Structural Analysis with Finite Elements - Friedel Hartmann & Casimir Katz, Literatura MES (FEM), EN

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Structural Analysis with Finite Elements
Friedel Hartmann Casimir Katz
Structural Analysis with
Finite Elements
With 408 Figures and 26 Tables
Friedel Hartmann
University of Kassel Structural Mechanics
Kurt-Wolters-Str. 3
Casimir Katz
85764 Oberschleissheim
ISBN-10 3-540-49698- x Springer Berlin Heidelberg New York
ISBN-13 978-3-540-49698-4 Springer Berlin Heidelberg New York
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The finite element method has become an indispensible tool in structural
analysis, and tells an unparalleled success story. With success, however, came
criticism, because it was noticeable that knowledge of the method among prac-
titioners did not keep up with success. Reviewing engineers complain that the
method is increasingly applied without an understanding of structural behav-
ior. Often a critical evaluation of computed results is missing, and frequently
a basic understanding of the limitations and possibilities of the method are
But a working knowledge of the fundamentals of the finite element method
classical structural mechanics is a prerequisite for any sound finite element
analysis. Only a well trained engineer will have the skills to critically examine
the computed results.
Finite element modeling is more than preparing a mesh connecting the
elements at the nodes and replacing the load by nodal forces. This is a popular
model but this model downgrades the complex structural reality in such a
way that—instead of being helpful—it misleads an engineer who is not well
acquainted with finite element techniques.
The object of this book is therefore to provide a foundation for the finite
element method from the standpoint of structural analysis, and to discuss
questions that arise in modeling structures with finite elements.
What encouraged us in writing this book was that—thanks to the inten-
sive research that is still going on in the finite element community—we can
explain the principles of finite element methods in a new way and from a new
perspective by making ample use of influence functions. This approach should
appeal in particular to structural engineers, because influence functions are a
genuine engineering concept and are thus deeply rooted in classical structural
mechanics, so that the structural engineer can use his engineering knowledge
and insight to assess the accuracy of finite element results or to discuss the
modeling of structures with finite elements.
Just as a change in the elastic properties of a structure changes the Green’s
functions or influence functions of the structure so a finite element mesh effects
a shift of the Green’s functions.
We have tried to concentrate on ideas, because we considered these and
not necessarily the technical details to be important. The emphasis should
be on structural mechanics and not on programming the finite elements, and
therefore we have also provided many illustrative examples.
Finite element technology was not developed by mathematicians, but by
engineers (Argyris, Clough, Zienkiewicz). They relied on heuristics, their in-
tuition and their engineering expertise, when in the tradition of medieval
craftsmen they designed and tested elements without fully understanding the
exact background. The results were empirically useful and engineers were
grateful because they could suddenly tackle questions which were previously
unanswerable. After these early achievements self-confidence grew, and a sec-
ond epoch followed that could be called baroque: the elements became more
and more complex (some finite element programs offered 50 or more ele-
ments) and enthusiasm prevailed. In the third phase, the epoch of “enlight-
ment” mathematicians became interested in the method and tried to analyze
the method with mathematical rigor. To some extent their efforts were futile
or extremely dicult, because engineers employed “techniques” (reduced inte-
gration, nonconforming elements, discrete Kirchhoff elements) which had no
analogy in the calculus of variations. But little by little knowledge increased,
the gap closed, and mathematicians felt secure enough with the method that
they could provide reliable estimates about the behavior of some elements.
We thus recognize that mathematics is an essential ingredient of finite ele-
ment technology.
One of the aims of this book is to teach structural engineers the theoretical
foundations of the finite element method, because this knowledge is invaluable
in the design of safe structures.
This book is an extended and revised version of the original German ver-
sion. We have dedicated the web page
to the book.
From this page the programs WINFEM (finite element program with focus on
influence functions and adaptive techniques), BE-SLABS (boundary element
analysis of slabs) and BE-PLATES (boundary element analysis of plates) can
be downloaded by readers who want to experiment with the methods. Addi-
tional information can also be found on
Friedel Hartmann
Munich August 2003
Casimir Katz
We thank Thomas Graetsch, who wrote the program WINFEM
and provided many illustrative examples for the approximation of influence functions
with finite elements, and Marc Damashek and William J. Gordon for their help in
preparing the manuscript. The permission of Oxford University Press to reprint the
picture on page 145 is greatly acknowledged.
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