelled in 2001. It was proposed to be a single-stage-to-orbit (SSTO) launch vehicle with a Boeing Linear Spike engine. The concept was similar to the Space ShuttleÂ’s verti cal-take-off-horizontallanding. However, it had no external boosters or fu el tanks. All the fuel tanks were embedded in the vehicle. This meant that th e size of the VentureStar would be much larger than the Space PAGE 32 32 Shuttle, which in turn implies a much larger surf ace area to be lined with TPS. The VentureStar program was stopped in 2001 due to various technological challe nges, and cost and schedule overruns. However, there were some useful techno logies developed for this program and one of them is the TPS that will be discussed here. Figure 2-4. Schematic of tile attachment to aluminum structure. One of the most important goals of TPS deve lopment for the VentureStar program was to overcome the numerous problems relating to the ceramic tiles on the Space Shuttle and to provide a robust TPS. A TPS of fully metallic construction was proposed in the 1990s [12Â–15]. This TPS was christened ARMOR TPS, where AR MOR stands for adaptable, robust, metallic, operable, and reusable [12]. Major portion of the space inside the VentureStar was to be occupied by the cryogenic fuel tanks. Therefore, the ARMOR TPS was designed to be attached to the cryogenic tank structure. Figure 2-5 sc hematically illustrates the design of the ARMOR TPS. The top surface was made of a metallic hone ycomb sandwich panel, which can withstand small aerodynamic pressure loads on the TPS. The primary job of this panel was to function as a hot structure and re-radiate most of the heat incident on the TPS. The top face sheet of the honeycomb panels was extended to partially overlap the adjacent panels to seal the panel-to- PAGE 33 33 panel gaps from ingress of hot gases during reen try. The top panel was insulated from the bottom using a thick layer of high temperat ure alumina fiber insulation, SaffilÂ®. The insulation material was contained on the sides by bulged, compliant si des made of thin gauge metal foil and at the bottom by a thin gauge metal foil backing. The bulg ed, compliant sides also helped in blocking the radiation between panel-to-panel gaps. The insulation material was vented to the vehicle internal pressure at the bottom, through the titani um foil, so that the aer odynamic pressure loads were borne by the top honeycomb panel. A pictur e frame made of thin gauge titanium box beams formed the TPS boundary on the bottom of the panel. This frame can be used to attach the TPS to the structure. The pressure loads on the top surface were transferred to the titanium box beam through four corner support brackets. The suppor t brackets had low bending stiffness to allow the top face sheet to expand almost freely and thus prevent large thermal stresses from developing in the top panel. The ARMOR TPS pa nels were mounted on a TPS Support Structure (TPSS). The TPSS connects the TPS panels to th e cryogenic tank structure. The top honeycomb panel and the compliant sides were made of tita nium alloy, Ti 1100, for temperatures up to 1100 F. For temperatures ranging fr om 1100 to 2000 F the top panel was made of Inconel 617 and the compliant sides were made of Inconel 718 [12]. ARMOR TPS combines the two concepts of hot structure and insulate d structure to design a lightweight and robust TPS. In fact, it also acts as a heat sink and absorbs a portion of the heat. Since it is made of fully metallic construction, it can be expected to be damage and impact resistant to a certain extent, something that wa s entirely missing in the Space Shuttle TPS. It can also withstand light aerodynamic pressure lo ads and acoustic loads produced by the propulsion system. However, it has no provision to withstand in-plane loads and also cannot withstand large aerodynamic pressure loads. PAGE 34 34 A B C Figure 2-5. ARMOR TPS construc tion. A) Cross-sectional view . B) ARMOR TPS mounted on TPSS and cryongenic tank wall. C) Full-vi ew. (Figures obtained from Reference [12]) Other TPS designs studied for reusable laun ch vehicles were mainly metallic TPS concepts. Prepackaged superalloy honeycomb pa nel was a predecessor to ARMOR TPS [12, 7: p.54] and with similar design featur es, as shown in Figure 2-6. It was developed and tested for the X33 during the 1990s. The top surface was made of Inconel honeycomb sandwich panel, as were the side closures. Inside, it was filled w ith high-temperature insulation and the bottom was closed out with a titaniu m foil backing. The panel has provisions to be attached with mechanical fasteners to a smooth substructure . The panels are also vented to the local atmospheric pressure so that the aerodynamic pressure loads are borne by the substructure rather than the honeycomb panel that forms the outer surface. The prepack aged superalloy honeycomb concept eventually gave way to a more weight efficient ARMOR TPS. PAGE 35 35 Figure 2-6. Prepackaged supera lloy honeycomb panel. (Figure obt ained from Reference [11]) Titanium and super alloy multiwall TPS [18,19] were explored in the 1970s and1980s. These designs consisted of a number of alternate la yers of flat and dimpled metallic foils stacked on top of each other and joined only at the dimple peaks. The multiple layers prevent the radiated heat from the top surface from reaching the botto m. In some designs, the gaps in between the plates were also evacuated to prevent heat transf er through gas conduction and convection [11 p.52]. The heat conduction through the metallic foils would have to follow a long path and this lead to a structure with low conductivity thr ough the panel thickness. The fabrication of the multi-wall TPS proved difficult and the evacuation of the gaps was impractical. The conductivity of the multi-wall TPS was also found to be tw ice that of the Space Shuttle tiles [18]. Another metallic TPS concept tested in the 1970s was a radiative metalli c TPS [20]. In this concept the top surface was made of radiative pane ls, which radiated most of the heat. The panel was corrugated to allow free thermal expansion in the direction transverse to the corrugations and also provide stiffness to resist panel flutter. Functionally graded metal foam-core sandwich panels were studied for TPS applications [21Â–23]. It was found that low relative density foam close to the top face sheet and high density foam close to the bottom face sheet provided a good insulation from high temperature. However, the foam-core TPS did not provide any significa nt advantages when compared to other TPS PAGE 36 36 concepts and there are difficulties in manufact uring of functionally-graded foams as well are attachment of foam s to face sheets. 2.3 Need for a load-bearing TPS: ITPS The first TPS concept for the human space flight used ablative TPS for space capsules Mercury, Gemini and Apollo. This was followed by the Space Shuttle Orbiter, which used ceramic tiles for thermal insulation. A fully metallic TPS concept called ARMOR TPS was proposed for the VentureStar program. In betw een, many other TPS concepts like titanium multiwall TPS and prepackaged honeycomb superalloy TPS were developed a nd tested. The common feature among all these different concepts was that all of them were designed as add-ons to the structure of the space vehicle. The TPS was not part of the structural design calculations. The function of the TPS was restricted to merely regula ting the heat flowing in and out of the vehicle. The thickness of the ablator or the ceramic tile or the insulation thickness was calculated based only on the heat transfer analysis. Of course, that is the reason they have been known as thermal protection systems. There are many problems associated with th ese add-on concepts, the chief among them being the compromise on the robustness of the ou ter surface of the vehicles, usually arising due to incompatibility of the TPS and the load-beari ng structure. For example, the Space Shuttle ceramic tiles needed to be separated from the stru cture of the vehicle usin g strain isolation pads. Apart from the brittleness of the tiles, this relatively weak bonding between the TPS and the structure also exposed the vehicle to failures like loosening and separa tion of tiles from the structure. The ablator TPS never caused catastr ophic failures during the space capsule flights. However, these TPS designs were based on approx imate analytical calculations and subsequent experimental observations. The analytical models were modified after each test flight to understand the ablation and struct ure response phenomena. The pe rformance of the TPS and the PAGE 37 37 structure were designated Â“acceptableÂ” or Â“satisf actoryÂ” [6]. These design practices probably lead to very conservative designs [6]. In othe r words, the TPS was probably much heavier than actually required. The ablators were also bese t with other problems lik e cracking and debonding from the structure, primarily due to mismatch in properties. In order to overcome the problems associ ated with the add-on TPS concepts an Integral Thermal Protection System , ITPS, is required. The basic idea behind this concept is to combine the load-bearing structure and the TPS into one single structure. The ARMOR TPS design implemented this concept Â“partia llyÂ”, in the sense that small aerodynamic pressure loads were borne by the TPS [13]. But the structural desi gn never really took thes e limited load-bearing capabilities of the TPS into account. Further th ere was no provision for in-plane loads in the ARMOR TPS design. The ITPS design, on the other hand, would have provisions to withstand considerable in-plane loads apar t and large aerodynamic pressure loads. Thus, the ITPS can be an integral element of the spacecraft skin rather than a mere add-on. The proposed ITPS design concept is illustra ted in Figure 2-7. ITPS panels have a corrugated-core construction with face sheets on top and bottom joined by a corrugated-core in between. The empty spaces in the corrugated-core can be filled with high-temperature insulation material like Saffil. This design is expected to effici ently combine the three passive TPS concepts of hot structure, insu lated structure and heat sink (dis cussed in Section 2.1) into one single structure. The top face sheet acts as a hot st ructure and radiates out a large portion of the incident heat. The insulation material in the core leads to low ther mal conductivity of the structure. Although the whole TPS panel acts as a heat sink for the heat absorbed, preliminary analyses indicate that the most effective mean s of adding thermal mass to the ITPS is at the bottom face sheet. Thus, the bottom face sheet has been illustrated as a heat sink in Figure 2-7. PAGE 38 38 The corrugated-core provides a structural conne ction between the top an d bottom surfaces of the ITPS. Figure 2-7. Corrugated-core sandwich stru cture construction for ITPS applications. 2.4 ITPS Design Challenges It is an easy design practice to de-link the T PS and the structural designs, that is, first obtain a structural design and then size the T PS to fit the requirements. In this way the technologies for the two designs can be devel oped independent of one another. Delays in overcoming technical challenges in one design will not lead to delays in the development of the other. When the two are assembled to form th e space vehicle, some relatively minor design changes can be implemented to successfully deve lop the final vehicle assembly. For example, in the design of the Space Shuttle the structur al design process and the ceramic TPS tile development were two different tasks. When they were assembled, however, there was a problem of compatibility, which was solved by usi ng SIPs and tiles of small dimensions. In the case of ITPS design, the structural design and th e TPS design are very mu ch interlinked. This makes the vehicle design process even more comp licated. This could also be one of the reasons why this route of TPS development was not pursued in the past. The geometric design variables of the ITPS need to be altered in such a way so as to obtain a minimum weight structure that can satisfy the various requirements of a TPS and a loadHot Structure ( to p face sheet ) Insulated Structure (corrugated-core filled with insulation material ) Heat Sink ( bottom face sheet ) PAGE 39 39 bearing member. This is a formidable task give n the often-conflicting requirements of a TPS and a load-bearing structure and explai ns why such a structure has not been developed over the years. It is very much a possibility that the outcome of this effort could be to establish that such a structure is not feasible or, even when feas ible, it may be a prohibitively heavy design. Nevertheless, it is a good concept worth investing so me research efforts, especially since such a design could not be found a nywhere in literature. The ITPS is not being designed with any partic ular vehicle in mind a nd is not a Â“one-sizefits-allÂ” design. For different ve hicles, the ITPS designs and geom etries have to be suitably modified as per the thermal and structural requ irements. It may not be able to withstand high heating rates and large integrated heat loads because it is a passive TPS concept. It may need to be combined with other TPS concepts such as ablative TPS when used on space capsules, for instance. It can replace the structure below the ablators of Apollo TPS, shown in Figure 2-2. Some of the obvious design challenges asso ciated with the IT PS development are discussed below with the aid of the dimensi ons of the proposed corrugated-core ITPS design. This will demonstrate the typical difficu lties associated with an ITPS design. Thickness of the Webs. Decreasing the thickness of the webs helps to reduce the mass of the ITPS. The thermal protection requirements dict ate that the conductivity of the core be as low as possible. This would result in less heat be ing conducted away from the top face sheet and would raise the temperature of the top surface close to the radi ation equilibrium temperature resulting in majority of the incident heat be ing re-radiated out. Since the conductivity of the insulation material is a material selection issue, the only way to decrease the conduc tivity of the core is to decrease the thickness of the webs. But this would weak en the structural link between top and bottom face sheets. Large transverse aerodynamic pressure load s on the top face sheet PAGE 40 40 could cause the webs to buckle. In this case, the mass and ther mal protection requirements agree with one another but contradict the structural requirements Height of the Panel. The height of the panel is the mid-plane to mid-plane distance between the two face sheets. The thermal protecti on requirements dictate that the height be as large as possible to increase th e heat conduction path. However, this would not only increase the weight of the TPS considerably, but also make the webs longer and more susceptible to buckling due to transverse loads. In this case, the mass and structural requirement s agree with one another while contradicting the ther mal protection requirements. Spacing between two Webs. Increasing the lateral spacing be tween the webs helps keep the areal density of the ITPS low ( Areal density is the mass per unit area of the ITPS). However, this would lead to a design in which there would be long unsu pported sections of face sheets between the webs that may be susceptible to buc kling due to in-plane mechanical or thermal compressive loads. Increasing the spacing also m eans that the heat incident on a larger area would be conducted by a lesser number of webs. Thus, in this case, the mass and thermal protection requirements agree with one another while contradicting the structural requirements. Thickness of Top Face Sheet. Decreasing the thickness of the top face sheet helps reduce the ITPS mass. But thinner top face sheet is very much susceptible to buckling due to in-plane thermal compressive loads. Additionally, a thin face sheet may deflect excessively under transverse pressure loads and this may cause a transition from lamina r to turbulent boundary conditions [13], which in turn may cause severe local aerodynamic heating. Thus, in this case, the mass and structural requirements in conflic t with each other while the thermal protection requirements do not have a significant influence. PAGE 41 41 Angle of Corrugations. This is the angle that the webs make with the face sheets. Keeping this angle close to 90 would lead to the lightest ITPS desi gn. However, it would also shorten the heat conduction path and make the webs susceptible to buckling due to transverse pressure loads. In this case, the thermal protection and struct ural requirements agree with one another while contradicting the mass requirements. Thickness of the Bottom Face Sheet. Decreasing the thickness of the bottom face sheet helps keep the mass of the ITPS low. However, the bottom face sheet of the ITPS is the most effective thermal mass and, therefore, its thickne ss may be required to be high in order to increase the heat sink capacity of the ITPS. A thick bottom face sheet would also be capable of withstanding higher in-plane loads. Again, the thermal protection and st ructural requirements agree with one another while cont radicting the mass requirements. The discussion above effectively demonstrates the challenges associ ated with the ITPS design. The aim of the current research is to identify more of these issues and to develop methodologies towards designing an ITPS. 2.5 Choice of Constraints This section elaborates on the reasons behind the choice of the constraints for the optimization problem (see the subsection The Optimization Problem in Section 1.4). ITPS panels form the outer skin of the vehi cle, which encompasses the crew compartment (in space capsules) or liquid fuel tanks (in X33 like design). The temperature of the bottom surface determines the amount of heat flowing in to the vehicle interiors. Thus, peak bottom surface temperature is an important constraint. While peak temperature of any part of the IT PS panel should be within allowable limits, only the peak bottom surface temperature considered cr itical. This is because initial heat transfer PAGE 42 42 analyses had indicated that the peak temperatur e of the top surface is always close to the radiation equilibrium temperature, as will be dem onstrated in the Chapter 3. It is predominantly determined by the emissivity of the top surf ace, which typically has a value of 0.8 to 0.85 [12,13]. Increasing the emissivity is a manufact uring and material selection issue and not a design issue. The