Boundary Element Techniques in Computer-Aided Engineering

441 Pages·1984·11.74 MB·English

by  C. Brebbia (auth.)

Boundary Element Techniques in Computer
Aided Engineering
NATO ASI Series
Advanced Science Institutes Series
A Series presenting the results of activities sponsored by the NATO Science
Committee, which aims at the dissemination of advanced scientific and technological
knowledge, with a view to strengthening links between scientific communities.
The Series is published by an international board of publishers in conjunction with the
NATO Scientific Affairs Division
A Life Sciences Plenum Publishing Corporation
B Physics London and New York
C Mathematical and D. Reidel Publishing Company
Physical Sciences Dordrecht and Boston
D Behavioural and Martinus Nijhoff Publishers
Social Sciences DordrechtiBoston/Lancaster
E Applied Sciences
F Computer and Springer-Verlag
Systems Sciences BerlinlHeidelberglNew York
G Ecological Sciences
Series E: Applied Sciences - No. 84
Boundary Element Techniques
in Computer-Aided Engineering
edited by
C.A. Brebbia
Institute for Computational Mechanics
Ashurst, Southampton S04 2AA
UK
1984 Martinus Nijhoff Publishers
Dordrecht / Boston / Lancaster
Published in co-operation with NATO Scientific Affairs Division
Proceedings of the NATO Advanced Study Institute on Boundary Elements in CAD,
Southampton, England, September 19-30, 1983
Library of Congress Cataloging in Publication Data
NATO Advanced Study Institute on Boundary Elements in
CAD (1983 : Southampton, Hampshire)
Boundary element techniques in computer aided
engineering.
(NATO advanced science lost i tutes series. Series E.
Applied sciences; 84)
"Proceedings of the NATO Advanced Study Institute on
Boundary Elements in CAD, Southampton, England,
September 19-30, 1983"--T .p. verso.
Includes bibliographies and index.
1. Boundary value problems--Data processing-
Congresses. 2. Engineering--Data processing--Congresses.
I. Brebbia, C. A. II. North Atlantic Treaty Organiza
tion. Scientific Affairs Division. III. Title.
IV. Series: NATO advanced institutes series. Series E,
Applied sciences; no. 84.
TA347.B69N37 1983 515.3'5'O~.854 84-16710
ISBN 90-247-3065-1
ISBN-13: 978-94-009-6194-4 e-ISBN-13: 978-94-009-6192-0
DOl: 10.1007/978-94-009-6192-0
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190 Old Derby Street, Hingham, MA 02043, USA
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publishers,
Martinus Nijhoff Publishers, P.O. Box 163, 3300 AD Dordrecht, The Netherlands
Copyright © 1984 by Martinus Nijhoff Publishers, Dordrecht
Softcover reprint of the hardcover 1s t edition 1984
TABLE OF CONTENTS
PREFACE XI
Chapter 1. Weighted Residual Formulation of AT-?l ')ximate Methods
by C.A. Brebbia Page 1
1.1. Introduction
1.2. Basic Definition
1.3. Approximate Solutions
1.4. Method of Weighted Residuals
1.5. Weak Formulations
1.6. The Inverse Problem
1.7. Conclusions
References
Chapter~ Boundary Element Methods
by J.J. Connor and C.A. Brebbia Page 23
2.1. Fundamentals of Functional Analysis
2.2. Generalized Green's Formula
2.3. Variational Formulation
2.4. Weighted Residual Scheme
2.5. Boundary Element Formulation of Poisson's Equation
2.6. Fundamental Solutions
2.7. Boundary Discretisation and Systems Equations
2.8. Computation of Integrals - 2D case
Bibliography
Chapter 3. Boundary Integral Equations
by M.A. Jaswon Page 57
3.1. Simple-layer Formulations
3.2. Double-layer Formulations
3.3. Direct Formulations
3.4. Indirect Vector Formulations
3.5. Direct Formulations
References
v
Chapter 4. Scalar and Vector Potential Theory
by M.A. Jaswon Page 71
4.1. The Simple-layer Potential
4.2. The Double-layer Potential
4.3. Green's Formula
4.4. Identification of Scalar and Vector Symbolism
4.5. Somig1iana's Identity
4.6. Rigid-body Displacement Field
References
Chapter 5. Potential Problems in Two Dimensions Page 85
by G.T. Symm
5.1. Introduction
5.2. Flow past an Obstacle
5.3. Discretisation
5.4. Green's Boundary Formula
5.5. Applications
5.6. Boundary Singularities
5.7. Composite Domains
5.8. Conclusion
References
Chapter 6. Three-dimensional Axisymmetrica1 Potential Problems
by G.T. Symm Page 101
6.1. Introduction
6.2. The Newtonian Potential
6.3. Discretisation
6.4. General Domain
6.5. Axisymmetric Problems
