Thermal Structures for Aerospace Applications

494 Pages·1996·21.91 MB·English

by  Earl A. Thornton

Purchased from American Institute of Aeronautics and Astronautics

Thermal Structures
for Aerospace
Applications
Earl A. Thornton
University of Virginia
Charlottesville, Virginia
1A1AA
EDUCATION SERIES
J. S. Przemieniecki
Series Editor-in-Chief
Air Force Institute of Technology
Wright-Patterson Air Force Base, Ohio
Published by
American Institute of Aeronautics and Astronautics, Inc.
1801 Alexander Bell Drive, Reston, Virginia 20191-4344
Purchased from American Institute of Aeronautics and Astronautics

American Institute of Aeronautics and Astronautics, Inc., Reston, Virginia
Library of Congress Cataloging-in-Publication Data
Thornton, Earl A. (Earl Arthur). 1936-
Thermal structures for aerospace applications/Earl A. Thornton.
p. cm. - (AIAA education series)
Includes bibliographical references and index.
1. Space vehicles - Thermodynamics. 2. Airframes - Design and
construction. 3. Thermal stresses. 4. Aerothermodynamics.
I. Title. II. Series.
TL800, T48 1996 629.47-dc20 96-30497
ISBN 1-56347-190-6
Copyright (c) 1996 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.
Printed in the United States. No part of this publication may be reproduced, distributed, or transmitted,
in any form or by any means, or stored in a database or retrieval system, without the prior written
permission of the publisher.
Data and information appearing in this book are for informational purposes only. AIAA is not responsi-
ble for any injury or damage resulting from use or reliance, nor does AIAA warrant that use or reliance
will be free from privately owned rights.
Purchased from American Institute of Aeronautics and Astronautics

Texts Published in the AIAA Education Series
Thermal Structures for Aerospace Applications
Earl A. Thornton, 1996
Structural Loads Analysis for Commercial Transport Aircraft:
Theory and Practice
Ted L. Lomax, 1996
Spacecraft Propulsion
Charles D. Brown, 1996
Helicopter Flight Dynamics: The Theory and Application of Flying Qualities and
Simulation Modeling
Gareth Padfield, 1996
Flying Qualities and Right Testing of the Airplane
Darrol Stinton, 1996
Flight Performance of Aircraft
S. K. Ojha, 1995
Operations Research Analysis in Quality Test and Evaluation
Donald L. Giadrosich, 1995
Radar and Laser Cross Section Engineering
David C.Jenn, 1995
Introduction to the Control of Dynamic Systems
Frederick O. Smetana, 1994
Tailless Aircraft in Theory and Practice
Karl Nickel and Michael Wohlfahrt, 1994
Mathematical Methods in Defense Analyses
Second Edition
J. S. Przemieniecki, 1994
Hypersonic Aerothermodynamics
John J. Bertin, 1994
Hypersonic Airbreathing Propulsion
William H. Heiser and David T. Pratt, 1994
Practical Intake Aerodynamic Design
E. L. Goldsmith and J. Seddon, Editors, 1993
Acquisition of Defense Systems
J. S. Przemieniecki, Editor, 1993
Dynamics of Atmospheric Re-Entry
Frank J. Regan and Satya M. Anandakrishnan, 1993
Introduction to Dynamics and Control of Flexible Structures
John L. Junkins and Youdan Kim, 1993
Spacecraft Mission Design
Charles D. Brown, 1992
Rotary Wing Structural Dynamics and Aeroelasticity
Richard L. Bielawa, 1992
Aircraft Design: A Conceptual Approach
Second Edition
Daniel P. Raymer, 1992
Optimization of Observation and Control Processes
Veniamin V. Malyshev, Mihkail N. Krasilshikov, and Valeri I. Karlov, 1992
Nonlinear Analysis of Shell Structures
Anthony N. Paiazotto and Scott T. Dennis, 1992
Orbital Mechanics
Vladimir A. Chobotov, 1991
Critical Technologies for National Defense
Air Force Institute of Technology, 1991
(Continued on next page)
Purchased from American Institute of Aeronautics and Astronautics