amount of heat entering into the vehicle can be decreased considerably by decreasing the heat conduction path. This will in crease the top surface temperature slightly and thus more heat is radiated out. However, this in crease in temperature is small, typically of the order of 40 K. Thus, the top surface temperature is not a quantity that can be significantly influenced by changing the ITPS design. It is determined by the radiation equilibrium temperature which is determined by the incident heat flux on the vehicle and the emissivity of the top surface. The temperature of the rest of the structure is then dictated only by the limit imposed on the bottom face sheet. When the whole ITPS panel buckles as a plate, it is referred to as global buckling . When the buckling is limited to a part of the panel, such as one of the webs or a section of the face sheets, it is referred to as local buckling . Global buckling may not be a factor influencing the ITPS design because the ITPS panel is expected to be a thick panel. However, local buckling can be a major design driver because the ITPS structure is made of thin plates, which are susceptible to buckling due to compressive stresses. The third constraint deals with the maximum stresses allowed by the materials. It should be noted that some parts of the structure are at very high temperatures and temperature dependence of material properties, like yi eld stress and YoungÂ’s modulus, should be taken into account. Constraint 4 imposes the limits on the defl ection of the top surface because excessive deflection of the top surface could lead to extr emely high local aerodynami c heating [13]. Due to PAGE 43 43 heat input, the temperature of the whole panel in creases. Some of the heat is transferred to the stringers, for example, and the whole vehicle gr ows in size. This overall deflection is not of a major concern, as it does not change the aer odynamic profile of the vehicle significantly. However, local deflections, such as face sheet dimpling, can lead to severe local aerodynamic heating. Therefore, when the limit on top surf ace deflection is imposed, the overall increase in size of the vehicle should be deducted from it. 2.6 Background on Corrugated-Core and Truss-Core Sandwich Structures The ITPS panel geometry considered for this re search work is similar to corrugated-core and truss-core sandwich structures . Therefore, it is relevant to present the literature survey related to these structures in order to distinguish the current research effort as well as to put the work in perspective. There are 3 major research groups that have fo cused their research efforts on truss-core and corrugated-core sandwich panels: Wicks and Hutc hinson [24,25], Lu, et al [26,27], and Evans, et al [28Â–35]. Wicks and Hutchinson de rived simple analytical formulas to approximate the forces and moments between the trusses and the face plates. These formulas were used for imposing the constraints in the optimization problem to obt ain a panel with minimu m weight for a given applied load. Panels were designed for bending a nd transverse shear loads and the constraints imposed were related to face sheet and core yielding and buckling. Lu, et al [26,27], used two different approach es to optimize truss-co re sandwich panels for bending, transverse shear and compression loading. In the first approach [26], they directly combine finite element analysis with optimizatio n techniques. Details a bout the finite element analysis were not provided in the paper. In th e second approach [27], ho mogenization techniques and unit cell analysis were used to obtain analy tical formulas for the stresses in the trusses and the face sheets. Some comparison of the analytical formulas and 3-d finite element analysis was PAGE 44 44 also presented. In both cases the panels were optimized to minimize mass and increase the natural frequency while constraints were impos ed by considering face sheet and core yielding and buckling. Evans, et al [28Â–35], developed analytical form ulas for forces in various members of both truss-core and corrugated-core panels using unit cell analysis. The core geometries analyzed were truss-cores with tetragonal, pyramidal, and kagome configurations [29,31,32] and prismatic cores with corrugated and diam ond (or textile) configuratio ns [28,30,32,33]. The analytical formulas were compared with simple finite elem ent unit cell models for ve rifying their accuracy [29,31,34]. Comparison of forces and stresses for a full sandwich panel was not carried out. The optimizations were carried out to obtain mini mum weight structures while satisfying the buckling and yielding criteria. In all the above mentioned analyses, bending, transverse shear and crushing loads were considered for analysis. Further, the height of these sandwich panels was between 10 to 20 mm. This kind of approximate analysis is not very suitable for ITPS applications because the ITPS panels have much larger height , typically above 80 mm, and a fa r fewer number of unit cells per panel, typically 4 to 10. Even though the geometry of the ITPS panels is similar to sandwich panels, the large height-to-leng th ratio and the small number of unit cells in the ITPS panels make the panel behavior different. One of the bigg est disadvantages of the analytical methods is that they cannot accurately pred ict the stresses and deflections at the panel edges where the boundary conditions are imposed. In many cases, the maximum stresses or buckling occurs at the panel edges and could be the deciding factor in the optimization. One of the most severe loads influencing the design of ITPS panels is the larg e temperature gradient between the top and the bottom face sheet. The research works on truss-co re and corrugated-core sandwich structures PAGE 45 45 that has been summarized in this section do no t consider such a load in their optimization procedures. 2.7 Background on Multi-Disciplinary Optimi zation and Response Surface Approximation Techniques Optimization to design an ITPS panel is a mu ltidisciplinary optimization process as it combines the two fields of heat transfer and st ructural analysis. The ge ometric design variables (Section 1.4) influence both the heat transfer and structural respons e of the structure. Therefore, there is need to study the various optimiza tion techniques used for MDO problems. The background on multi-disciplinary optimization (MDO) relevant to this research work can be obtained from two important revi ew effortsÂ—one by Sobieszczanski-Sobieski and Haftka [36] and the other by Guruswamy and Obayashi [37]. Br ief summary of the two papers is presented here along with relevant examples. Reference [36] summarizes the various me thods used by researchers to tackle MDO problems and focuses particularly on aerospace desi gn optimization. It was surmised that in most cases it is impractical to couple design space search (DSS) to a multidisciplinary analysis as this could lead to a very frequent calls to analysis execution. In the ITPS design, an attempt was unsuccessfully made to directly couple the MATLAB optimizer ( fmincon ) to the ABAQUS FE analysis package. After several calls to the analysis software the optimizer was unable to find a feasible search direction. While the inability to find a feasible search direction was blamed on the lack of robustness on the part of fmincon , it is also true that even with a robust optimization algorithm the search would require a very large number of FE analysis calls. Further, it cannot be guaranteed that the optimized design is actual ly a global optimum and not a local optimum. Many approximation concepts have been deve loped to reduce the cost of optimization procedures [36,63]. The methods listed in Re ference [36] are sequential approximate PAGE 46 46 optimization [38], global reduced-basis approx imations [39], variable-complexity modeling technique [40Â–41] and response su rface (RS) approximation tec hnique [42Â–47]. The first three techniques use a mixture of simple analytical formulas and complicated analyses. The simple formulas allow a quick move towards the optimum, while the complicated analyses help in Â“course correctionÂ” during the opt imization procedure. Although th ese methods reduce the cost of optimization compared to DSS, other costs are added such as development of an algorithm to effectively combine the simple and complicated analyses, because, such an algorithm would most probably be problem specific and, therefor e, general software packages may not be available. Surrogate-based multi-fidelity methods for multi-objective optimization are discussed in Reference [64]. The response surface (RS) technique is a much simpler process wherein RS approximations are used to repres ent the objective and constraint f unctions (usually) in the form of polynomials. The polynomials are obtained by f itting design variables to data computed at a set of carefully chosen design points. More advantages and ex amples of usage of the RS technique are presented later in the section. Reference [37] also summarizes MDO efforts in aeroelastic optimization but concentrates on research work using high fidelity methods. Typical examples of high-fidelity methods are finite element methods for structural analysis an d finite difference or finite volume approaches for solving the Euler/Navier-Stokes equations. Research efforts in optimization using highfidelity methods are classified into 3 categories. The first 2 categories deal with procedures that are characterized by multidisciplinary coupling at analytical and sensitivity levels. The third category is one of uncoupled analysis and is of interest for the ITPS design optimization. The optimization procedure is uncoupled at the anal ytical level by means of RS approximations. PAGE 47 47 Once the RS approximations are obtained, the coupling takes place during the optimization procedure. This coupling is analytical in nature and is very inexpensive [37]. Some of the advantages associated with RS approximations technique, drawn from References [36] and [37] are listed below, along with their relevan ce to the ITPS design: 1. Each analysis deals with a single discipline at the analysis level, which is usually the most computationally intensive stage of the MDO process. This does not particularly apply to the optimization procedure used for ITPS de sign as there are no distinct thermal or structural design variables. 2. The RS approximation Â“smooth out numeri cal noiseÂ” [36,37,42], which usually mislead the optimizer during gradient search. Thus, the derivative based optimizers can converge rapidly to the optimum. For example, the sm allest buckling Eigen value can be a very unyieldy response as the first buck ling mode may occur in a comp letely different region of the design space depending on the combination of design variables. Thus, there could be huge kinks in this response, which can lead to increase in the number of iterations or, in worst case, failure to find the optimum value. 3. RS approximations act as global approximations because they typically span over whole or a large part of the design space. These approxi mations Â“permit visualizations of the entire design spaceÂ” [36]. In the case of ITPS desi gn, the RS approximations span over the whole design space. 4. Once the RS approximations are generated, the optimization procedure becomes very inexpensive. The availability of objective function and c onstraints in the form of polynomials makes it very easy for the optimizer to carry out sensitivity analyses and determine the search directions. In the ITPS design, the MATLAB optimizer, fmincon , can rapidly converge to the optimal solution (i f it exists) and it does so in less than 10 iterations. 5. Due to the global nature of the RS approximati ons, they can be used repeatedly for design studies with multi-objective optimization. It is also very easy to change the optimization parameters to gradually build a problem database. RS approximation technique became popular in the mid 1990s and since then it has been used in various MDO problems. Some of the app lications are mentioned here to illustrate the wide variety of fields in whic h RS approximation technique has been utilized [48Â–61]. Some of these are discussed here. As is the case with mo st MDO problems, this technique was applied for aeroelasticity problems [50] and related aerospace optimization designs [49,51,54]. RS PAGE 48 48 approximations were used to smooth out noise in approximating the range and cruise drag on a high-speed civil transport for different airc raft designs [48]. Quadratic polynomial RS approximations were used for the design of aircra ft engine turbine blade component wherein heat transfer, natural frequency and structural stre ss were taken into account [53]. Automotive crashworthiness design is anot her field where the RS approximations were used [55,56] to optimize various factors such as impact forces on the passengers, vibratio n characteristics of the vehicle and general crashworthin ess. RS approximations were us ed for a heavy duty tire design to optimize for flexibility and durability [57] . Polynomials were used to approximate the responses of mass and stiffness of th e tires, and strain in the tire. A major disadvantage associated with RS approxi mations is that they are very expensive to generate when the number of desi gn variables is large. The larger the number of variables, the larger is the number of design points required to create the appr oximations. However, in the case of ITPS design, the number of variables varies fro m 5 to 8 and the number of analyses required to generate sufficiently accurate approximati ons is manageable. Thus, RS approximations technique is the most suitable method for ITPS design optimization which requires high fidelity finite element heat transfer, bucklin g, stress and deflections analyses. PAGE 49 49 CHAPTER 3 FINITE ELEMENT MOD ELS AND ANALYSES This chapter presents a description of the fi nite element models and analyses for heat transfer, stress analysis and buckling analysis of the ITPS panels. These FE analyses will be used for generation of response surface approximations. 3.1 Finite Element Analysis for Heat Transfer Finite element heat transfer analysis he lps determine the peak bottom face sheet temperature, which is required to impose the temperature constraint in the ITPS design optimization, and provides the temperature dist ribution in the panel that can be used for buckling, stress and deflection analyses. First the choice of incident heat flux profile is explained followed by a discussion on the choice of heat transfer boundary conditions. Then comparison of 1-D and 2-D heat transfer FE models is presented. Finally, th e procedure to obtain peak temperatures and temperature distribution is outlined. 3.1.1 Incident Heat Flux and Radiation Equilibrium Temperature Incident heat flux on the vehicle depends on the sh ape of the vehicle, th e trajectories of the ascent and reentry and is completely different fo r vehicle ascent and reentry conditions. For the design process, incident heat flux of a Space Shuttle-like vehicle is used. Figure 3-1A shows the heat flux input for as cent conditions, while Fi gures 3-1B and 3-1C show the heat flux during reentry on the windwar d and leeward centerlin es of the vehicle, respectively, obtained from Reference [9]. The heating profiles for wi ndward and leeward sides are similar during ascent [9]. Windward centerl ine is a line drawn on the vehicle surface connecting the nose to tail on the bottom side of the vehicle, wh ile leeward centerline joins the nose and tail on the top side. Different curves on each figure are for heating rates at different PAGE 50 50 points along the centerlines. The distance x , on the charts, indicates the distance from the tip of the nose of the vehicle. The nose-ti p of the vehicle corresponds to x = 0.0 inches. The heating rates are extremely high for points closer to the nose of the vehi cle. Comparing Figures 3-1A and 3-1B, it is evident that the reentry heating rate s are more severe than the heating rates during ascent, that is, the heating rates increase more st eeply and the total integrated heat load is much larger during reentry. Thus, it can be inferred th at the reentry heating rates would be most influential in the ITPS design and, th erefore, they were used for heat transfer FE analysis for the design process. Radiation equilibrium temperature is the temp erature of a surface at which the amount of heat radiated by the surface is equal to the amount of incident heat flux onto the surface. The radiation equation of a surface radiating h eat to the ambient can be written as, ) (4 4 amb surf radT T q (3.1) where qrad is the radiated heat flux per un it area of the radiating surface, is the emissivity of the surface, is the Stefan-Boltzmann constant ( = 5.67 Ã— 10-8 W/m2-K4), Tsurf is the temperature of the radiating surface, and Tamb is the temperature of the ambient. When Tsurf is equal to the radiation equilibrium temperature of the surface, TEq, then qrad will be equal to the incident heat flux, qin, on the surface. The top surface temperature of a TPS will be cl ose to the radiation equilibrium temperature when heat is input onto the surface. Thus the ra diation equilibrium temp erature is the primary parameter in choosing the material for the top surf ace of the ITPS. Only those materials that have a service temperature higher than the radiation equilibrium temperature can be used on the top surface. The peak radiation equilibrium temperatur es for reentry heat fluxes (Figure 3-1B) are shown in Table 3-1. PAGE 51 51 A B C Figure 3-1. Heating profiles of a Shuttle-like ve hicle, obtained from Reference [9]. A) During ascent on vehicle windward. B) During reentr y on vehicle windward centerline. C) During reentry on vehicl e leeward centerline. Table 3-1. Peak radiation equili brium temperatures for reentry he at fluxes. An emissivity of 0.8 and ambient temperature of -30Â°C we re used to obtain these values. x (inches) Peak Teq (K) 26.3 1,457 40.4 1,447 72.3 1,317 205.7 1,151 1362 821 PAGE 52 52 A typical heating rate used for design is s hown in Figure 3-2, which corresponds to a point, x = 827 inches [8]. Peak radiation equilibrium temp erature for this heating profile is 968 K. This heating rate was chosen for the design because it would allow the use of some of the frequently used high temperature metallic alloys like titanium alloys and Inconel. Figure 3-2. Typical heating pr ofile used for the ITPS design. 