6.6. Conclusion
References
VI
Chapter 7. Heat Transfer Applications
by H.L.G. Pina Page III
7.1. Introduction
7.2. Integral Equations associated with Steady Heat
Conduction Problems
7.3. Nume.rical Solution of the Integral Equations
7.4. Poisson's Equation
7.5. Non-homogeneous Bodies; Method·of Subregions
7.6. Anisotropic Bodies
References
Chapter 8. Numerical Inteji!ration and other C2S!utational Technigues
by H.L.G. Pina Page 127
8.1. Introduction
8.2. Isoparametr1c Elements
8.3. Numerical Integration
References
Chapter 9. Startinji! to work with Boundar~ Elements
by G. Kuich Page 141
9.1. Introduction
9.2. The Boundary Element Method
9.3. Advantages and Disadvantages of the BEM compared
to FEM
9.4. Introduction to BEASY
9.5. Examples
9.6. Conclusions
References
Chapter 10. Experiences in Boundary Element Applications
by G. Kuich Page 159
10.1 Introduction
10.2. Pre- and Post Processing
10.3. C.A.D. Coupling
10.4. Installation on Different Computers
10.5. Recommendations for BEM use
VII
Chapter 11. Electrostatics Problems
by R. Adey Page 177
11.1. Introduction
11. 2. Theoretical Basis
U.3. Boundary Elements
11.4. Applications
U.S. Conclusions
References
Chapter 12. A Boundary Element Solution of the Wave Equation
by D.J. Danson Page 191
12.1. Introduction
12.2. Theoretical Development
12.3. Boundary Conditions
12.4. Numerical Implementation
12.5. Velocities and Pressures
12.6. Identification of Areas in Shadow
12.7. Test Example
12.8. Conclusions
References
Chapter 13. Elasticity Problems
by D.J. Danson Page 201
13.1. Introduction
13.2. Governing Equations
13.3. Boundary Integral Formulation
13.4. Two Dimensional Elasticity Problems
13.5. Three Dimensional Elasticity Problems
13.6. Axisymmetric Elasticity Problems
References
Appendix
Chapter 14. Elasticity Problems with Body Forces
by D.J. Danson Page 239
14.1. Introduction
14.2. Transformation to Boundary Integrals
14.3. 2D Body Forces
14.4. 3D Body Forces
14.5. Axisymmetric Body Forces
References
Appendix
VIII
ChaEter 15. Time DeEendent Problems
by C.A. Brebbia Page 261
l5.I. Introduction
15.2. Time Dependent Diffusion
15.3. The Scalar Wave Equation
15.4. Transient Elastodynamics
15.5. Mass Matrix Representation
15.6. Conclusions
References
ChaEter 16. Time DeEendent Potential Problems
by H. Pina Page 293
l6.I. Introduction
16.2. Integral Formulation of Heat Conduction Problems
16.3. Numerical Solution of the Integral Equations
16.4. Conclusions
References
Chapter 17. Plate Bending Problems Page 315
by M. Stern
17.I. Pre liminarie s
17.2. Reciprocal Work Relation
17 .3. Boundary Integral Representations
17.4. Concluding Remarks
References
Chapter 18. A Choice of Fundamental Solutions
by M. Stern Page 327
18.1. Introductory Remarks
18.2. A simple example: 2D Heat Conduction
18.3. A more significant example: Plane Elastostatics
18.4. Concluding Remarks
References
Chapter 19. Formulation for Cracks in Plate Bending
by M. Stern Page 345
19.1. Fundamental Solutions for Cracks
19.2. Augmented Boundary Integral Equations
19.3. Concluding Remarks
References
IX
Chapter 20. Fracture Mechanics Stress Analysis, I.
by C. Atkinson Page 355
20.1 Introduction
20.2. Stress Intensity Factors
20.3. Integral Equation Methods for Crack Tip
Stress Analysis
References
Chapter 21. Fracture Mechanics Stress Analysis, II
by C. Atkinson Page 377
21.1. Introduction
21.2. Invariant Integral based on the Energy
Momentum Tensor
21.3. Invariant Integrals deduced from Betti's
Reciprocal Theorem
21.4. Some Numerical Results for a Nocht Problem
21.5. A Problem of Debond Stress Analysis
References
Chapter 22. BEM in Geomechanics
by R. Butterfield Page 399
22.1. Introduction
22.2. Notation and some Basic Ideas
22.3. BEM applied to the Interaction between
Structures and the Supporting Ground
22.4. Inhomogeneity, Zoning and Layering
22.5. E1astop1asticity
22.6. Concluding Remarks
References
Chapter 23. An Asymptotic Error Analysis and Underlying Mathematical
Principles for Boundary Element Methods
by W.L. Wendland Page 417
23.1. Projection Methods and Garding's Inequality
23.2. Examples of Strongly Elliptic Boundary Integral
Equations
23.3. Asymptotic Convergence of Ga1erkin type Boundary
Element Methods
23.4. Asymptotic Convergence of Collocation Methods
References
Subject Index Page 437
x