Texts Published in the AIAA Education Series (Continued)
Defense Analyses Software
J. S. Przemieniecki, 1991
Inlets for Supersonic Missiles
John J. Mahoney, 1991
Space Vehicle Design
Michael D. Griffin and James R. French, 1991
Introduction to Mathematical Methods in Defense Analyses
J. S. Przemieniecki, 1990
Basic Helicopter Aerodynamics
J. Seddon, 1990
Aircraft Propulsion Systems Technology and Design
Gordon C. Gates, Editor, 1989
Boundary Layers
A. D. Young, 1989
Aircraft Design: A Conceptual Approach
Daniel P. Raymer, 1989
Gust Loads on Aircraft: Concepts and Applications
Frederic M. Hoblit, 1988
Aircraft Landing Gear Design: Principles and Practices
Norman S. Currey, 1988
Mechanical Reliability: Theory, Models and Applications
B. S. Dhillon, 1988
Re-Entry Aerodynamics
Wilbur L. Hankey, 1988
Aerothermodynamics of Gas Turbine and Rocket Propulsion,
Revised and Enlarged
Gordon C. Gates, 1988
Advanced Classical Thermodynamics
George Emanuel, 1988
Radar Electronic Warfare
August Golden Jr., 1988
An Introduction to the Mathematics and Methods of Astrodynamics
Richard H. Battin, 1987
Aircraft Engine Design
Jack D. Mattingly, William H. Heiser, and Daniel H. Daley, 1987
Gasdynamics: Theory and Applications
George Emanuel, 1986
Composite Materials for Aircraft Structures
Brian C. Hoskins and Alan A. Baker, Editors, 1986
Intake Aerodynamics
J. Seddon and E. L. Goldsmith, 1985
Fundamentals of Aircraft Combat Survivability Analysis and Design Robert E. Ball, 1985
Aerothermodynamics of Aircraft Engine Components
Gordon C. Gates, Editor, 1985
Aerothermodynamics of Gas Turbine and Rocket Propulsion
Gordon C. Gates, 1984
Re-Entry Vehicle Dynamics
Frank J. Regan, 1984
Published by
American Institute of Aeronautics and Astronautics, Inc., Reston, Virginia
Purchased from American Institute of Aeronautics and Astronautics

Foreword
Aircraft structures designed for supersonic flight are subjected to aerodynamic
heating caused by the air in the boundary layer being progressively slowed down.
This process generates heat and consequently all external surfaces on the aircraft
are heated. This in turn leads to nonuniform transient temperatures that produce
thermal stresses and deformations. Likewise, spacecraft structures are subjected
to aerodynamic heating during launch and re-entry phases of their operations, in
addition to intensive solar radiation while operating in space.
The introduction of thermal effects into the theory of elasticity and structural
analysis dates back to the first half of the last century when the French scientist
J. M. C. Duhamel presented his papers on the generalization of the fir ^mental
theorems of elasticity to include thermal strains and stresses caused by n^_ ^i-
form temperature distribution in an elastic body. Since that time, technical literature
covered the subject very extensively, but only very few textbooks appeared on the
analysis and design of thermal structures. This recent addition to the AIAA Edu-
cation Series discusses specifically the thermal behavior of aerospace structures.
Thermal Structures for Aerospace Applications by Professor Earl A. Thornton is
an authoritative source on the subject of design and analysis of aerospace struc-
tures in a thermal environment. This new text allows the reader to develop a good
understanding of the physical behavior of thermal structures and to gain an appre-
ciation for the role of classical thermal and stress analyses for thermal structures.
In addition, the text discusses modern computational methods (e.g., finite element
thermal-structural analysis) which provide a better insight into the realistic behav-
ior of structural components or major structural assemblies subjected to thermal
loading.
The text provides not only the structural analysis for thermal structures but also
the accompanying thermal analysis, comprising aerodynamic heating and heat
transfer from and within the structure itself. Also, many specialized problems with
thermal aerospace structures are discussed, such as: thermally induced vibrations,
thermal buckling, and thermoviscoplasticity.
The AIAA Education Series embraces a broad spectrum of theory and applica-
tion of different disciplines in aeronautics and astronautics, including aerospace
design practice. The series also includes texts on defense science, engineering, and
technology. It serves as both teaching texts for students and reference materials
for practicing engineers and scientists. Thermal Structures for Aerospace Applica-
tions will be a valuable text for graduate level courses and aerospace design teams.
It complements several other texts on aircraft and spacecraft design previously
published in this series.
J. S. Przemieniecki
Editor-in-Chief
AIAA Education Series
Purchased from American Institute of Aeronautics and Astronautics

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Purchased from American Institute of Aeronautics and Astronautics