3.1.2 Loads, Boundary Conditions and Assumptions Loads and boundary conditions for the heat tran sfer problem are schematically illustrated in Figure 3-3. Initial temperature of the struct ure is assumed as 295 K (72 F). Heat flux is incident on the top surface of the top face sheet. A large portion of this heat is radiated out to the ambient by the top surface. The remaining heat is conducted into the ITPS. Some part of this heat is conducted to the bottom face sheet by th e insulation material and some by the webs. The bottom surface of the bottom face sheet is assumed to be perfec tly insulated. This is a worst case scenario where the bottom face sheet temperature would rise to a maximum as it cannot dissipate the heat. The optimization with such an assumption would lead to conservative designs. It is also 450 2175 1575 4500 Time from Rentry, sec Heat influx rate, Btu/ft2-s 3.0 3.5 PAGE 53 53 assumed that there is no lateral h eat flow out of the unit cell, that is, the heat flux incident on a unit cell is completely absorbed by that unit cell only. In an actual ITPS panel, heat would flow into the stringers and frames which could act as a thermal mass and there would be a lateral flow of heat in the panel from one unit cell to anot her. Thus this assumption could also lead to a conservative design as the amount of thermal ma ss is being reduced due to non-inclusion of stringers and frames in the preliminary design. However, the temperatur e distribution could be completely different in case of h eat flowing out of the unit cell. Th is is not taken into account in the design. Figure 3-3. Schematic of loading and boundary conditions for the heat transfer problem. Ambient temperatures for the top surface of top face sheet are assumed to be 213 K for initial reentry period (0 to 450 seconds), 243 K for second reentry phase (450 to 1575 seconds) and 273 K for final reentry phase (1575 to 2175 sec onds). The ambient temperatures are assumed values due to non-availability of this data. Initial heat transfer analyses indicate that the peak bottom face sheet temperature o ccurs after vehicle touchdown [8 ]. Therefore, after touchdown Bottom surface perfectly insulated Incident heat flux radiation to ambient Insulation material PAGE 54 54 the FE analysis continues for another 50 minutes in order to capture the te mperature rise of the bottom face sheet. During this period, along with ra diative heat transfer, c onvective heat transfer boundary conditions are imposed on the top surface to simulate the heat transfer to the surroundings while the vehicle is standing on the r unway. The value of conve ctive heat transfer coefficient, h , used was 6.5 W/m2-K (6.94Ã—10-4 Btu/s-ft2-Â°R) [8]. The ambient temperature during this period was assumed to be 295 K. The transient heat transfer analysis is divi ded into 4 load steps as shown in Table 3-2. These steps were chosen to approximately repr esent a typical Space Shuttle-like heat flux input on the top surface as shown in Figure 3-2. Step 1 simulates the initial reentry period, when the heating rate is linearly ra mped up from 0 to 3.0 Btu/ft2.sec (34,069 W/m2), Step 2 simulates the second phase of reentry, when the heating rate is linearly ramped up from 3.0 to 3.5 Btu/ft2.sec (34069 to 39748 W/m2), and Step 3 simulates the final reen try phase, when the heating rate is ramped down from 3.5 to 0.0 Btu/ft2.sec. During these load steps, the top surface has incident heat flux loading and radiation boundary conditio ns. During Step 4 (vehicle sitting on the runway) there is no heat input and the top surface ha s radiation and convec tive heat transfer boundary conditions. Table 3-2. Load steps in the FE heat transfer analysis. Load Step Time Period Heat Flux Input Time Step Size Ambient Temperature STEP 1 0 Â– 450 sec 0.0 Â– 3.0 Btu/ft2.sec Ramp linearly 30 sec 213 K STEP 2 450 Â–1575 sec 3.0 Â– 3.5 Btu/ft2.sec Ramp linearly 25 sec 243 K STEP 3 1575 Â–2175 sec 3.5 Â– 0.0 Btu/ft2.sec Ramp linearly 30 sec 273 K STEP 4 2175 Â–5175 sec Â— 50 sec 295 K PAGE 55 55 Other assumptions of note include the a ssumption of a perfect conduction interface between the face sheets (and webs) and the insulation materials, that is, there is no thermal contact resistance at the interface. The insulati on material is usually made of a low density porous material, such as SaffilÂ®, which is made of alumina fibers. Even though this insulation material is assumed to completely block out all the radiation from the top surface to other parts of the ITPS, there is some radiative heat transf er to the interior of the ITPS due to the porous nature of the insulation material [7,17]. Also, th ere could be a convectiv e heat transfer through the insulation material due to the air present in the pores [7,17]. For the design process, the radiative and convective heat tr ansfer through the insulation mate rial is ignored and only the conductive heat transfer is taken into account. 3.1.3 One-Dimensional and Two-Dimensional FE Models As explained in the previous section, there is no lateral heat flow across the unit cells. Thus, the FE heat transfer analysis was limited to unit cell analysis, instead of taking the whole ITPS panel into account. Furthe r, a 2-D FE model in the y-z plane (refer Figure 2-1 for the coordinate directions) is su fficient as there would be no temperature variation in the x -direction in this design. The heat transfer FE problem c ould be further simplified to a 1-D model. This would save considerable time for the transient heat transfer FE analysis. In order to show that a 1-D model can effectively do the job of a 2-D mo del, a comparative study was carried out. This section will describe the 1-D and 2-D models and show the comparative studies. All finite element analyses for this research were carried out using ABAQUSÂ® finite element software package. A typical 2-D FE model is shown along with its mesh in Figure 3-4. The solid portion of the ITPS is made of a titanium alloy (Ti-6Al4V) and the insulation material is Saffil. Temperature dependent material properties were used for both ma terials. Eight-node PAGE 56 56 quadrilateral heat transfer element is used for 2-D modeling (ABAQUS element DC2D8). The number of nodes used in the model wa s 10,149 and the number of elements was 3,306. A B Figure 3-4. Typical mesh for 2-d heat transfer problem A) the solid po rtion of ITPS only, B) complete ITPS including the insulation material in between the webs. A 1-D FE heat transfer model is just a straight line of length e qual to the height of the ITPS panel plus the thicknesses of the top and botto m face sheets. One-dimens ional 3-node (quadratic) heat transfer link element (ABAQUS element DC1D3) was used for 1-D modeling. 109 nodes and 54 link elements were used in this model. Figure 3-5 schematically illustrates a 1-D model. The corrugated-core of the panel is homogeni zed, while the top and bottom face sheets remain the same as in 2-D model. The homogenized properties of the core are calculated by the rule of mixtures formulas. The formulas below show the homogenized properties for density, specific heat and thermal conductivity. * 2 2 1 1 *V V V (3.2) * * 2 2 2 1 1 1 *V V C V C C (3.3) * 2 2 1 1 *sin A A k A k k (3.4) PAGE 57 57 stands for density, C for specific heat, and k for conductivity. The subscripts 1 and 2 represent titanium and Saffil, respectively, while the superscript * represents the properties of the homogenized core. V* is equal to the sum of V1 and V2. A stands for the cross-sectional area for the heat flow. Multiplying by sin implies that, for the titanium webs, the heat flux component in the panel-thickness direction only is taken into account for this calculation. This takes into account the angle of corrugations, , of the webs. Figure 3-5. Schematic representation of 1-D heat transfer model. Figure 3-6 shows the comparison between the 1-D and 2-D FE heat transfer analyses results for an ITPS panel with dimensions, tT = 2.0 mm, tB = 6.0 mm, tW = 3.0, = 82.0, d = 140 mm, p = 75 mm. Heat flux input, boundary conditions and materials selection were discussed in the previous section. Figure 3-6A shows the temperature versus re entry time for two locations on the 2-D model. Loc-1 and Loc-2 are two points on the top face sheet where the temperatures are at the extremes. For example, during the 3 reentr y phases when heat flux is incident on the top surface, Loc-1 will be at the highest temperature wh ile Loc-2 will be at the lowest temperature of all the locations on the top face sheet. The 1D heat transfer anal ysis does a good job of predicting the top face sheet temperature which is around the average of the temperatures at Loc1 and Loc-2 in the 2-D model. Figure 3-6B s hows the temperature variation with time on the bottom face sheet. Loc-3 and Loc-4 are two of th e extreme locations on the bottom face sheet. The 1-D model again does a good job compared to the 2-d model temperatures as the maximum difference is less than 5%. Figure 3-6C shows the temperature variations at 3 different locations Homogenized Core = SAFFIL + Ti PAGE 58 58 on the web. The 1-D model does a very good job of predicting the temperatures at all these locations. An important conclusion from Figure 36C is that the 1-D model does a good job in predicting the temperatur e distribution through the thickness of the ITPS panel. Thus we can conclude that the 1-d heat tr ansfer finite element model computes the temperatures and temperature distributions sufficiently accurately at all reentry times and can be reliably used for the design process. 3.1.4 Temperature vs. Reentry Time and Temperature Distribution Temperature versus reentry time curves for top and bottom face sheets and mid point of web are shown in Figure 3-7 for comparison purpos es. As mentioned earlier, the temperature on the bottom surface peaks after the vehicle landing (approximately 2175 sec). These curves were obtained from the 1-D h eat transfer analysis. Temperature distribution through the thickness of the ITPS panel is shown in Figure 3-8 at different reentry times. At 450 seconds, which is the end of the initial phase of reentry, the bottom face sheet is still at its initial temperature. This is the time at which the temperature gradient through the panel thickness is at its severest. The dist ribution at 1575 seconds is when top surface reaches its peak temperature, at 3455 seconds the bottom surface reaches its maximum temperature and at 1845 seconds the mid point of the web reaches its maximum temperature. Each of these temperature distributi ons can be accurately re presented by a complete cubic polynomial in one variable (z-coordina te) fitted using least squares approximation technique. PAGE 59 59 A B Loc2 Loc1 A200 300 400 500 600 700 800 900 1000 010002000300040005000Reentry Time (sec)Temperature (K) Loc-1 Loc-2 1-d Loc4 Loc3 B200 250 300 350 400 450 500 010002000300040005000Reentry Time (sec)Temperature (K) Loc-3 Loc-4 1-d PAGE 60 60 C Figure 3-6. Comparison of 1-d and 2-d heat transfer analyses. A) Top face sheet temperature. B) Bottom face sheet temperat ure. C) Web temperatures. The dimensions of the panel are tT = 2.0 mm, tB = 6.0 mm, tW = 3.0, = 82.0, d = 140 mm, p = 75 mm. 200 400 600 800 1000 010002000300040005000Reentry Time (sec)Temperature (K) Top Surface Mid-pt on Web Bottom Surface Figure 3-7. Temperature variati on vs. reentry times for top and bottom surfaces and web midpoint obtained from 1-d heat transfer analys is. Dimensions of th e ITPS panel are the same as listed in Figure 3-6. C200 300 400 500 600 700 800 010002000300040005000Reentry Time (sec)Temperature (K) 2-d 1-d Loc5 Loc 6 Loc 7 Loc 6 Loc 5 Loc 7 PAGE 61 61 200 400 600 800 1000 0255075100125150z-coordinate (mm)Temperature (K) 450 sec 1575 sec 3455 sec 1845 sec Figure 3-8. Temperature distribut ion through the thickness of the IT PS panel at different reentry times. Dimensions of the ITPS panel ar e the same as shown in Figure 3-6. 3.1.5 Obtaining Temperature Data from the FE Analysis After the 1-d transient heat transfer analys is has been performed on an ITPS model, temperature versus reentry time data at differe nt points on the ITPS can be obtained from the ABAQUS output file (similar to Figure 3.7). Usi ng this data the peak te mperatures of top and bottom face sheets can be obtained. As mentioned earlier, the peak top face sheet temperature helps determine the material to be used for the top face sheet. The peak bottom face sheet temperature is used in the design optimization process to impose the upper limit on the temperature attained by the bottom face sheet. Apart from the peak temperature values, the reentry time at which the peaks occur can also be obtained. The temperature at each node in the 1-d heat transfer model at each of these reentry times can be extracted from the ABAQUS output file. Combining the nodal temperature values with the nodal coordinates ( z -coordinate), the temperature di stribution through the thickness of the ITPS can be accurately obtained as one comp lete cubic polynomial at each reentry time of PAGE 62 62 interest. The coefficients of the cubic polynomia l are determined by least squares approximation technique. The temperature distribution polynomials at different reentry times can be used to impose the nodal temperatures in the stress and buckling FE analyses. 3.2 Finite Element Buckling Analysis ITPS panels are to be designed to withstand si gnificant transverse and in-plane mechanical loads and extreme thermal gradie nts through the panel th ickness. In order to make the ITPS economical, it is necessary to design panels which are large in size. This would imply that there would be large unsupported or partially supported s ections of thin plates subjected to various kinds of loads including thermal compressive stresses and in-plane mechanical compressive loads. Such sections would be susceptible to buckling. While local buckling, by itself, may not always lead to catastrophic failure, it could cont ribute indirectly. For exam ple, if the top surface buckles locally it could lead to extremely high local aerodynamic heating which could prove to be catastrophic. Finite element analysis for buckling is carri ed out using ABAQUS. In the finite element model, only the solid portion of the ITPS panel is taken into account, wh ich includes the face sheets and the web. The insulation material is not c onsidered to be a structural member. This is indeed true because Saffil insulation is a soft fibrous insulation with hardly any mechanical properties when compared to the properties of th e solid material that make up the webs and face sheets. Therefore, it can be safely omitted from all structural analyses without introducing any palpable error. The ITPS panel is made of thin plates. Theref ore, 3-D shell element is the most suitable element for modeling the structure. Eight-node shell element (ABAQUS element S8R) with 6 degrees of freedom at each node (3 displacements and 3 rotations) and reduced integration was PAGE 63 63 used for the buckling FE model. Around 5560 nodes and 1820 elements were used for each buckling model. A typical shell-element mesh for buckling analysis is shown in Figure 3-9. Figure 3-9. Typical FE shell element mesh for buckling analysis. Two unit cells are shown in this figure. The panel edges are marked A, B, C and D. In the heat transfer problem a unit-cell analysis was carried out. Unit cell analysis is not possible in the case of the buckling analysis because the boundary condi tions for the unit cell buckling problem are unknown. Therefore, the bu ckling analysis was carried out by including the whole ITPS panel in the FE model. This intr oduces an additional vari able into the problem, which is the length of the panel (considering only square shaped panels). Instead of the length, the number of unit-cells in the panel could be cons idered as a variable. Either the length or the number of unit cells need to be specified in order to completely define the geometry of the panel. Figure 3-9 shows one-quarter of an ITPS panel. The panel has a total of 4 unit cells. However, only 2 unit cells are necessary to model th e panel by taking into account the symmetry conditions. The boundary conditions on the ITPS panel depe nd on how the panels would be mounted on vehicle. For this research, it is assumed that the edges of the panels are mounted on the stringers and frames of the vehicl e. Usually, provision is made fo r the panels to expand slightly B A C D x y z PAGE 64 64 when heated. This arrangement precludes the development of large thermal stresses. The top face sheet experiences the highest temperatures and should be allowed to expand as much as possible. For this research work, it is assumed that the edges of the bottom face sheet of the panels are mounted on the stringers and frames and simply supported boundary conditions are imposed. The edges of the top face sheet are fixed with respect to all 3 rotations while allowing the displacements. In Figure 3-9, on Edges A and B are the actual edges of the panel. The bottom face sheet edge on these edges is fixed in z-dir ection displacement and the top face sheet edge is fixed in all three rotations while allowing a ll three displacements. Edges C and D are the symmetric edges of the FE model. On Edge C, the top and bottom face sheet edges and the web edges are fixed in x -direction displacement and y and z -direction rotations to simulate the symmetry boundary conditions. Similarly, the symmetry boundary conditions on Edge D are simulated by fixing the y -direction displacement and x and z -direction rotations. The loads for the buckling problem include te mperature loads, aerodyna mic pressure loads and in-plane inertial lo ads. Temperature loads were obtained in the form of through thickness temperature distributions from the heat transfer problem. The temperature distributions are cubic polynomials in one variable, the z -coordinate. Using these polynomials, temperature was imposed on each node of the 3-D buckling model. Th is implies that the top and bottom face sheet temperatures is uniform throughout the length and width of the panel. Although the temperature varies slightly in the x and y directions, this variation is ve ry small and can be neglected. The pressure loads are imposed on the top surface. In-plane loads are imposed only in the x -direction of the panel. These loads were imposed on the Edge A on the bottom face sheet only. The buckling problem in ABAQUS was mode led as an eigenvalue buckling prediction problem. It was used to estimate the critical (b ifurcation) load for the structure. The eigen PAGE 65 65 buckling analysis is a linear pe rturbation procedure in which the objective is to determine the loads at which the model stiffness matrix becomes singular, so that