Boundary Element Methods: Proceedings of the Third International Seminar, Irvine, California, July 1981

638 Pages·1981·15.004 MB·English

by  George T. Symm (auth.), Dr. Carlos A. Brebbia (eds.)

Boundary
Element Methods
Proceedings of the Third International Seminar,
Irvine, California, July 1981
Editor: C. A. Brebbia
Seminar sponsored by the International Society for Computational
Methods in Engineering
With 232 Figures
CML PUBLICATIONS
Springer-Verlag Berlin Heidelberg GmbH 1981
Dr. CARLOS A. BREBBIA
Computational Mechanical Centre
125 High Street
Southampton
England, SOl OAA
ISBN 978-3-662-11272-4 ISBN 978-3-662-11270-0 (eBook)
DOI 10.1007/978-3-662-11270-0
This work is subjekt to copyright. All rights are reserved, whether the whole or part of the material is oonoerned,
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© Springer-Verlag Berlin Heidelberg 1981
Originally published by Springer-Verlag Berlin Heidelberg New York in 1981
Softcover reprint of the hardcover I st edition 1981
The use of registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific
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neral use.
2061/3020 - 543210
v
CONTENTS
Introductory Remarks IX
C.A. Brebbia
SECTION I POTENTIAL AND FLUID FLOI-1 PROBLEMS
Two Methods for Computing the Capacitance of a 3
Quadrilateral
G.T. Symm
Boundary Element Solutions to the Eddy Current Problem 14
S.J. Salon, J.M. Sahneider and S. Uda
Numerical Solution of the Diffusion Equation by a 26
Potential Method
D.A.S. Curran, B.A. Lewis and M. Cross
The Application of Boundary Elements to Steady and 37
Unsteady Potential Fluid Flow Problems in Two and Three
Dimensions
P.H.L. Groenenboom
Computing Strategy in the Integral Equation Solution of 53
Limiting Gravity Waves in Water
J.M. Williams
SECTION II ELASTICITY PROBLEMS 69
On the Construction of the Boundary Integral 71
Representation and Connected Integral Equations for
Homogeneous Problems of Plane Linear Elastostatics
M. Pignole
Regular Boundary Integral Equations for Stress 85
Analysis
C. Patterson and M.A. Sheikh
A Boundary Element Formulation of Problems in Linear 105
Isotropic Elasticity with Body Forces
D.J. Danson
VI
A Comparative Study of Several Boundary Elements in 123
Elasticity
M.F. Seabra Pereira, C.A. Mota Soares and
L.M. Oliveira Faria
Non-Conforming Boundary Elements for Stress Analysis 137
C. Patterson and M.A. Sheikh
The Displacement Discontinuity Method in Three 153
Dimensions
W. Scott Dunbar and D.L. Anderson
A Unified Second Order Boundary Element Method for 174
Structures Analysis
M. Dubois
Method of Boundary Integral Equations for Analysis of 183
Three Dimensional Crack Problems
J. Balas and J. Sladek
Cyclic Symmetry and Sliding Between Structures by the 206
Boundary Integral Equation Method
A. Chaudouet
On Boundary Integral Equations for Circular 224
Cylindrical Shells
H. Antes
The Boundary Element Method applied to Two- 239
Dimensional Contact Problems with Friction
T. Andersson
Quasistatic Indentation of a Rubber covered Roll by a 259
Rigid Roll - The Boundary Element Solution
R.C. Batra
An Improved Boundary Element Method for Plate 272
Vibrations
G.K.K. Wong and J.R. Hutchinson
SECTION III GEOMECHANICS 291
Boundary Elements applied to Soil-Foundation 293
Interaction
M. Ottenstreuer and G. Schmid
The Implementation of Boundary Element Codes in 310
Geotechnical Engineering
L.A. Wood
Boundary Integral Method for Porous Media 325
M. Predeleanu
VII
SECTION IV MATERIAL PROBLEMS 335
Numerical Analysis of Cyclic Plasticity using the 337
Boundary Integral Equation Method
M. Brunet
New Developments in Elastoplastic Analysis 350
J.C.F. Telles and C.A. Brebbia
The Boundary Element Method for the Solution of 371
No-Tension Materials
W.S. Venturini and C. Brebbia
SECTION V NUMERICAL TECHNIQUES AND MATHEMATICAL 397
PRINCIPLES
Some Theoretical Aspects of Boundary Integral 399
Equations
M.A. Jaswon
On The Asymptotic Convergence of Boundary Integral 412
Methods
W.L. Wendland
Boundary Methods. C-Complete Systems for the 431
Biharmonic Equations
H. Gourgeon and I. Herrera
The Effect of Mesh Refinement in the Boundary Element 442
Solution of Laplace's Equation with Singularities
H.L.G. Pina, J.L.M. Fernandes and C.A. Brebbia
Boundary Element and Linear Programming Method in 457
Optimization of Partial Differential Equation
Systems
T. Futagami
Approximate Fundamental Solutions and Alternative 472
Formulations
S. Walker
An Efficient Algorithm for the Numerical Evaluation 489
of Boundary Integral Equations
M. Vahle and D.L. Sikarskie
Solution of the Dirichlet Problem using the Reduction 504
to Fredholm Integral Equations
J. Caldwell
BEMSTAT -A New Type of Boundary Element Program for 518
Two-Dimensional Elasticity Problems
L. Bolteus and 0. Tullberg
VIII
SECTION VI COUPLING OF BOUNDARY AND FINITE ELEMENT 539
METHODS
Interfacing Finite Element and Boundary Element 541
Discretizations
C.A. Felippa
The Derivation of Stiffness Matrices from Integral 552
Equations
F. Hartmann
Three Dimensional Super-Element by the Boundary 567
Integral Equation Method for Elastostatics