Table
of
Contents
Preface............................................................ xiii
Chapter 1. High-Speed Flight....................................... 1
1.1 Introduction.................................................... 1
1.2 Evolution of Thermal Structures.................................. 1
1.3 Aerodynamic Heating ........................................... 8
1.4 Aerothermal Load Effects on Flight Structures.................... 15
1.5 Design of Thermal Structures ................................... 18
1.6 Closing Remarks .............................................. 20
References.................................................... 20
Problems ..................................................... 23
Selected Bibliography: Supersonic Transports .................... 24
Chapter 2. Orbiting Space Structures .............................. 27
2.1 Introduction................................................... 27
2.2 Microwave Radiometer Spacecraft............................... 27
2.3 Environmental Heating......................................... 29
2.4 Thermal Behavior ............................................. 35
2.5 Structural Behavior ............................................ 37
2.6 Closing Remarks .............................................. 40
References.................................................... 41
Problems ..................................................... 42
Chapter 3. Concepts from Continuum Mechanics................... 45
3.1 Introduction................................................... 45
3.2 Continuum.................................................... 45
3.3 Stress Tensor.................................................. 45
3.4 Strain Tensor.................................................. 48
3.5 Conservation Equations ........................................ 48
3.6 Boundary and Initial Conditions................................. 54
3.7 Constitutive Relations .......................................... 55
3.8 Closing Remarks .............................................. 58
References.................................................... 59
Problems ..................................................... 59
Selected Bibliography: Hyperbolic Heat Conduction .............. 60
Chapter 4. Heat Transfer in Structures............................. 63
4.1 Introduction................................................... 63
ix
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4.2 Problem Formulation........................................... 63
4.3 Thermal Response with Infinite Thermal Conductivity ............. 65
4.4 Transient One-Dimensional Conduction Problems................. 69
4.5 Temperatures in Thin-Walled Structures.......................... 85
4.6 Computational Methods ........................................ 91
4.7 Temperatures in Aircraft Structures............................. 100
4.8 Thin-Walled Tube with Radiation .............................. 118
4.9 Convectively Cooled Structures ................................ 122
4.10 Closing Remarks ............................................. 130
References................................................... 131
Problems .................................................... 132
Selected Bibliography: Temperatures in Aircraft Structures ....... 138
Chapter 5. Thermoelasticity ...................................... 141
5.1 Introduction.................................................. 141
5.2 Thermoelasticity Formulations ................................. 141
5.3 Dynamic Response in Semi-infinite Solids ...................... 154
5.4 Fundamental Quasistatic Problems ............................. 164
5.5 Two-Dimensional Thermoelastic Problems ...................... 167
5.6 Torsion...................................................... 179
5.7 Closing Remarks ............................................. 182
References................................................... 182
Problems .................................................... 183
Chapter 6. Thermal Structures Problems: Rods and Beams ........ 187
6.1 Introduction.................................................. 187
6.2 Rods ........................................................ 187
6.3 Beams....................................................... 195
6.4 Beam Problems .............................................. 231
6.5 Closing Remarks ............................................. 246
References................................................... 246
Problems .................................................... 248
Chapter 7. Thermal Structures Problems: Plates................... 253
7.1 Introduction.................................................. 253
7.2 Small-Deflection Formulation.................................. 253
7.3 Large-Deflection Formulation.................................. 262
7.4 Plate Problems ............................................... 268
7.5 Closing Remarks ............................................. 280
References................................................... 280
Problems .................................................... 281
Chapter 8. Finite Element Thermal-Structural Analysis............ 285
8.1 Introduction.................................................. 285
8.2 Thermal Analysis............................................. 286
8.3 Structural Analysis ........................................... 305
8.4 Closing Remarks ............................................. 334
References................................................... 335
Problems .................................................... 336
Purchased from American Institute of Aeronautics and Astronautics

Chapter 9. Thermally Induced Vibrations......................... 343
9.1 Introduction.................................................. 343
9.2 Historical Review.............................................346
9.3 Uncoupled, Thermally Induced Flexural Vibrations .............. 355
9.4 Coupled, Thermally Induced Flexural Vibrations................. 360
9.5 Rubble Space Telescope Solar Arrays...........................369
9.6 Closing Remarks ............................................. 389
References................................................... 390
Problems .................................................... 394
Selected Bibliography: Effects of Temperature on Structural
Vibration Characteristics .................................. 395
Chapter 10. Thermal Buckling.................................... 397
10.1 Introduction..................................................397
10.2 Thermal Buckling of Beam Columns ........................... 398
10.3 Thermal Buckling of Plates .................................... 413
10.4 Thermal Buckling of Shells................................... .426
10.5 Closing Remarks ............................................. 435
References................................................... 435
Problems .................................................... 437
Chapter 11. Thermoviscoplasticity................................ 443
11.1 Introduction.................................................. 443
11.2 Unified Constitutive Models ................................... 444
11.3 Finite Element Analysis ....................................... 451
11.4 Applications ................................................. 455
11.5 Closing Remarks ............................................. 459
References................................................... 460
Problems .................................................... 461
Appendix: Finite Element Development of von Karman Plate
Equations....................................................... 463
Subject Index...................................................... 467
Index of Authors Cited............................................. 475