the equation 0 Ku (3.5) has nontrivial solutions. K is the tangent stiffness matrix when loads are applied and u is the nontrivial displacement solutions. The buckling eigenva lues or loads are estimated relative to the base state of the structure. The base state incl udes all the boundary conditions and the noncritical loads called pre-loads , P , if there are any such loads. In the buckling eigenvalue step an incremental load, Q , is applied to the structure. The equation for the buckling problem then becomes 00 i iu K K (3.6) K0 is the stiffness matrix co rresponding to the base state which includes the preloads, K is the differential initial stress and load stiffness ma trix due to the incremental loading pattern ( Q ), i are the eigenvalues, ui are the buckling mode shapes or eigenvectors, where the subscript i refers to the ith buckling mode. Solving the eigenvalue probl em Equation (3.6) gives the eigenvalues and the eigenvectors. The critical buckling load for each buckling mode will then be the sum of preloads plus the scaled incremental load, P + iQ . If the eigenvalue is equal to 0.7, then it implies that at 70% of the applied load th e structure would buckle according to the corresponding buckling mode. If the smallest eige nvalue is above unity, then the structure will not buckle under the applied loads. In case of the ITPS design, all loads are critical and therefore the value of P is equal to zero. For the ITPS buckling problem, the FE analys is was divided into two steps. Step 1 corresponds to the base state. In this state a ll the boundary conditions were imposed. In Step 2 (eigenvalue step), temperature, pressu re and in-plane loads were imposed. PAGE 66 66 In ABAQUS buckling analysis, temperature de pendent material properties are not taken into account in the buckling step. The material properties imposed in the base step are Â“carried overÂ” into the buckling step. The ba se state temperature in buckling an alysis is equal to the initial stress free temperature, typically 295 K. Thus th e material properties us ed in the buckling steps are the properties corres ponding to this temperature. Even if additional nodal temperatures are imposed in the buckling step, the properties used for eigenvalue calculations will be the same as those corresponding to the initial te mperature. Taking into account th e range of temperatures that an ITPS is subjected to, this will clearly not yi eld an accurate solution as the material properties can vary to a large extent with temperature. A method was designed to approximately im pose the temperature dependent material properties on the ITPS structure. As mentione d earlier in this s ection, the temperature distribution on the ITPS panel is known in advan ce from the heat transfer analysis (cubic polynomial in z -coordinate). From this the top and botto m face sheet temperatures were obtained and the material properties corresponding to this temperature were imposed on the face sheets. In case of webs, however, the temperature varies th rough the thickness of the panel. Therefore, each web was divided into 10 partitions from top to bottom as shown in Figure 3-10. The average temperature in each partition was obtained from the temperature distribution data. Material properties corresponding to the average temperat ure of each partition were assigned to that particular partition. It should be noted that since the temperatur e distribution is a function of z coordinate only, all partitions with the same z-coordinate will be assigned the same material properties. In ABAQUS buckling eigenvalue problem, th e desired number of eigenvalues can be specified. For example, if 15 eigenvalues ar e desired, then ABAQUS extracts the first 15 PAGE 67 67 smallest eigenvalues and the corresponding ei genvectors. There may be many negative eigenvalues in the first 15 values. In order to avoid negative eigenvalu es, a minimum eigenvalue of interest may be specified. Typically, a small positive value, example 10-6, is specified, so that all the 15 eigenvalues obtained from the analysis are positive. Figure 3-10. Typical ITPS panel illustrating the manner in which the webs are partitioned into 10 regions to impose approximate temper ature dependent material properties. The output data of interest from the buckling analysis are the smallest eigenvalues. These values can be obtained from the ABAQUS data f iles, which have the extension Â‘.datÂ’. The eigen vector corresponding to each eigenvalue can be obtai ned from the output file in the form of nodal displacements. The nodal displacement data for bu ckling problems are normalized so that the maximum nodal displacement is always equal to unity. By obtaining the node number whose displacement is equal to unity and combining this with the nodal coordi nates data, the buckling position can be identified. For exam ple if the node with maximum disp lacement is in the top face sheet, then the buckling eigenvalue corresponds to top face sheet buckling. The buckling modes can also be visualized in the ABAQUS visualization modul e window. Typical buckling modes are shown in Figure 3-11. The pos ition of buckling can be usef ul when the buckling response surface approximations are obtained separately fo r web buckling and top face sheet buckling, for example (more details in Chapter 5). PAGE 68 68 3.3 Stress and Deflection Analysis Stress analysis of the ITPS panel is carried out using the same geometry and mesh as the buckling analysis. The buckling step is replaced by static stress analysis step. In stress analysis case, ABAQUS is capable of taking into account the temperature dependent material properties. Therefore, even though the web is partitioned into 10 regions, all the regions are give the same temperature dependent material properties as the web material. The ABAQUS solver automatically assigns the material properties to each element according to the temperature imposed on the element. A B Figure 3-11. Typical buckling modes of the ITPS panel. A) Web buckling. B) Top face sheet buckling. From the stress analysis models, deflections and von Mises stress values can be obtained. The z -direction deflection of the top face sheet can be obtained separately from the ABAQUS output files. Similarly, the von Mises stresses for each section of the ITPS can be obtained separately. PAGE 69 69 CHAPTER 4 RESPONSE SURFACE APPROXIMATIONS AND OPTIMIZATION PROCEDURE This chapter explains the process for genera tion of response surface approximations used to approximately represent the constraints of the optimization problem. Then the optimization procedure is presented. 4.1 Response Surface Approximations For the current ITPS design problem, a quadra tic response surface approximation of each constraint was adopted to solve the optimi zation problem. These response surface (RS) approximations are functions of the design vari ables. The procedure for obtaining these RS approximations is outlined below. A quadratic RS approximation in 7 variables has 36 coefficients and hence at least 36 function evaluations are required to determine all the coefficients. Usually, the number of function evaluations, N , required for obtaining a sufficiently accurate approxima tion is twice the minimum number of coefficients and depends upon the nature of the problem at hand. For ITPS design, N has been typically found to be greater than 150 in order to obtain sufficiently accurate approximations. The major reason fo r this unusually high value of N is the RS approximation for buckling eigenvalues. RS approximation for the peak bottom face sheet temperature has been found to be sufficiently accurate even for N equal to 100. However, the buckling eigenvalue response has large kinks, which are difficult to capture using a quadratic polynomial function. As a result the number of responses has to be increased in order to get an accurate polynomial. An RS approximation obtained using leas t squares approximation method cannot be guaranteed to be accurate if a variable value is chosen outside its range. To avoid ill-conditioned matrices while implementing the Least Squares Approximation technique, normalized values of the variable should be used so that each variable varies between zero and unity. PAGE 70 70 Optimized Latin Hypercube Sampling (LHS)technique was used for the design of experiments to obtain N different combinations of the desi gn variables, also referred to as design points . In the LHS technique the specified ra nge of each variable is divided into N equal intervals. Then, one value from each interval fo r each variable is randomly chosen. These values are randomly combined to generate N design points. The optimized LHS technique performs iterations to maximize the minimum distance betw een two values of a variable. This scheme precludes the possibility of the variables being clustered in any region of the design space and ensures uniform distributions of the points in the design space. 4.1.1 Response Surface Approximations for Maximum Bottom Face Sheet Temperature Transient 1-D heat transfer analys is was carried out for each of the N design points using ABAQUS. As described in Section 3.1.5, the peak bottom face sheet temperature was obtained for each of these design points and the coefficien ts of the RS approximation were obtained by least squares approximation. RS approximation for peak bottom face sheet temperature is usually quite accurate. More discussion about accuracy is given later in Chapter 5. 4.1.2 Response Surface Approximations for Buckling For buckling problem the RS approximations were obtained for the smallest buckling eigenvalue. The same design of experiments used for heat transfer analysis was used for the buckling analysis. Using the combination of va riables obtained by Optimized LH Sampling, the 3-D FE model for buckling was created and anal yzed as described in Chapter 3. The first 15 positive eigenvalues were obtained for each design point. The buckling position for each of these eigenvalues was then identified. From this data the smallest eigen buckling value for top face sheet, web and bottom face sheet were obtained. Using these eigenvalues and the normalized values of the design variables, RS approximati ons can be obtained for the smallest buckling eigenvalue in each section separately. PAGE 71 71 For some design points, the buckling value for a particular section does not figure in the first 15 values. For example, if the total numbe r of design points is 200, then web buckling may figure in the first 15 values fo r only 180 of these design points. In that case, only these 180 points will be considered for the generation of the web buckling RS approximation. If the number of design points availabl e for RS approximation generati on is less than the minimum required for the least squares approximation, then that particular constraint will not be considered for the optimization procedure. This can be ju stified by stating that for the range of design variables chosen for this optimization, buckling of that particular section will not be an influential factor. However, if that particular constraint proves to be critical at the optimum design, then the variable bounds need to be suitable altered so as to include sufficient number of design points at which this cons traint generates a response. 4.1.3 Response Surface Approximations for Stress and Deflection RS approximations for stresses were obt ained by extracting the maximum von Mises stresses for each design point. Maximum stresses were obtained separately for each of the 3 sections top face sheet, bottom face sheet and web. For each of these (shell) sections, von Mises stresses were obtained at the top surface and bottom surface separately and the higher value among the two was considered for the generation of the RS approximations. The maximum and minimum z -direction displacements are obt ained separately for the top face sheet and the absolute value of the differenc e is used for the deflection generation of RS approximations. 4.2 Procedure for Generation of Response Surfaces Approximations Typically, it has been observed that more than 150 functi on evaluations are required to generate sufficiently accurate response surface approximations for 6 design variables. This would imply that a large number of FE experiments need to be carried out for one optimization. PAGE 72 72 Further, the process has to be repeated whenever there is a change in the design geometry or other parameters like heat load, pressure load and boundary conditi ons. It is a formidable number of FE analyses to be carried out manually. A MatlabÂ® code has been developed for this purpose called the ITPS Optimizer . The ITPS optimizer activates ABAQUSÂ® and performs the FE heat tran sfer, buckling and stress analyses automatically. The functions of ITPS Optimizer ar e illustrated by the flow chart in Figure 4-1. 1-Dheat transfer analysis Obtain maximum bottom face sheet temperature and temperature distributions at different reentry times. 3-Dthermal buckling analysis Obtain buckling eigen values and vectors; identify the smallest eigen values for each of TFS, BFS and web. 3-Dlinear stress analysis Obtain stress values in different section of the panel; extract nodal displacements on the top face sheet. Maximum BFS temperatures Smallest buckling eigen values Stresses in different sections of TPS p anel Max top face sheet deflection Design of Experiments (Latin-Hypercube Sampling) Temperature distribution at different reentry times Figure 4-1. Flowchart illust rating the procedure followed by the ITPS Optimizer. Rounded boxes represent inputs for FE analyses, r ectangles for FE analyses and ellispses represent FE output. Temperature distributions are output of heat tr ansfer analysis and input for buckling and linear stress anal ysis. The dotted rect angle containing the ellipses represents the data output from ITPS Optimizer, which is used for generating response surface approximations. The ITPS Optimizer first obtains a design of experiments using Latin-Hypercube Sampling technique. In MatlabÂ®, the function lhsdesign ( ) can be used for this purpose. A statement of the form NV = lhsdesign(NExpts, NVars,'criterion', 'maximin', 'iterations',NIter) PAGE 73 73 will assign a matrix of NExpts rows and NVars columns to the matrix NV . NExpts is the number of experiments and NVars stands for the number of variables. The last four commands in the parenthesis are for maximizing the minimum dist ance between the variable values by iterating NIter times, typically 200. This will ensure that the variables are properly spaced in their respective ranges. The matrix NV will have values between 0 and 1 only. These values may be viewed as normalized variables, normalized by the ranges of the resp ective intervals of the variables. They are scaled to obtai n the exact variable values matrix V . Each row of V represents one combination of the variables or one design point. Using the NExpts combinations of variables the FE experiments are carried out. Using the values of variables in the matrix V , the ITPS Optimizer creates a 1-d heat transfer FE model starting w ith the first combination. This is done by creating an ABAQUS Script File which is written us ing Python language commands. This script file contains all the geometry commands by which a line is drawn and partitioned into 3 sections top and bottom face sheets and homogenized core. Then material assignment commands are used to assign the material properties to the respective sections . The properties of the homogenized core are calculated using Equations (3.2)Â–( 3.4). Commands for creating lo ad steps, applying loads and boundary conditions, and meshing commands are also written into the Script File. All these Python language commands are written into the Script File using Matlab M-file commands. The script files are saved with an extension Â‘ .pyÂ’. Once the script f ile is ready, ABAQUSÂ® is invoked to read the script file. The invocation is achieved using the following M-file statement system(abaqus cae noGUI= filename .py) ABAQUSÂ® executes the Python commands in the scri pt file and creates a Â‘.caeÂ’ file, which is the geometric model. The Script File al so includes commands which create an ABAQUSÂ® PAGE 74 74 Input File. An ABAQUSÂ® Input file is a link between ABAQUS CAE and ABAQUS Solver. An input file contains all the node numbers and coordinates, element numbers, node and element sets, material property information, load steps, loads and boundary conditions information. All this information is in a format recognizable by the ABAQUS Solvers. For this research ABAQUS Standard Solver is used. Usually, the input file is modified by the ITPS Optimizer to put in all the desired information. The input file s are required to be sa ved using the extension Â‘.inpÂ’. This input file is then submitted to the ABAQUS Standard solver using the following statement system(ABQ651 analysis job=" job name " INTERACTIVE) This command is for ABAQUS version 6.5-1. If a different version is used then the command is different. For example the command is ABQ631 , if ABAQUS version 6.3-1 is used. ABAQUS solver solves the FE problem and cr eates an output database (ODB) file, which contains all the FE solution information. Require d information can be extracted from the ODB files by creating and executing ot her script files that contain suitable output extraction python commands. Temperature versus time output and noda l temperatures at different reentry times of interest are extracted and printed out in the form of text files. Data from these text files is then obtained and the peak temperatures are determined. Also, the nodal temperature data is used to compute cubic polynomials for temperature distri bution through the thickness of the ITPS panel at different reentry times of interest. The ITPS Optimizer process for buckling is similar to that for heat tran sfer analysis. Script files are created and executed to obtain a 3-D sh ell model and FE mesh of the panel. The input file contains all of this information. This input file is modified to impose nodal temperatures on the model using the temperature distributions obta ined from heat transfer analysis. Since the PAGE 75 75 buckling analysis is carried out at different re entry times, new input file s are created for each reentry time containing the nodal temperature loads from the corresponding temperature distribution data. These input f iles are then submitted to ABAQUS solver and output database files and Â‘.datÂ’ files are obtai ned. eigenvalues are obtained from the Â‘.datÂ’ files. At each eigenvalue, the nodal displacements are extracte d for the output database file by creating and executing scripts files. The nodal displacements ar e listed in text files from which the ITPS optimizer extracts the data and determines the buckling position for each eigenvalue. The ITPS optimizer procedure for stress and de flection analysis uses the same mesh and input files as the bucklin g analysis. However in this case, the buckling step is changed to static analysis and the material properties are also suitably altered to accommodate the temperature dependent material properties. Using script f iles, nodal displacements of top face sheet and von Mises stress of various sections in the ITPS panel are printed to text files. The ITPS optimizer extracts the data from these text files and determines the maximum values required for the generation of response surface approximations. 