F. Volait
The Coupling of Boundary and Finite Element Methods 575
for Infinite Domain Problems in Elasto-Plasticity
G. Beer and J.L. Meek
A Finite Element - Boundary Integral Scheme to 592
Simulate Rock-Effects on the Liner of an Underground
Intersection
B.A. Dendrou and S.A. Dendrou
The Use of Green's Functions in the Numerical Analysis 609
of Potential, Elastic and Plate Bending Problems
C. Katz
IX
INTRODUCTORY REMARKS
C.A. Brebbia
I . HISTORICAL NOTE
The great interest that finite element methods have
attracted in the engineering community since the beginning of
1960's has had two important consequences. I) it stimulated
an impressive amount of work in computational techniques and
efficient engineering software; 2) substantial research into
basic physical principles such as variational techniques,
weighted residuals, etc. was originated.
The first of the above points came as a natural conse
quence of the emergence of new and powerful computers which
were able to solve engineering problems involving large
amounts of numerical storage and manipulation. The development
of mathematical techniques and basic principles came instead
in response to the need of extending finite element modelling,
assessing convergence and accuracy and understanding the
relationship of finite elements to more classical variational
principles and weighted residual techniques.
These techniques can be traced to pre-computer times [1 ,2]
and involve different ways of solving the governing equations
of a problem, i.e, Galerkin, collocation, least-squares, line
techniques, matrix progression or transfer, the combination of
different techniques, etc. Fortunately they were not forgotten
and they reappeared in the finite element literature, sometimes
with different names, such as Galerkin finite elements, finite
element strip-method, some time integration schemes, etc.
Another important development iu approximate analysis was the
investigation of mixed principles and the realization that
physical problems c&< be expressed and solved in many different
ways in accordance with the part or equations of the problem
that we need to approximate. These approximations are of
fundamental importance for the computer implementation of the
different numerical techniques. Mixed methods can be traced
to Reissner [3] and more specifically for finite elements to
X
Pian [4]. An excellent exposition of mixed methods in
structural mechanics can be found in the book by Washizu [s].
[ntegral equation techniques were until recently considered
to be a different type of analytical method, somewhat unrelated
to approximate methods. They became popular in Westem Ettrope
through the work of a series of Russian authors, such as
Muskhelishvili [6], Mikhlin [7], Kupradze [8], and Smi mov [9]
but were not very popular with engineers. A predecessor of
some of this work was Kellogg [10] who applied integral equations
for the solution of Laplace's type problems. Integral equation
techniques were mainly used in fluid mechanics and general
potential problems and known as the ' source' method which is
an ' indirect' method of analysis; i.e. the unknowns are not
the physical variables of the problem. Work on this method
continued throughout the 1960s and 1970s in the pioneering work
of Jaswon ITU and Symm [12], Massonet [13], Hess [14] and many
others.
It is difficult to point out precisely who was the first
one to propose the 'direct' method of anal~sis. It is found
in a different form, in Kupradze' s book IB J • It seems fair
however from the engineering point of view to consider that
the method originated in the work of Cruse and Rizzo [Is] in
elastostatics. ·
Since the early 1960s a small research group started
working at Southampton University, on the applications of
integral e!}uations to solve stress analysis problems. Hadid's
thesis [l6j partly based on Hadjin's [!7] work was published
in 1964 and dealt with the use of integral equations in shell
analysis. Unfortunately the presentation of the problem, the
difficulty of defining the appropriate Green's functions and
the parallel emergence of the finite element method all con
tributed to minimize the importance of this work. This work
was continued through a series of theses dealing mainly with
elastostatics problems. Recent developments in finite elements
had started to find their way into the formulation of boundary
integral equations, specially in the idea of using general
curved elements. Finally the question of how to effectively
relate the boundary integral equations to other ap~roximate
techniques was solved using weighted residuals [18J • The
work at the Southampton University group culminated with the
first book in 1978 for which the title "Boundary Elements" was
used Qe].
More recently this work has been e~anded to encompass
time dependent and non-linear problems L20]. Two important
International Conferences were held at Southampton University
in 19 78 and 1980. The edited Proceedings of these conferences
- the only ones so far on this topic - are now standard
references [21 ,22].