Springer Series in Computational Mechanics
Edited by S. N. Atluri
D. E. Beskos
(Editor)
Boundary Element Analysis
of Plates and Shells
With 112Figures
Springer-Verlag
Berlin Heidelberg NewYork
London Paris Tokyo
Hong Kong Barcelona Budapest
Editor of the series:
Prof. S. N. Atluri
Center for Computational Machanics
Georgia Institute of Technology
Atlanta, GA 30332-0356
USA
Editors of this volume:
Prof. Dimitri E. Beskos
Department of Civil Engineering
University ofPatras
G R-26110 Patras
Greece
ISBN-13: 978-3-642-45696-1
001: 10.1007/978-3-642-45694-7
e-ISBN-13: 978-3-642-45694-7
Library of Congress Cataloging-in-Publication Data
Boundary element analysis of plates and shells / by D. E. Beskos.
(Springer series in computational mechanics)
1. Plates (Engineering) 2. Shells (Engineering) 3. Boundary element methods.
I. Beskos, D. E. II. Series.
TA660.P6B68 1991
624.1'776'0l51535--dc20 91-31928
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concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broad­
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September 9, 1965, in its current version, and permission for use must always be obtained from
Springer-Verlag. Violations are liable for prosecution act under the German Copyright Law.
© Springer-Verlag Berlin Heidelberg 1991
Softcover reprint of the hardcover 15t edition 1991
The use of general descriptive names, registered names, trademarks, etc. in this publication does not
imply, even in the absence of a specific statement, that such names are exempt from the relevant protec­
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Typesetting: Camera ready by authors
61/3020-543210- Printed on acid-free paper
Preface
Plates and shells constitute a large class of
surface type of
structures with one of their dimensions, their thickness, much
smaller than the other two dimensions. The analysis of the be­
havior of these structures under static and dynamic
loads
of great interest to scientists and engineers both
from
theoretical and the practical viewpoint. Indeed,
is
the
the analysis
of these structures represents a very challenging and attracti­
ve theoretical problem, as well as a problem of
great practi­
cal significance, associated with applications in many enginee­
ring fields, such as civil, mechanical, aerospace, etc.
It is
the
well known that numberical methods of solution, such as
Finite Difference
Element Method
sing this
and
Method (FDM) and especially the Finite
(FEM) are
class of
loading conditions
During the
has emerged
of various
some
the only practical means for analy­
surface structures under complex boundary
and/or realistic
last 20
years the
as a
powerful tool
complex problems
material
Boundary Element
for the
behavior.
Method (BEM)
numerical
of mechanics.
This
solution
method
has
distinct advantages over domain type techniques, such as
the FDM
and the
FEM for
a wide class of structural analysis
problems. Information concerning the application of the BEM to
plate
and shell
short
sections or
the BEM
analysis can
chapters in
be found in the form of rather
a number
of books devoted to
and its applications to various fields of engineering
science and mechanics. These sections or chapters, however,
deal mainly with static analysis of plates and shells and do
not cover the more recent exciting developments in the area.
No
specific book
plates and
dealing exclusively
shells by
with the
analysis
of
the BEM and covering all the aspects of
their behavior up to date exists in the literature.
The present book represents an effort to fill this
gap in the
literature by combining tutorial and state-of-the-art
of the BEM as applied to plates and shells.
aspects
It aims at infor­
ming scientists and engineers engaged in the analysis
of
VI
surface type of structures, about the use
and the advantages
of this technique, the most recent developments
in the field
and the pertinent literature for further study.
The reader is
expected to have a basic knowledge of plate and
shell theory
and applied mathematics.
The book
is divided
into nine
very well
known for
cover all
the aspects
existing to
chapter
to
the basic
literature. More specifically,
direct BEM and serves as an introduction
ideas of
the method. chapter two
and forced vibrations of linear elastic plates
plate systems
by the
(field) BEM
conventional direct
BEM
and
the
in the time and frequency domains. Static
dynamic analysis of linear elastic Vlasov-Reisner shallow
shells
time
in the
a comprehensive treatment of the static
concepts and
considers free
and
in the field, which
linear elastic Kirchhoff plates and plate systems
the conventional
domain
by persons
of plate and shell analysis by the BEM
this date
by
and
their contributions
one provides
analysis of
chapters, written
by the
direct BEM
and frequency
Nonlinearities
and dynamic
elastic
and the
domains is
domain (field) BEM in the
the subject of chapter three.
are discussed in the next two chapters. Static
analysis of
plates and
shells exhibiting
large
deformations and inelastic material behavior are dis­
cussed in chapter four and five, respectively. Linear and non­
linear stability analysis of plates, plate systems and shallow
shells is
described in
some special
stic plates
harmonic
methods for
static and dynamic analysis of ela­
including the
indirect BEM, the BEM based on bi­
analysis and the BEM employing finite domain Green's
functions. The
static and
namic
special case
of Reissner-Mindlin plates under
dynamic conditions
Finally, chapter
for
chapter six. Chapter seven deals with
nine discusses
analysing elastic
is taken
up in chapter eight.
two boundary type of methods
plates and shells under static and dy­
conditions, namely the boundary collocation and briefly
the edge function method.
The editor would like to express his appreciation to all those
who helped him during the course of preparing this
Professor S.N. Atluri, the editor of the
book:
to
Springer Series in
VII
computational Mechanics, for his encouragement
and personal
participation by writing one of the chapters of
the book,
to
all the authors for their efforts and cooperation,to the publishing house of Springer-Verlag for their prompt
and to his wife Georgia for her patience and
cooperation
understanding.
Patras, Greece 1991
Dimitri E. Beskos
Editor
Con~n~
Static Analysis of Plates
F. Hartmann
Dynamic Analysis of Plates
D.E. Beskos
Static and Dynamic Analysis of Shells
D.E. Beskos
Large Deformation Analysis of Plates and Shells
S.N. Atluri and D.S. Pipkins
Inelastic Analysis of Plates and Shells
S. Mukherjee and B. Poddar
Stability Analysis of Plates and Shells
G.D. Manolis
Special Methods for Plate Analysis
J. T. Katsikadelis
Static and Dynamic Analysis of Reissner-Mindlin Plates
H. Antes
Analysis of Plates and Shells by Boundary Collocation
J.R. Hutchinson
1
35
93
141
167
193
221
312
341