4.3 Optimization Procedure Optimization was carried out with a MATLAB c ode developed for this purpose. The code uses in-built subroutine fmincon ( ). The response surface approximations obtained from the ITPS Optimizer were input into this code to impose constraints. The optimization process was carried out 10 times with a different starting point at each optimization. The different starting points were obtained by Latin-Hyperc ube Sampling so that they are spread out uniformly in the design space. If different optimized designs are obtained for different starting points, then the design with lowest weight is c hosen as the optimized design. PAGE 76 76 CHAPTER 5 ITPS DESIGNS In the previous two chapters, the finite element analyses and procedure for optimization were discussed. This will be followed by optimizati on and design of ITPS panels in this chapter. First, the loads, boundary conditions and other input parameters in the ITPS design will be discussed. Two types of designs have been explor ed Â– a) corrugated-core and b) truss-core. The design of truss-core structures will be presented in the second part of the chapter. The truss-cores were found to be unable to withstand the large th ermal stresses generated in the ITPS panels. A discussion on the difficulties in truss-core modeling and the r easons for these cores being unfit for ITPS panels will be presented in the last part of this chapter. 5.1 Selection of Loads, Boundary Condi tions and Other Input Parameters The ITPS design has been performed generical ly without any specific vehicle in mind. Although, the future space vehicles are most probabl y of the space capsule type, most of the data for these vehicles is not available. So the loads considered for this design were typical of a Space Shuttle-like vehicle. A discussion on the reentry heat flux input for a Space Shuttle Orbiter-like vehicle has been presented in Section 3.1.1. For this research wo rk, metal alloys have been used for the ITPS panels. Therefore, heat flux input profiles that produce temperatures that are below service temperatures of these alloys can only be used. Th e heat flux profile chosen for the design of the corrugated-core panels has been shown in Figure 5-1. The radiation equilibrium temperature (see S ection 3.1.1 for details) for the peak heat flux is 946 K for an emissivity of 0.8 and ambient temp erature of 295 K. The peak temperature of top face sheet is usually close to th e radiation equilibrium temperatur e. Therefore, titanium alloy (Ti6Al-4V) has been chosen for the top face sheet and web material. For the bottom face sheet, PAGE 77 77 beryllium alloy has been chosen. Temperature depe ndent material properties have been listed in Appendix. Further discussion a bout material selection and recommendations for choice of materials will be presented in the Chapter 6. Figure 5-1. Heat flux input used for th e design of corrugated-core structures. The bottom face sheet of the ITPS panel is assu med to be perfectly insulated. Some of the other input parameters for the heat transfer problem are (See Section 3.1.1 for more details) Emissivity of the top surface: 0.8 Coefficient of convection on the top surface after landing: 5.0 Wm-2K-1 Ambient temperature for 0 to 450 sec: 213 K Ambient temperature for 450 to 1575 sec: 243 K Ambient temperature for 1575 to 2175 sec: 273 K Ambient temperature after landing: 295 K Initial temperature of the st ructure before reentry: 295 K Aerodynamic pressure load on a Space Shuttl e-like design is shown during reentry in Figure 5-2. The external pressure is close to zer o during the reentry phase and becomes equal to atmospheric pressure after landi ng. Therefore, during the reentry phase, the pressure load on the external surface is taken equal to zero. Usually, the crew compartment is separated from the 450 2175 1575 4500 Time from Rentry, sec Heat influx rate, Btu/ft2-s 3.0 PAGE 78 78 outer shell, which is the TPS. The crew compartment is under pressure suitable to human comfort. The space between the crew compartment a nd the outer shell is assumed to be vented to the outer atmosphere. Therefore, before reentry, this vented space would be at zero pressure (pressure in the Space). During reentry phase the pressure load on both sides of TPS is zero and hence there is no pressure load applied on the ITPS panels during reentry phase. After the vehicle lands, the outside pressure is equal to the atmospheric pressure . Even though the space between crew compartment and the TPS is vented to the atmosphere, there will be a certain lag time before the pressure on both sides of the TPS becomes equal. During this lag time, there is a pressure load on the outer surface. Taking the worst case scenario into consideration, the pressure load on the outer surface is consid ered equal to 1 atmosphere or 101,325 Pa. To summarize, the pressure load on the ITPS panels is equal to zero in all buckling and stress analysis cases before landing and is equal to 1 atmosphere after landing. Another mechanical load on the ITPS is the in-p lane inertial load during the reentry phase. The inertial load is compressive in nature during the reentry phase because the vehicle is slowing down due to aerodynamic braking. Typical weight of space capsules is estimated to be around 10,000 kg and maximum estimated load due to aerodynamic braking is 5g, equal to 5Ã—9.8 = 49 m/s2. Therefore, the total load on the back shell of a space capsul e is equal to a maximum of 490,000 N. Assuming that the space capsules have a di ameter of 5 meters, the in-plane load on the backshell of the space capsule can be obtained by dividing th e total load by the circumference of the backshell and is approximate ly equal to 30,000 N/m. This in-plane load is applied to the ITPS buckling and stress analysis only during reen try phase. After landing, no inplane load is applied on the ITPS.A summary of the pressure load a nd in-plane loads in presented in Table 5-1. PAGE 79 79 0.E+00 2.E+04 4.E+04 6.E+04 8.E+04 1.E+05 1.E+05 050010001500200025003000Reentry Time (sec)Aerodynamic Pressure (Pa) Figure 5-2. Aerodynamic pressure load on the TP S for a Space Shuttle-like design. The pressure remains close to zero during reentry phas e and becomes equal to the atmospheric pressure after landing. The boundary conditions for the buckling and st ress analysis cases are dependent upon the way in which the ITPS panel is connected to the vehicle. For this resear ch work, it is assumed that the bottom face sheet is conn ected to the stringers and frames of the vehicle. Usually, an allowance in the connections is provided in such a way that th e bottom face sheet is allowed to expand so as to minimize the thermal stresses de veloped in the structure. So, simply supported boundary conditions are imposed on the bot tom face sheet edges of the panel. Table 5-1. Summary of mechani cal loads applied on the ITPS panel for buckling and stress analysis cases. Reentry Phase No pressure load on the top surface In-plane load of 30,000 N/m After Landing Pressure load of 1 atm on t op surface No in-plane load The top face sheet is usually the thinnest se ction of the ITPS pane l. Excessive thermal compressive stresses can cause the top face sh eet to buckle. Therefore, a good design would PAGE 80 80 allow the top face sheet to expand freely. However, the free edges are susceptible to buckling if left free. It is assumed that the panel edges ar e closed out by a thin metal foil connecting the top face sheet to the bottom face sheet. These foils help in containing the insulation material within the panel. The mechanical properties of the metal foil are assumed to be negligible. However, the foil applies certain restraint on th e top face sheet edges. This rest raint is approximately simulated by restraining the rotations on the edges of the to p face sheet. Such a constraint would apply mild restraint on the top face sheet edges while preclu ding the development of large thermal stresses. Thus the panel edges on the top face sheet are restrained in rotations and no constraints are placed on the displacements. It is clearly evident that there are a number of assumptions involve d in the various input parameters, loads and boundary conditions on the IT PS panel. One of the most important reasons for these assumptions is because this design pro cess is for a generic IT PS panel as there is no specific vehicle for which it is being designed. Most of the assumptions were made in order to obtain a reasonable ITPS design. It is almost impo ssible to proceed with th e design process if all the parameters were to be close to reality, b ecause not all parameters are well defined for the design problem at hand. The signifi cance of all these input parame ters is studied by individually varying these parameters and obs erving their effect on the ITPS design. The results for these analyses will be presented in the Chapter 6. 5.2 Corrugated-Core Designs The following 6 geometric variables completely describe a unit cell of a corrugated-core ITPS panel, as shown in Figure 1-2 and reproduced here as Figure 5-3, 7. Thickness of top face sheet, tT, 8. Thickness of webs, tW, 9. Thickness of bottom face sheet, tB, 10. Angle of corrugations, , PAGE 81 81 11. Height of the sandwich pane l (center-to-center distance between top and bottom face sheets), h , 12. Length of a unit-cell of the sandwich panel, 2 p . Figure 5-3. A unit cell of a corrugated-core IT PS panel illustrating the 6 design variables. An additional design variable introduced here is the number of unit cells, n , in one panel. Thus there are 7 design variab les in all. The product of n and 2 p gives the length of the whole ITPS panel, L . It makes more sense to have L as a design variable rather than 2 p . Therefore, the sixth design variable 2 p is replaced by L . The range of each variable is listed in Table 5-2. These ranges were chosen based on many optimization studies. The ranges were wider for initial studies. They were narrowed down subsequently, as the optimization studies provided insight into the behavior of the ITPS panel. For example, initial range for the top face sheet thickness, tT, was 0.5 to 5 mm. However, optimization studies with different loads, boundary conditions and materials indicated that typical values of tT are closer to 1.0 mm. T hus the range was narrowed down and this also helped in improving the accuracy of the RS approximations. Titanium alloy, Ti-6Al-4V, is used for top f ace sheet and web and a beryllium alloy is used for the bottom face sheet. All the input parame ters, loads and boundary conditions have been discussed in the previous section. The in-plane loads (dis cussed in previous section) are applied tT tW h 2p z y tB PAGE 82 82 on the bottom face sheet at the panel edge, becau se these loads are transmitted by the stringers and frames to the bottom face sheet. Table 5-2. Ranges of the 7 design vari ables for corrugatedcore ITPS panels tT 1Â–2 mm tB 2Â–8 mm tW 1Â–2 mm 80Â°Â–100Â° h 80Â–120 mm L 450Â–900 mm n 4Â–10 At this point, it is necessary to identify the Â“critical reentry timesÂ”, which means the reentry times at which the loads on the ITPS pa nel cause failure in the form of buckling, excessive stress or deflection. One of the critical reentry times is that at which the temperature difference between the top face sheet and the bott om face sheet is maximum. At this time, the thermal stresses can be expected to be at the ma ximum. This happens at the initial portion of the reentry phase when the top face sheet is close to its peak temperature and the bottom face sheet is still close to its initial temper ature. At this point there are in-plane loads applied on the ITPS panel as well. The combined effect of thermal load s and in-plane mechanical loads is of interest at this point. This critical reentry time will, henceforth, be referred to as Â‘ tmax TÂ’. Another critical time of inte rest occurs after landing and when the bottom face sheet reaches its peak temperature value. This is th e time when the stresses in the bottom face sheet might be at the maximum. Further, at this time external pressure load s are imposed on the ITPS panel. The combined effects of temperature and pre ssure loads are of intere st at this point. This time will, henceforth, be referred to as Â‘ tmaxBFTÂ’. PAGE 83 83 The ITPS Optimizer first carries out the heat tr ansfer analysis and obtains the temperature distribution at tmax T and tmaxBFT. These temperature distributio ns along with the respective mechanical loads are imposed on the struct ure to carry out the buckling and stress. 5.2.1 Accuracy of Response Surface Approximations The minimum number of responses for obtai ning response surface approximations with 7 design variables is 36. For the corrugated-core design, FE analyses we re carried out at 250 design points obtained by optimized Latin-Hype rcube Sampling Technique (see Section 4.2). The accuracy of temperature and deflection re sponse surface approximations is presented in Table 5-3, buckling in Table 5-4 and st resses in Table 5-5. The column header Â‘eRMS %Â’ stands for percentage of the root mean square error when compared to the average response value. Column header Â‘ePRESS %Â’ stands for percentage of PRESS error when compared to the average response value. PRESS is an acronym for Pred icted Error Sum of Squares and is a better indicator of the accuracy of th e response surface approximations. The procedure for calculating the PRESS error is as follows. Consider that there are N response values from which the response surface approximation is calculated. First calculate the response surface approximation R1 using responses 2 to ( N 1) by leaving out the first response. Now determine the error ( e1) of R1 by substituting the variable values corresponding to response 1 into this response surface a pproximation. Similarly calculate R2 to RN and the corresponding errors e2 to eN. The root mean square of the errors e1 to eN is the PRESS error for the response surface approximation. The buckling response surface approximations are calculated only for tmax T because it was found that the eigenvalues for tmaxBFT are always higher that those at tmax T. Therefore, eigenvalues at tmaxBFT will not be among the active constraint s for the ITPS design. Further, there is no bottom face sheet buckling case because the number of responses for this case is not PAGE 84 84 sufficient to obtain the respons e surface approximation. The bottom face sheet buckling will not be an active constraint in the design process. Table 5-3. Table showing the accuracy of the re sponse surface approximations for peak bottom face sheet temperature and top face sheet deflections. Min MaxeRMS %ePRESS % Temperature (K) 365 673 1.33 4.35 tmax T 1.6 8.4 0.54 1.46 Deflections (mm) tmaxBFT 0.65 7.4 5.8 13.3 The large error in the top f ace sheet buckling response surf ace approximation is due to availability of less number of responses. Am ong the 250 design points, only 190 points yielded top face sheet buckling eigenvalues. That is, in the remaining design points, the top face sheet buckling did not figure in the first 15 eigenvalues (see Section 4.1.2 for details). Compared to the top face sheet, 234 out of 250 design points yielde d web buckling eigenvalues and that is the reason for the higher accuracy of the res ponse surface approximation corresponding to web buckling. Table 5-4. Table showing the accuracy of the re sponse surface approxima tions for top face sheet and web buckling eigenvalues. The column Â‘# of points usedÂ’ lists the number of design points used for calculating the response surface approximation. MinMaxeRMS %ePRESS %# of Points used Top face sheet buckling tmax T 0.2511.2 6.6 22.8 190 Web buckling tmax T 0.2 3.97 3.32 11.4 234 Combined buckling tmax T 0.2 3.97 4.69 16.8 250 The last row in Table 5-4 referred to as Â‘C ombined bucklingÂ’ is the response surface approximation obtained by using the lowest eigenvalues at each design point, irrespective of top face sheet buckling or web buckling. Note that for case of Â“combined bucklingÂ” 250 out of 250 responses are available for the calculation of the response surface approximation. Yet, it can be observed that this response surface approximation has a higher PRESS error than that compared to the web buckling case. Thus, it is a very good practice to separately obtain response surface PAGE 85 85 approximations for top face sheet and web buckling in spite of the large error in top face sheet buckling case. Another advantage of splitting the buckling response su rface approximation is that the active constraints can be separately iden tified in the optimization procedure, which is not possible in the case of Â‘Combined buc klingÂ’ response surface approximation. The accuracy of the response surface approxima tions corresponding to stresses is shown in Table 5-5. The FE analysis of the corrugatedcore ITPS panel showed that there are stress concentrations at the panel edges at the juncti on between the webs and the face sheets as shown in Figure 5-4. These stress concentrations are an ar tifact of the FE model, that is, they can be classified as modeling errors. In actual corrugated-core construc tion, due to the manner in which the webs are attached to the face sheets there will be no such stress concentrations. These stresses are not Â“true stressesÂ”. Therefore, the stresses at this panel e dge (shown by arrows in Figure 5-4) are separated from the stresses in the rest of the panel. The first 3 rows in Table 5-5 show the stresses in the rest of the panel, while the ones in the last 3 rows are the edges stresses. One of the major reasons for the large errors in some of the response surface approximations is due to the in clusion of the design variable n (the number of unit cells in the panel. Unlike the other 6 variables that influe nce only the sizing of the panel, the variable n changes the entire geometry and stress transfer mechanisms in the ITPS panel. This leads to a large variation in the eigenvalues and stresses an d decreases the accuracy of the response surface approximations. In spite of the large PRESS erro rs, the response surface approximations can be expected to be qualitatively re asonable and lead to the design cl ose to the real design. It is worthwhile to point out the fact that the percentage RMS error is smaller than 6% in all cases. At this juncture, it is also a ppropriate to highlight the fact th at the objective of this research is not to accurately design an IT PS panel, but only to investigate the feasibility of such a PAGE 86 86 structure for ITPS applications. An actual ITPS would involve a lot more factors than those considered in this research. Some of the other factors are manufacturing as pects such as joining of dissimilar materials and crashwor thiness of the structure. In th is light, the design process with the above listed response surface ap proximations will shed valuable light into the issues related to the design of corrugated-core panels for ITPS applications. Table 5-5. Table showing the accur acy of the response surface appr oximations for stresses in the ITPS panel. The stresses are expressed in MPa. MinMaxeRMS %ePRESS % tmax T 240 884 2.37 9.34 Bottom face sheet stresses tmaxBFT93 688 3.78 12.4 tmax T 67 236 1.52 5.71 Top face sheet stresses tmaxBFT46 397 5.67 16.9 tmax T 97 436 1.26 4.68 Web stresses tmaxBFT73 263 2.44 8.03 tmax T 181 727 2.06 9.28 Bottom face sheet stresses at panel edges tmaxBFT92 442 3.64 13.04 tmax T 73 253 2.67 7.0 Top face sheet stresses at panel edges tmaxBFT55 276 4.94 11.46 tmax T 251 10601.14 4.92 Web stresses at panel edges tmaxBFT122 640 3.54 11.06 5.2.2 Optimized Corrugated-Core Panel Designs The response surface approximations, discussed in the previous section, are used for the design optimization of the corrugated-core pa nels. The optimization procedure has been described in Section 4.3. The following constraints were imposed on the optimization problem 1. Peak bottom face sheet temperature 200 Â°C 2. Buckling Eigen Value 1.25 3. Top face sheet deflection 6.0 mm 4. Factor of Safety for stresses = 1.2 The temperature and deflection constraints we re similar to those imposed on the ARMOR TPS [12]. Although, the limit for minimum buck ling eigenvalue is 1.0, a value of 1.25 was PAGE 87 87 chosen to account for the inaccuracy of th e buckling response surface approximations. For stresses, typical factor of safety is 1.5. Howeve r, a value higher than 1.2 did not produce feasible results in the optimization procedure due to high stresses in bottom face sheet. Figure 5-4. A typical FE contour plot illustrating the stresses at the panel edges at the junction between the face sheets and the webs. The arrows point to the areas of stress concentrations. The optimized designs are listed in Table 56. The first column of the table lists the intervals within which the respective variables va ry. There are 4 designs li sted in the table and each is obtained by imposing an additional constraint on the number of unit cells, n . For example, for Design 1 the number of unit cells is made equal to 4, for Design 2 the number of unit cells is made equal to 10 and so on. Design 1 is the lightest of all, while Design 2 has the advantage of be ing the longest of all panels and also has the shortest panel height . Design 3 and 4 are heav ier and do not have any apparent advantages over the ot her designs. Longer panels require less number of stringers and frames in the space vehicle. This could help reduce the overall weight of the vehicle outer structure. PAGE 88 88 The active constraints for Design 1 are stresse s in the bottom face sheet, web buckling and top face sheet buckling. For Design 2, apart from these constraints the peak bottom face sheet temperature constraint also become active. In order to better understa nd the behavior of the panels, it is necessary to unders tand the buckling modes and stress distribution in these panels. Table 5-6. Table listing the optimized designs for corrugated-core panels Design 1 Design 2Design 3Design 4 Range of design variables Mass (lb/ft2) 4.846 8.199 8.351 8.93 1Â–2 mm tT (mm) 1.2 1.2 1.32 1.2 2Â–8 mm tB (mm) 3.84 7.49 5.49 7.75 1Â–2 mm tW (mm) 1.01 1.63 1.36 1.62 80Â°Â–100Â° (deg) 100.0 80.0 100.0 80.0 80Â–120 mm h (mm) 101.9 80.0 120.0 83.82 450Â–900 mm L ( mm) 450.0 682.9 450.0 496.9 4Â–10 n 4 10 6 8 The web and top face sheet buckling modes fo r Design 1 and Design 2 are shown in Figure 5-5. As mentioned in Chapter 3, only one quarter of each panel is modeled in the FE model by taking advantage of symmetry. In Figure 5-5A, the panel edges and the symmetry edges are labelled. All the other figures are shown with th e same orientation. In the web buckling case, the buckling modes in both designs are sim ilar. These buckling modes happen at tmax T when the temperature difference between the bottom face sh eet and top face sheet is maximum. The top face sheet is close to its peak temperature and tends to expand. However, the bottom face sheet, which is at much lower temperature, resists th is expansion. As the webs transmit the forces between the two plates, they experience large flexur al loads. The web that buckles is the farthest from the center of the panel and experiences the highest load. Boundary conditions imposed on the bottom face sheet edges also provide resistance to deformation and this effect is experienced by the web closest to the panel edge. PAGE 89 89 A B C D Figure 5-5. Buckling modes for optimized designs . A) Web buckling for Design 1. B) Top face sheet buckling for Design 1. C) Web buck ling for Design 2. D) Top face sheet buckling for Design 2. At tmax T, the top of the webs are at a much hi gher temperature when compared to the bottom. Thus the web deformation would be as illustrated in Figure 5-6. This deformation is resisted by the face sheets and the resistance by the bottom face sheet is much higher because it is the thickest section of the panel and is also the most constrained member of the panel. This leads to very high stresses in the bottom face sheet, particularly at the web-bottom face sheet junction closest to the panel edge. The stress di stribution in the bottom face sheet is shown in Figure 5-7A. Stresses are highest at the region pointed to by the arrow. This region corresponds to the centerline (dash-dot line) in Figure 5-6 wher e the vertical displacement is the highest in the web. The stress distribution in the top face sheet and the webs are also shown in Figure 5-7. As mentioned earlier, stresses are highest in the sections closest to the panel edges. Panel edge symmetry edge symmetry edge Panel edge PAGE 90 90 Figure 5-6. Typical web deforma tion tendency due to the temperature gradient in the panel. A B C Figure 5-7. Von Mises stress distri bution in the ITPS panel, Design 1, tmax T. A) Bottom face sheet stresses. B) Web stresses. C) Top face sheet stresses. 5.2.3 Buckling Eigen Values, Deflections a nd Stresses at Differe nt Reentry Times The two reentry times at which the buckling and stress analyses were carried out are tmax T, when the temperature gradient in the structure is most severe, and tmaxBFT, when the bottom face sheet reaches its peak temperature. These two times were chosen on the basis of intuition of where the critical stress and buckling cases could o ccur. In order to determine whether these two High temperature side Low temperature side z -axis PAGE 91 91 reentry times are the only critical cases, a st udy was conducted to understand the variation of smallest buckling eigenvalues, maximum deflec tions and maximum stresses with respect to reentry time. These studies were conducted on the ITPS panels with dimensions of Designs 1 and 2. Figures 5-7A, 5-7B and 5-7C illustrate the results of the ITPS panel Design 1. During the reentry phase (0 to 2175 seconds) in-plane loads are applied on the panel and after landing (after 2175 seconds) pressure load is applied on the top face sheet (see Section 5 .1 for details). In all the three figures, the temperature variation of top face sheet, bo ttom face sheet and the temperature difference between the two face sheets has been illustrated and the values correspond to the axis on the left. Absolute valu e of the temperature difference has been plotted. The increase in temperature difference after landing is a result of plotting this absolute value. A little while after landing the bottom face sheet temperature b ecomes higher than the top face sheet temperature and the difference increase s till the bottom face sheet reaches its peak temperature and drops down after that. tmax T is at 650 seconds and tmaxBFT is at 3025 seconds. From Figure 5-7A, it can be observed that th e minima for top face sheet and web buckling is at 450 seconds. This time is different from tmax T (650 seconds) and is the point where the temperature of the bottom face sheet is still close to its initia l temperature of 295 K. Another interesting point is the second minima in the we b buckling curve which oc curs immediately after landing. The reason for this dip in the curve is due to the application of pr essure load on the top face sheet after landing. However, even though this pressure load is unchanged after landing, it can be observed that the web buck ling eigenvalue increases. The reason for this is that the ITPS panel begins to cool down after landing and the average temperature of the web also decreases. PAGE 92 92 As the stiffness of the webs (YoungÂ’s modulus) in creases with decrease in temperature, the buckling eigenvalue of the web also increases. Figure 5-7B shows the variati on of top face sheet deflection with reentry time. Absolute value of the deflection has been plotted in this figure. The first maxima occurs at 650 seconds corresponding to the time when temperature di fference between the face sheets is maximum. This temperature difference causes the top f ace sheet to bow Â“convex-upÂ”. After landing the pressure load causes the top face sheet to deflec t downward (concave-up). Since, the plot is for absolute value of deflection, the curve rises agai n after landing and the se cond maxima occurs at around 3,025 seconds, which corresponds to the time when bottom face sheet reaches its peak temperature value. The increase in deflection duri ng the early phase of cool-down (after landing) can be attributed to the increas e in bottom face sheet temperature, which decreases the stiffness of the bottom face sheet material. Figure 5-7C shows the variation of stresses with respect to re entry time. The stresses peak at either 450 or 650 seconds and then again at around 3,025 seconds. The reentry behavior of the ITPS panel corr esponding to Design 2 is shown in Figure 5-8. The buckling behavior, Figure 5-8A, during reen try phase is similar to that of Design 1. However, the second minima that occurs in Design 1 after landing is not pres ent in this case. The difference is due to the large number of webs (number of unit cells = 10) in Design 2. The pressure load is distributed among the webs a nd so this buckling mode does not surface here. Deflection values, Figure 5-8B, ar e higher for Design 2 because the pa nel is longer in this case. The larger panel length also leads to higher stresses, Figure 5-8C, in Design 2. PAGE 93 93 A 0 200 400 600 800 1000 05001000150020002500300035004000Reentry Time (sec)Temperature (K)0 1 2 3 4 5 6Buckling Eigen Value Top face sheet Temperature Bottom Face Sheet Temperature Temperature Difference Web buckling Eigen value Top face sheet buckling Eigen value tmax T tmaxBFT B 0 200 400 600 800 1000 05001000150020002500300035004000Reentry Time (sec)Temperature (K)0.0 0.5 1.0 1.5 2.0 2.5Top Face Sheet Deflection (mm) Top face sheet Temperature Bottom Face Sheet Temperature Temperature Difference Top face sheet deflection tmax T tmaxBFT PAGE 94 94 C 0 200 400 600 800 1000 05001000150020002500300035004000Reentry Time (sec)Temperature (K)0 50 100 150 200 250 300Stresses (Mpa) Top face sheet Temperature Bottom Face Sheet Temperature Temperature Difference Bottom Face Sheet Stresses Web Stresses Top Face Sheet Stresses tmax T tmaxBFT Figure 5-7. ITPS panel behavior w ith respect to reentry time fo r Design 1. In all three figures, the temperature variation of top face sheet, bottom face sheet and the temperature difference between the two have been plotte d. A) Buckling eigenvalues. B) Top face sheet deflection (maximum allowable deflecti on is 6 mm). C) Stresses in top face sheet, bottom face sheet and webs. Allowable stress in top face sheet and webs is 620 MPa and in bottom f ace sheet is 290 MPa. The important conclusions of this study are th e identification of critical reentry times for buckling and stress analyses. The cri tical times for buckling analyses are 450 seconds (when the temperature of the bo ttom face sheet is cl ose to its initial temperature), and 2225 seconds (just after landing and at the beginni ng of the application of pressure load). The critical times for stress and deflection analyses are: when the temperature difference between the face sheets is maximum, and when the bottom face sheet temperature is maximum. PAGE 95 95 A 0 200 400 600 800 1000 05001000150020002500300035004000Reentry Time (sec)Temperature (K)0 2 4 6 8 10 12Buckling Eigen Value Top face sheet Temperature Bottom Face Sheet Temperature Temperature Difference Web buckling Eigen value Top face sheet buckling Eigen value tmax T tmaxBFT B 0 200 400 600 800 1000 05001000150020002500300035004000Reentry Time (sec)Temperature (K)0.0 1.0 2.0 3.0 4.0 5.0 6.0Top Face Sheet Deflection (mm) Top face sheet Temperature Bottom Face Sheet Temperature Temperature Difference Top face sheet deflection tmax T tmaxBFT PAGE 96 96 C 0 200 400 600 800 1000 05001000150020002500300035004000Reentry Time (sec)Temperature (K)0 50 100 150 200 250 300 350 400 450Stresses (Mpa) Top face sheet Temperature Bottom Face Sheet Temperature Temperature Difference Bottom Face Sheet Stresses Web Stresses Top Face Sheet Stresses tmax T tmaxBFT Figure 5-8. ITPS panel behavior w ith respect to reentry time fo r Design 2. In all three figures, the temperature variation of top face sheet, bottom face sheet and the temperature difference between the two have been plotte d. A) Buckling eigenvalues. B) Top face sheet deflection (maximum allowable deflecti on is 6 mm). C) Stresses in top face sheet, bottom face sheet and webs. Allowable stress in top face sheet and webs is 620 MPa and in bottom f ace sheet is 290 MPa. Due to the boundary conditions imposed on the panel edge, bottom face sheet stresses for both designs are close to the limit stress of 340 MPa for Beryllium. The reasons for the high stresses have been discussed in the previous s ection. It has been observed from the optimization procedure that increasing the factor of safety to more than 1.2 does not yield any optimized designs as the bottom face sheet stress constr aints cannot be satisfie d. As many of the input parameters assumed for the study are approximate in nature, there is very little room to tweak these values to study their effect on the weight of the ITPS. Therefore, there is a need to relax the boundary conditions in order to reduce the stre sses developed in the bottom face sheet. New PAGE 97 97 boundary conditions and the subsequent optimized designs are described in the following section. 5.2.4 Optimized Designs with Changed Boundary Conditions In order to reduce the stresses in the botto m face sheet the boundary constraints were relaxed. Simply supported boundary conditions, which were prev iously imposed on both the panel edges, were imposed only on Edge A of Fi gure 3-9, and Edge B was left free. All other loads and boundary conditions were same as the previous corrugated-core design. The constraints imposed in the optimization problem we re also same except for the factor of safety on stresses, which was increased to 1.5, which is the usual value used in structural design. The accuracy of response surface approximations was si milar to those listed in Tables 5-3 to 5-5. The new optimized designs are shown in Table 5-7. All four designs have the same active constraints: Bottom face sheet temperature Top face sheet deflection Web buckling eigenvalue The deflection constraint becomes active because the panels in the new designs are longer. Due to the new boundary conditions, none of the st ress constraints are active in spite of the increase in the factor of safety. Web buckling was observed to be caused by pressure load on the top face sheet (which is applied after landing). Comparison of values predicted by response su rface approximations and the finite element analysis are presented in Tabl e 5-8 for Designs I and IV. Valu es are close to one another indicating that the response surface approximations are sufficiently accurate. As expected buckling eigenvalues show the largest error. However, the conservative value of 1.25 on buckling eigenvalue constraint s is sufficient to take th is inaccuracy into account. PAGE 98 98 Table 5-7. Table listing the optimized designs for corrugated-core panels with relaxed boundary conditions on the bottom face sheet. Design I Design IIDesign IIIDesign IV Range of design variables Mass (lb/ft2) 3.613 4.342 5.071 5.793 1.2Â–1.6 mm tT (mm) 1.2 1.2 1.2 1.2 2Â–8 mm tB (mm) 2.883 3.40 3.91 4.38 1.2Â–2 mm tW (mm) 1.2 1.2 1.2 1.2 80Â°Â–100Â° (deg) 88.44 89.31 89.8 90.1 80Â–120 mm h (mm) 87.15 88.95 89.99 90.42 450Â–900 mm L ( mm) 772.5 797.53 816.69 830.82 4Â–10 n 4 6 8 10 Table 5-8. Comparison of values predicted by response surface approximations and finite element analysis for Designs I and IV. The percentage difference is computed with respect to FE values. Design I Design IV RS ApproxFE % DiffRS Approx FE % Diff Temperature (K) 495.0 490.01.0 495.0 497.0 -0.4 575 sec 6.0 6.2 -3.2 6.0 6.1 -1.6 Deflection (mm) 2625 sec 5.0 4.7 6.4 3.1 3.0 3.3 TFS Buckling 450 sec 2.2 1.73 27.2 4.3 4.7 -8.5 Web Buckling 2225 sec 1.25 1.20 4.2 1.25 1.6 -21.9 575 sec 50.2 48.4 3.7 57.4 59.1 -2.9 Bottom Face Sheet Stresses (MPa) 2625 sec 45.4 46.5 -2.4 42.0 46.0 -8.7 575 sec 71.4 71.2 0.3 69.6 62.8 10.8 Top Face Sheet Stresses (MPa) 2625 sec 226.1 227.3-0.5 65.6 57.5 14.1 575 sec 79.6 78.6 1.3 88.8 90.5 -1.9 Web Stresses (MPa) 2625 sec 121.7 114.06.8 116.3 115.8 0.4 5.3 Truss-Core Structures for ITPS Truss core structures were explored for the ITPS applications as they were perceived to provide a lighter structure when compared to the corrugated-core structures. One of the major advantages of truss-core structur es is that the trusses provide a much smaller path for heat flow and this would lead to a better insulated ITPS. Tru sses are structurally superi or to plates (webs in corrugated-cores) in carrying comp ressive loads that would arise as a result of pressure loads on the top face sheet. They are also better suited to carry bending loads when compared to plates. Unlike the corrugated-core webs, trusses do not te nd to exert large forces on the face sheets and PAGE 99 99 they also do not offer large restraining forces on the face sheets that would lead to higher stresses. In spite of the seemingly overwhelming adva ntages of truss-cores when compared to corrugated-cores, it was found that the trusses are too weak to w ithstand the large bending forces created in them by the severe thermal gradient in the ITPS panels. Trusses also produce large stress concentrations in the face sheets at the points of attachment s. In this section, some of the work done on the truss-core structures is presente d for the advantage of researchers who want to pursue this line of design for ITPS applications. A typical FE model with truss-cores is shown in Figure 5-9A. As in the case of corrugatedcores, the face sheets were modeled with the shel l element. The trusses were modeled with the 3node (quadratic) beam element (ABAQUS elem ent B32 and B32OS). All loads and boundary conditions imposed were similar to the corruga ted-core models. ABAQUS has a provision to specify the beam cross-section. Various cross-se ctions like pipe-, box-, solid-rectangularand solid-circular-sections were used. It was found that the I-section produce d the minimum stresses of all cross-sections, when oriented in a proper direction. Irrespective of the beam crosssection, stress singularity at the beam-plate attachment points was found to be big problem in the FE mo deling of truss-core pa nels. In Figure 5-9A, some of the attachment points are pointed to by the arrows where the stresses produced are the highest. As expected, the stresses in the face sheets and the webs ar e highest in regions closest to the panel edges. At first look, the high stresses at the attachment points ap peared to be a case of stress concentration arising out of a modeling error. However, on closer examination it was found that there exists a singularity in the face sh eets due to the point loads and moments exerted by the beams on the face sheets. In Figures 5-9B -5-9D a patch of the top face sheet near the PAGE 100 100 corner-most junction point is show n with increasing mesh refineme nt in the model. The stresses at the junction node are listed be low each patch. The stresses in the top face sheet increase with mesh refinement almost doubling in magnitude whenever the element size is reduced by half. The stresses in the beams, however, do not show such a drastic change. In fact, the stresses in the beams decrease with mesh refinement. It is quite cl ear that the stresses in this model are not true stresses as their magnitude is heavily influenced by the mesh refinement. Further, the mesh refinement also alters the force and moment inte ractions between the plates and the beams. As the mesh is refined, the patch around the juncti on points becomes more compliant and thus a decrease in the beam stresses can be observed. In order to further understa nd the shell-beam interacti ons, an FE experiment was conducted, where in one unit cell of the truss-core model was modeled with beam elements and shell elements, as shown in Figure 5-10. The bot tom face sheet was constrained on the edges and an arbitrary edge load was applied on the t op face sheet. The stresses for increasing mesh refinement are listed in Table 5-9. As expected, the beam model exhibited stress singularity and the top face sheet stresses increased with mesh refinement. The shell model, however, showed a slight increase in stresses and it can be inte rpreted that the stresses in this case are stress concentrations arising as a result of modeling error. Singularities do not affect the stresses in the beam. In both cases stresses in truss tend to converge with mesh refinement. However, the stresses are much lower for the beam model. It can be concluded that the force and moments exerted by the face sheet on the tr uss are not accurate in the case of beam model. This is an additional inaccuracy in the beam model, apart from the stress singularities. PAGE 101 101 A B C D Figure 5-9. Stress singularity at beam-plate junction points. A) Full FE model showing stress singularity points at various junction points. B)Â–D) A patch of the top face sheet at the junction point closest to the panel corn er shown for increasing mesh refinements. The von Mises stresses (listed below the patche s) in the top face sheet at the junction node are listed as Â‘TFSÂ’ and the web stresses are listed as Â‘BeamÂ’. In order to study the actual stresses in the truss-core ITPS model, the entire panel was modeled with shell elements as shown in Figur e 5-11. Such a model is difficult to implement with the ITPS Optimizer because each model anal ysis is very time consuming. The stresses in the trusses, Figure 5-11C, were found to be over 1 GPa. Increasi ng the stiffness of the trusses by increasing the wall thickness of th e trusses leads to higher stre ss concentrations in the face sheets. TFS: 1.55 GPa Beam: 0.753 GPa TFS: 2.71 GPa B ea m: 0 . 6 71 G P a TFS: 5.32 GPa Beam: 0.590 GPa PAGE 102 102 A B Figure 5-10. FE experiment to compare beam m odel to a more realistic shell model. A) The trusses are modeled with the beam element. B) Trusses are modeled as the shell element. In both cases the truss section is a pipe cross-section. The arrows show the load. The bottom face sheet is comp letely restrained on the edges. Table 5-9. Table comparing stresses in beam m odel and shell model. All stresses are listed in MPa. Mesh1 is the coarsest and the refineme nt increases with Meshes 2, 3 and 4, with the element size being half of the pr evious mesh at each refinement. Top face sheet Web Beam modelShell modelBeam modelShell model Mesh 1 386.9 306.8 55.3 301.4 Mesh 2 837.4 320.9 56.34 337.4 Mesh 3 1650 358.3 57.05 378.2 Mesh 4 3114 384.4 57.59 385.3 The results presented in this section provide insight into the behavior of truss-core structures subjected to typical ITPS loads. Feas ible light weight designs could not be obtained with the truss-cores. Therefore, this line of design improvement was not considered further in the design process. It should be note d, however, that a suitable geom etric rearrangement of the trusscores could possibly lead to better desi gns and should be explored in future. PAGE 103 103 A B C Figure 5-11. Truss-core model with only shell elements. A) Entire FE model is shown with deformation due to temperature load. B) Cl ose-up of the corner junction points where stresses are maximum. C) Only the tr usses are shown to illustrate the stress distribution. PAGE 104 104 CHAPTER 6 EFFECT OF INPUT PARAMETERS ON THE ITPS DESIGN In Chapter 5, the ITPS designs for corrugatedcore structures were presented. The various input parameters used for these design were appr oximate in nature. Some of the reasons for using approximate values were the lack of availability of the exact data, diffi culties in modeling and analysis, and lack of clear understa nding of the expected capabiliti es of the ITPS. It should also be mentioned that these designs do not constitu te a final design for an ITPS structure. Many other issues like joining of dissimilar materials and manner of attachment of the ITPS panels to the vehicle are beyond the scope of this research work. In this chapter, many of these input paramete rs are varied and the resulting effects on the ITPS designs are studied. The para meters that are varied are: Heat transfer parameters Emissivity of top face sheet Heat loss from bottom face sheet Initial temperature of the structure (p rior to beginning of reentry phase) Coefficient of convection on top face sheet after landing. Loads and boundary conditions Pressure load on top face sheet In-plane load on bottom face sheet Boundary conditions on the ITPS panel The heat transfer parameters were mostly assu med values and, therefore, it is necessary to verify whether or not these values have a huge impact on the ITPS design. The loads and boundary conditions were studied because the IT PS design will be significantly influenced by the type of vehicle, the magnitude of the load s (which are generally different for different PAGE 105 105 positions on the vehicle), and manner in which the panels are attached to the vehicle (which determine the boundary conditions on the panel). Apart from providing an insight into the significance of the assumptions of input parameters, this study will also help formulate a set of guidelines for ITPS design. For example, the studies on the effects of material properties will help in material selection for ITPS panels. Effect of initial temperature on structure can help determine whether it is beneficial to alter the reentry trajectory to Â“pre-heatÂ” the vehicle before the actual reentry. 6.1 Sensitivity of ITPS Designs to Heat Transfer Parameters 6.1.1 Changing the Emissivity of the Top Surface of ITPS The emissivity of the top surface determines the temperature of the top face sheet and the heat radiated out by the ITPS. Thus, it determin es the amount of heat allowed into the ITPS. While a high emissivity increases the peak temper ature of the top face sheet, it also benefits in decreasing the amount of heat entering the ITPS. Table 6-1. Table showing the change in ITPS desi gn due to decrease in emissivity value to 0.7. The values in parentheses in the row head ed by Â“MassÂ” are the percentage difference in the ITPS mass when compared to the baseline designs (Table 5-7). Design I Design IIDesign IIIDesign IV Range of design variables Mass (lb/ft2) 3.796 (+5.1%) 4.544 (+4.7%) 5.297 (+4.5%) 6.047 (+4.4%) 1.2Â–1.6 mm tT (mm) 1.2 1.2 1.2 1.2 2Â–8 mm tB (mm) 3.322 3.852 4.38 4.91 1.2Â–2 mm tW (mm) 1.2 1.2 1.2 1.2 80Â°Â–100Â° (deg) 88.4 89.27 89.77 90.04 80Â–120 mm h (mm) 86.6 88.7 89.85 90.16 450Â–900 mm L ( mm) 751.6 777.7 797.2 810.7 4Â–10 n 4 6 8 10 The optimization procedure (Section 5.2.4) was carried out for the ITPS by reducing the emissivity from 0.8 to 0.7. The change in heat flux, entering the ITPS through the top surface, due to the two different emissivity values is illustrated in Figure 6-1. Compare this to the PAGE 106 106 maximum heat flux input on the ITPS, which is 34069 W/m2. The amount of heat entering the ITPS is only a small fraction of the total heat flux input. This demonstrates the effectiveness of the top face sheet acting as a hot structure (Section 2.1). Although, th e curves show a very slight difference in total integrated heat, the peak va lues show a difference of about 25%. The change in ITPS designs are presented in Table 6-1. Th e ITPS mass increases by about 5% compared to baseline designs. It can be conc luded that emissivity has a marg inal impact on the ITPS design and a small difference in the choice of the emissi vity values does not throw off the optimized designs by much. Another important point to observe is that the change in design variables is reflected only in the bott om face sheet thickness (tB), which increases by approximately 15%. This shows that the bottom face sheet acts as the most effective heat sink among all the sections in the ITPS. 6.1.2 Allowing Heat Loss from the Bottom Face Sheet In the baseline designs, the bottom face sheet wa s assumed to be perfectly insulated. This is a conservative approach as far the peak botto m face sheet temperature constraint is concerned. In reality, the bottom face sheet loses heat to the in terior of the vehicle in the form of radiation to the surroundings and conduction thro ugh the attachment points. In or der to simulate the heat loss from the bottom face sheet, an emissivity of 0.2 was prescribed to the bottom surface. With this emissivity value, the peak heat flux from the bottom face sheet was equal to 418 W/m2 compared to peak heat flux value of 9,000 W/m2 (Figure 6-1) entering the top surface of the ITPS. The amount of heat loss is very small compared to the heat entering the ITPS. The heat entering top surface was same in both cases with the differenc e being less than 1% during the reentry phase. Even this slight difference leads to 7Â–10% decr ease in the optimized ITPS mass, as shown in Table 6-2. The only major change in the variab les is the reduction of the bottom face sheet PAGE 107 107 thickness. Thus, it can be concluded that the heat loss from the bottom face sheet plays a significant role in determining the optimized mass of the ITPS. -6000 -4000 -2000 0 2000 4000 6000 8000 10000 0100020003000400050006000Reentry Time (sec)Heat Flux (W/m2)-20 -10 0 10 20 30 40% Difference Emissivity = 0.8 Emissivity = 0.7 % difference Figure 6-1. Heat flux entering the ITPS through the top surface for two different emissivity values imposed on Design I of Table 57. The dotted line shows the percentage difference between the two by comparing it w ith the average heat flux load. Positive value of heat flux imply heat entering th e ITPS and negative values imply heat exiting the ITPS. 6.1.3 Increasing the initial te mperature of the structure The initial temperature of the structure was increased to 395 K. Initial temperature in the baseline model was 295 K. This resulted in an increase in the ITPS mass by 17 to 27%, as shown in Table 6-3. This increase is due to the reduc tion in the thermal capacity of the structure as a result of increase in initial temperature. In the case of the designs in which all the edges of the bottom face sheet were simply supported (Section 5.2.2 and 5.2.3), the bottom face shee t stress constraint had a major impact on PAGE 108 108 the ITPS design. The bottom face sheet stresse s were largest at the reentry time ( tmax T) when the temperature gradient in the panel was the highes t (details in Section 5.2.2 and 5.2.3). In this case, an increase in the initial temperat ure of the structure results in a decrease in the magnitude of the temperature gradient. Thus, the stresses in the bottom face sheet decrease. As a result, the ITPS weight reduces considerably. This is an illustration of the im pact of boundary conditions on the ITPS design. In ITPS designs where stress cons traints are not active, the ITPS mass increases with increase in initial temperature of the stru cture, whereas in the case of the designs where stresses created due to the temperature gradient have an influence over the ITPS design, the ITPS mass decreases with increase in initial temperature. Table 6-2. Table showing the change in ITPS de sign due to loss of heat from the bottom face sheet corresponding to a bottom face sheet emissivity value of 0.2. The values in parentheses in the row headed by Â“MassÂ” ar e the percentage difference in the ITPS mass when compared to the baseline designs (Table 5-7). Design I Design IIDesign IIIDesign IV Range of design variables Mass (lb/ft2) 3.233 (-10.5%) 3.917 (-9.8%) 4.660 (-8.1%) 5.398 (-6.8%) 1.2Â–1.6 mm tT (mm) 1.2 1.2 1.2 1.2 2Â–8 mm tB (mm) 2.0 2.22 2.71 3.18 1.2Â–2 mm tW (mm) 1.2 1.2 1.2 1.2 80Â°Â–100Â° (deg) 90.51 89.42 89.82 90.06 80Â–120 mm h (mm) 82.75 89.71 91.61 92.6 450Â–900 mm L ( mm) 755.8 800.8 823.83 840.68 4Â–10 n 4 6 8 10 Table 6-3. ITPS designs with increase in initial temperature to 395 K. Initi al temperature in the baseline model was 295 K. Design I Design IIDesign IIIDesign IV Range of design variables Mass (lb/ft2) 4.208 (+27.5%) 5.152 (+18.7%) 6.117 (+17.1%) 6.904 (+19.2%) 1.2Â–1.6 mm tT (mm) 1.2 1.2 1.2 1.2 2Â–8 mm tB (mm) 3.5 6.26 7.46 5.71 1.2Â–2 mm tW (mm) 1.2 1.2 1.2 1.2 80Â°Â–100Â° (deg) 88.66 87.8 89.0 88.42 80Â–120 mm h (mm) 120 86.1 88.14 116.84 450Â–900 mm L ( mm) 883.8 900.0 900.0 900.0 4Â–10 n 4 6 8 10 PAGE 109 109 6.2 Sensitivity of ITPS Designs to Loads and Boundary Conditions 6.2.1 Effect of Boundary Conditions The effect of boundary conditions can be understood by comparing the ITPS designs in Tables 5-6 and 5-7. For designs in Table 5-6, simply supported boundary conditions were imposed on the bottom face sheet ed ges on all four sides of the pa nel. For designs in Table 5-7, the boundary conditions were relaxed by removi ng the simply supported boundary conditions on the edges that are parallel to the webs. The reduction in ITPS weight due to relaxation of the boundary conditions was of the order of 25Â–48%. The major reason for this reduction in weight is due to the decrease in stresses in the bo ttom face sheet. In the relaxed boundary conditions designs, stress constraints were not active. Th erefore, the bottom face sheet thickness was reduced significantly. Other advantages of relaxi ng the boundary conditions ar e that the length of the panels is significantly higher and the panel height is also re duced considerably. Relaxation of constraints on the bottom face sheet leads to redu ction in stresses in a ll sections of the ITPS panel. Thus, it can be concluded that the boundary conditions play a major role in influencing the ITPS design. 6.2.2 Increasing the Pressure Load on the Top Surface The pressure load on the top face sheet was doubled to 2 atmospheres (202,650 Pa). The changes in ITPS designs are presented in Table 6-4. There was a marginal increase of 1 to 5% in the ITPS mass. Higher pressure may cause great er increase in ITPS mass. However, for the spacecraft surfaces that are not stagnant regions like nose cone or wing leading edges on the Space Shuttle, the pressures experienced on the t op surface are typically less than 1 atmosphere. Therefore, the corrugated-core ITPS structures can withstand these lo ads with a sufficient margin. PAGE 110 110 Table 6-4. ITPS designs with incr ease in pressure load to 2 atmo spheres. Pressure load in the baseline model was 1 atmosphere. Design I Design IIDesign IIIDesign IV Range of design variables Mass (lb/ft2) 3.805 (+5.3%) 4.43 (+2.0%) 5.145 (+1.5%) 5.86 (+1.2%) 1.2Â–1.6 mm tT (mm) 1.2 1.2 1.2 1.2 2Â–8 mm tB (mm) 3.43 3.96 4.47 4.96 1.2Â–2 mm tW (mm) 1.2 1.2 1.2 1.2 80Â°Â–100Â° (deg) 88.9 89.5 89.9 90.1 80Â–120 mm h (mm) 80.49 80.9 82.7 83.6 450Â–900 mm L ( mm) 700.3 765.1 786.5 802.3 4Â–10 n 4 6 8 10 6.2.3 Increasing the In-Plane Load The in-plane load was increased from 30,000 N/m in the baseline models to 150,000 N/m. While the baseline load is a typical load fo r the backshell of a space capsule, 150,000 N/m is a typical load experienced by the mi d-section of the Space Shuttle. The increase in the ITPS mass is negligible. A large portion of the in-plane load is borne by the bottom face sheet. Even the bottom face sheet is a long plate; the webs attached to it act as stiffeners and prevent it from buckling. Thus, the corrugated-core ITPS structure is able to withstand significantly large inplane loads without any in crease in the ITPS mass. Table 6-5. ITPS designs with increase in in-pla ne load to 150,000 N/m. In-plane load in the baseline model was 30,000 N/m. Design I Design IIDesign IIIDesign IV Range of design variables Mass (lb/ft2) 3.631 (+0.5%) 4.366 (+0.6%) 5.099 (+0.6%) 5.826 (+0.6%) 1.2Â–1.6 mm tT (mm) 1.2 1.2 1.2 1.2 2Â–8 mm tB (mm) 2.89 3.41 3.91 4.38 1.2Â–2 mm tW (mm) 1.2 1.2 1.2 1.2 80Â°Â–100Â° (deg) 88.5 89.35 89.8 90.1 80Â–120 mm h (mm) 87.4 89.2 90.3 90.8 450Â–900 mm L ( mm) 763.9 789.9 809.9 824.7 4Â–10 n 4 6 8 10 PAGE 111 111 CHAPTER 7 CONCLUSIONS AND FUTURE WORK 7.1 Conclusions The weight of optimized ITPS designs (present ed in Chapter 6) ranged from 3.5 to 5 lb/ft2. Typical weights of ARMOR TPS (developed fo r VentureStar) ranged between 2 to 3 lb/ft2. Taking into account the capability of the ITPS to withstand substantially higher loads as compared to ARMOR TPS, the ITPS weight can be considered to be reasonably good. As mentioned earlier, the aim of this design is not to design the IT PS for any particular vehicle, but to study the feasibility of the ITPS concept. Therefore, the characteristics that influence ITPS design are of major interest and th e conclusions drawn from the results presented in Chapters 5 and 6 are outlined here. Some gene ral conclusions drawn from this research work are listed below. 1. Designs with a small number of strong supports (corrugated-cores) are more suitable for ITPS applications when compared to de signs with large number of weak supports (trusscores). 2. The most severe load influencing the ITPS design is the large thermal gradient through the thickness of the ITPS panel . Any future designs should focus on geometries that take this thermal gradient into account be fore considering other loads. 3. Emissivity of the top face sheet has a moderate impact on the ITPS weight . Considering that emissivity of a surface falls under the purview of manufacturing, not much can be done to improve the emissivity value through the design process. However, keeping the value as high as possible always helps in re ducing the heat coming in and reduces the ITPS weight. 4. Bottom face sheet is the most efficient heat sink of all the sections in the ITPS panel . The optimizer tends to increase the heat capaci ty of the structure by first increasing the thickness of the bottom face sh eet. If this thickness reaches the upper bound, then the optimizer increases the thickness of the ITPS pa nel, which increases the insulation capacity of the panel along with the heat capacity. Th e bottom face sheet is usually made of low density, high heat capacity materials like Aluminum and Beryllium and that is one of the major reasons why the optimizer prefers to increase the bottom face sheet thickness first before increasing the height of the panel. PAGE 112 112 5. Since bottom face sheet is typical ly the thickest section of the ITPS, a designer should take care so that majority of the loads are borne by the bottom face sheet. One of the examples for this research work is the manner in wh ich in-plane loads we re imposed only on the bottom face sheet. 6. Even a relatively small heat loss from the bottom face sheet can lead to a significant weight reduction in the ITPS . While assumption of perfectly insulated boundary condition leads to a conservative design, one must guard against excess conserva tism. It is difficult to estimate the exact amount of heat lost fr om the bottom face sheet as it depends on the vehicle architecture and could be different at differe nt regions even on the same vehicle. Although it is preferred to be conservative in th e generic designs of an ITPS, final designs should definitely take the heat loss into consideration as it could lead to considerable savings in launch weight. 7. Boundary conditions exert the most signi ficant influence on the ITPS design . Tighter constraints can render the panel too heavy or in some cases th e design may not be feasible. Boundary conditions are dependent on the manner in which the ITPS panels are attached to the frame of the vehicle. During the prelimin ary design process and when the exact vehicle configuration is not availabl e, it is difficult to obtain the correct boundary conditions. Therefore, the design process should be carri ed out with different boundary conditions to obtain a set of generic desi gns that can later be narrowed down when the vehicle specifications become clearer. 8. Increase in pressure load by 2 times and in -plane load by 5 times lead to a marginal increase in ITPS mass. The corrugated-core st ructures possess a s ound inherent design to withstand these loads. Conclusions for truss-core stru ctures for ITPS applications: 9. Truss-cores produce large stress concentrations at the junctio n points between the trusses and face sheets. Stress concentrations in the tr uss-core design could be a result of modeling error. In reality the area of c ontact between the truss and face sheets is much larger and this would lead to lower stresses. It is necessary to explore methods to reduce the magnitude of the stresses so as to eliminate the modeling error. 10. The trusses in truss-core designs considered in this research were too weak to withstand the forces produced as a result of large ther mal gradients in the structure. If the trusses were to be made stiffer, then the stress concen trations at the truss-pl ate junctions increase significantly. 11. The trusses closer to the pane l edges experienced a disproport ionately high amount of load when compared to the trusses close to the cente r of the panel. Other truss-core geometries (arrangement of trusses with respect to the face sheet) need to be explored so as to distribute the loads more evenly among the trusses. PAGE 113 113 Some material trade-off studies for corruga ted-core ITPS were car ried out during the preliminary stages of the ITPS design process. Th e results were not presented in the dissertation because the input parameters for the designs we re altered significantly as the design process evolved. In the light of these di fferent input parameters the resu lts of older designs would not appear coherent. A companion study [62] used the code developed for this research work to carry out a more meaningful material trade-off study. However, this study did not take the deflection and stress constraints into consid eration for the optimization pro cess. Some of the conclusions that can be drawn from these combined studies are presented below. 12. Beryllium alloys are superior to Aluminum all oys in all aspects. Use of Beryllium alloys also facilitates in designing a much lighter ITPS. Therefore, in sp ite of the toxicity concerns of Beryllium, it is worthwhile to use Beryllium alloys in the ITPS designs. 13. Titanium alloys have excellent high temperat ure properties and are suitable for top face sheet and web material. However, the service te mperature of these alloys limits their use to low heat flux regions. 14. Inconel alloys, with a higher se rvice temperature than titani um alloys, allow ITPS design for higher heat flux. However, high density of inconel leads to prohibitively high ITPS weight in corrugate d-core structures. 15. Ceramic matrix composites, for example Next el-718/Alumina Silicate, have many superior properties like low density, high service temper ature, stiffness comparable to aluminum, low thermal conductivity and low coefficient of thermal expansion. However, very low tensile strength of these materials is their Â“A chillesÂ’ heelÂ”. Otherwise, these materials are the most suitable for ITPS designs for top face sheet and web. 7.2 Future Work Now that a general framework for the ITPS design has been established with this research work, new structure geometries need to be expl ored. Corrugated-core st ructure design provides a lot of insight into the factors a ffecting typical ITPS designs. It is necessary to build on these to improve the structure geometry for a lighter ITPS. A drastic change like a transition to truss-core structures should be avoided. Inst ead, the active constr aints in the corrugated-core designs should be studied and step-wise changes in geometry should be implemented. PAGE 114 114 The excessive thermal deflection of the webs, due to thermal gradients, causes large stresses in the webs and bottom face sheet. A classi c technique to relieve thermal stresses is to provide local provisions for expans ion of the structure so as not to accumulate high stresses. One of the changes that need to be immediately explor ed is to divide each web in the length-direction. If the web in Figure 5-6 were to be split into tw o parts along the centerline (dotted line in Figure 5-6), and a small gap provided between the two pa rtitions, then the thermal deflection can be cut into half. This will reduce the stresses consid erably while not adversely affecting the load carrying capacity of the panel. Buckling of the edges is another major f actor influencing the design. For example, buckling of the web-edges close to the panel ed ges is one of the first buckling modes. By tactically placing stiffeners in the webs and f ace sheets, such buckling modes can be prevented. Stiffeners do not add to the we ight or heat conduction path of the ITPS significantly, while drastically improving the buckling resistance of the structure. Th erefore, this line of design improvement has a potential for redu cing the ITPS weight considerably. Although truss-core geometries considered fo r this research did not yield a feasible structure, other geometries need to be explor ed that can distribute the thermal stresses more evenly over all the trusses. In th e truss-cores used for this resear ch, the trusses close to the panel edges experienced large loads due to the top face sheet expansion, while the trusses close to the center of the panel experienced ve ry small loads. One of the sugge stions to improve this design is to arrange all the trusses so that they tilt towa rds the center point of the panel. This will impart more loads to the interior trusses. Stress concentr ation in the top face shee t will still be a problem in these structures. Ther e is a need to device a method to ove rcome the stress concentrations that arise as a result of FE modeling. In practice, these stresses will be much lower due to the manner PAGE 115 115 in which the trusses are attached to the face sheets. A method to overcome the stress singularities in the beam-plate models for truss-core structures can help reduce the cost of FE calculations to a large extent. In this research work, heat flux loads for a Space Shuttle-like vehi cle were considered. Most future space vehicles are likely to be spac e capsules like Apollo. The heat loads for space capsules are many times higher than the loads on th e Shuttle. As of now there are no materials that have service temperature to withstand these loads. Therefore, ablative materials have to be used to provide thermal protecti on. It would be very interesting to combine the ablative materials with ITPS structures so that th e ablative material thickness cont rols the amount of heat flowing into the structure. The number of FE experiments carried out to obtain the response surface approximations was manageable for the corrugated-core design. However, as the design gets complicated, the number of design variable will increase. Therefore, methods to reduce the number of FE analyses need to be explored in future. One of the s uggestions is to couple approximate analytical formulas with the accurate FE analysis to carry out a multi-fidelity optimization procedure. PAGE 116 116 APPENDIX A MATERIAL PROPERTIES USED FOR THE RESEARCH WORK Material Properties for Titanium Alloy: Ti-6Al-4V Density: 4429 kg/m3 PoissonÂ’s Ratio: 0.31 Table A-1. Temperature dependent material prop erties of Ti-6Al-4V. Thermal Conductivity (W/m/K) Temperature (K) Specific heat (J/kg/K) Temperature (K) CTE (K-1) Temperature (K) 1.545 24.00 562.706 277.83 6.22E-06 17.06 5.002 147.44 547.215 362.44 7.82E-06 105.67 7.011 272.28 594.107 531.67 8.58E-06 248.36 7.551 356.83 625.508 613.56 9.12E-06 411.78 8.221 435.89 703.801 784.11 9.57E-06 569.61 9.992 563.56 751.112 871.33 1.01E-05 759.44 10.857 623.17 798.423 950.78 1.03E-05 956.33 12.477 741.17 866.249 1030.78 1.03E-05 1041.89 13.846 866.33 908.117 1094.67 1.03E-05 1137.44 14.365 921.89 944.961 1143.56 YoungÂ’s Modulus (GPa) Temperature (K) Yield Stress (MPa) Temperature (K) 1.29E+11 19.83 1.61E+0927.17 1.14E+11 172.00 1.28E+09118.44 1.13E+11 229.49 1.19E+09149.72 1.10E+11 288.47 1.10E+09178.67 1.07E+11 338.61 1.03E+09210.91 1.03E+11 390.22 9.53E+08253.23 9.53E+10 497.83 8.11E+08349.00 9.19E+10 552.44 7.54E+08386.78 8.83E+10 602.56 6.90E+08428.00 8.20E+10 695.44 5.87E+08518.17 7.81E+10 735.28 5.57E+08574.94 7.24E+10 766.22 5.38E+08638.44 6.458E+10 791.28 5.13E+08693.00 5.676E+10 810.50 4.81E+08745.33 4.964E+10 866.33 3.96E+08806.56 4.413E+10 921.89 3.861E+10 977.44 PAGE 117 117 Material Properties for In conel Alloy: Inconel-718 Density: 8221 kg/m3. Table A-2. Temperature dependent material prop erties of Inconel-718. Thermal Conductivity (W/m/K) Temperature (K) Specific heat (J/kg/K) Temperature (K) CTE (K-1) Temperature (K) 11.032 261.36 386.36 205.45 8.92E-06 33.33 12.070 329.61 403.02 263.89 9.89E-06 91.72 12.967 394.56 419.52 321.28 1.07E-05 145.72 13.967 461.78 437.94 386.39 1.13E-05 190.83 15.040 537.78 460.97 448.17 1.19E-05 245.93 16.075 603.78 479.81 513.22 1.24E-05 328.56 16.937 666.56 500.32 582.67 1.29E-05 391.33 17.948 739.33 521.26 653.33 1.32E-05 458.39 18.761 794.39 541.77 718.39 1.37E-05 548.78 19.592 849.67 560.61 784.56 1.39E-05 627.00 20.354 903.56 581.13 851.89 1.42E-05 717.28 21.184 960.78 599.97 918.00 1.44E-05 800.94 22.153 1026.89 624.67 996.33 1.47E-05 883.56 22.915 1080.78 647.70 1062.44 1.52E-05 976.33 23.884 1143.56 670.31 1146.33 1.58E-05 1048.56 1.68E-05 1132.44 YoungÂ’s Modulus (GPa) Temperature (K) PoissonÂ’s Ratio Temperature (K) Yield Stress (MPa) Temperature (K) 2.12E+11 89.61 0.255 91.78 1.24E+09 35.50 2.07E+11 197.39 0.276 161.89 1.20E+09 80.44 2.03E+11 281.77 0.287 250.19 1.16E+09 127.17 1.99E+11 383.22 0.290 340.17 1.11E+09 182.83 1.94E+11 483.28 0.287 452.83 1.06E+09 254.08 1.89E+11 570.72 0.282 559.50 1.01E+09 351.94 1.83E+11 667.50 0.279 655.44 9.76E+08 469.94 1.77E+11 761.28 0.280 759.17 9.59E+08 596.83 1.72E+11 847.44 0.286 873.56 9.36E+08 728.11 1.63E+11 940.78 0.297 986.33 8.98E+08 855.22 1.56E+11 1026.89 0.312 1073.00 8.43E+08 917.44 1.47E+11 1098.56 0.330 1161.33 7.67E+08 959.67 1.38E+11 1169.11 0.352 1241.89 6.85E+08 988.56 1.24E+11 1248.56 0.377 1312.44 6.11E+08 1013.00 1.12E+11 1314.11 0.406 1364.11 5.31E+08 1035.22 9.93E+10 1364.11 4.55E+08 1057.44 PAGE 118 118 Material Properties for Beryllium Alloy Density: 1855 kg/m3 PoissonÂ’s ratio: 0.063 Table A-3. Temperature dependent mate rial properties of Beryllium alloy. Thermal Conductivity (W/m/K) Temperature (K) Specific heat (J/kg/K) Temperature (K) CTE (K-1) Temperature (K) 180.618 279.18 1775.622258.3461 1.11E-05 265.02 174.050 299.17 2025.574343.9444 1.14E-05 295.41 160.648 365.22 2160.389392.2222 1.22E-05 366.00 137.527 493.67 2565.671583.2222 1.36E-05 529.83 127.764 571.67 2740.679717.1111 1.4E-05 581.22 118.001 661.11 2838.650795.7778 1.45E-05 688.00 109.480 754.56 2990.631953 1.48E-05 733.72 102.158 840.22 3054.6891029.667 1.53E-05 840.78 94.880 933.56 3159.3591165.222 1.55E-05 884.11 88.756 1026.89 3206.6701216.889 1.57E-05 966.33 85.117 1112.44 3324.7381345.778 1.58E-05 1015.78 79.037 1206.33 3382.0971399.111 1.6E-05 1090.22 75.354 1319.11 3486.7671490.222 1.61E-05 1137.44 71.715 1400.78 3533.6591534.667 1.63E-05 1198.56 69.274 1474.67 3628.2811622.444 YoungÂ’s Modulus (GPa) Temperature (K) Yield Stress (MPa) Temperature (K) 2.93E+11 255.78 3.44E+08 256.90 2.91E+11 282.86 3.45E+08 280.33 2.89E+11 371.11 3.32E+08 334.89 2.86E+11 420.61 3.20E+08 371.50 2.79E+11 520.50 2.98E+08 455.67 2.73E+11 570.00 2.83E+08 508.67 2.52E+11 686.94 2.46E+08 624.83 2.32E+11 762.78 2.10E+08 708.22 2.22E+11 797.61 1.93E+08 740.94 1.87E+11 871.89 1.56E+08 806.39 1.71E+11 899.11 1.38E+08 834.67 1.38E+11 954.11 1.06E+08 883.00 1.19E+11 981.89 9.01E+07 908.00 8.54E+10 1028.00 5.66E+07 959.11 7.19E+10 1049.11 4.35E+07 988.00 PAGE 119 119 Material Properties for SAFFILÂ® at a pressure of 1 atmosphere. Density: 24 kg/m3 Table A-4. Temperature dependent material properties of SAFFILÂ®. Thermal Conductivity (W/m/K) Temperature (K) Specific heat (J/kg/K) Temperature (K) 0.02669 252.78 686.64 252.78 0.02916 272.78 724.32 272.78 0.04359 372.78 950.40 372.78 0.06251 472.78 1021.58 472.78 0.08673 572.78 1092.75 572.78 0.11739 672.78 1138.81 672.78 0.15402 772.78 1172.30 772.78 0.19813 872.78 1197.42 872.78 0.24972 972.78 1222.55 972.78 0.30879 1072.78 1239.29 1072.78 0.37683 1172.78 1251.85 1172.78 0.45309 1272.78 1260.23 1272.78 0.53833 1372.78 1268.60 1372.78 0.63254 1472.78 1272.79 1472.78 PAGE 120 120 LIST OF REFERENCES 1. Futron Corporation, Â“Space Transportation Cost s: Trends in Price Per to Orbit 1990 Â– 2000,Â” White Paper , September 6, 2002. ( http://www.google.com/search?q=cache:Y_XJTWtXy0J:www.futron.com/pdf/FutronLaunchCostWP. pdf+cost+of+payloa d&hl=en&gl=us&ct=c lnk&cd=5&client=firefox-a . Last accessed on Decemeber 25, 2006). 2. 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PAGE 126 126 BIOGRAPHICAL SKETCH Satish Bapanapalli was born on January 1, 1980, in Hyderabad, the capital city of the state of Andhra Pradesh, India. He grew up in H yderabad, where he subsequently received his Bachelor of Technology degree in Mechanical Engineering from the JNTU College of Engineering in June 2001. He came to the United States in August of 2001 and received a Master of Science degree in Mechanic al Engineering from the Washi ngton State University, Pullman, WA, in August 2003. His MS thesis involved pred iction of manufacturinginduced distortion in advanced fiber-reinforced polymer composites. He joined the PhD program at the University of Florida in August 2003. Initially he worked on a pr oject involving predicti on of microcracking in composite laminates. Subsequently, he work ed on his PhD dissertat ion involving Integral Thermal Protection Systems. While obtaining his PhD, he spent 4 months during the summer of 2006 as a PhD Intern at the Pacific Northwes t National Laboratory (P NNL), Richland, WA. After his PhD studies, Satish Bapanapalli joined PNNL as a Scientist and is working in inverse methods in hydroforming of metals and propert y prediction of injection-molded long fiber composites for automotive applications. |