Preface

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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 practitioners

did not keep up with success. Reviewing engineers complain that the

method is increasingly applied without an understanding of structural behavior.

Often a critical evaluation of computed results is missing, and frequently

a basic understanding of the limitations and possibilities of the method are

nonexistent.

But a working knowledge of the fundamentals of the finite element method

and 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 intensive

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

VI Preface

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 intuition

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 second

epoch followed that could be called baroque: the elements became more

and more complex (some finite element programs offered 50 or more elements)

and enthusiasm prevailed. In the third phase, the epoch of “enlightment”

mathematicians became interested in the method and tried to analyze

the method with mathematical rigor. To some extent their efforts were futile

or extremely difficult, because engineers employed “techniques” (reduced integration,

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 element

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 version.

We have dedicated the web page http://www.winfem.de 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. Additional

information can also be found on http://www.sofistik.com.

FriedelHartmann@uni-kassel.de Casimir.Katz@sofistik.de

Kassel Friedel Hartmann

Munich August 2003 Casimir Katz

Acknowledgement. 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.

Preface to the second edition

One of the joys of writing a book is that the authors learn more about a subject.

This does not stop after a book is finished. So we have added additional

sections to the text

• The Dirac energy

• How to predict changes

• The influence of a single element

• Retrofitting structures

• Generalized finite element methods (X-FEM)

• Cables

• Hierarchical elements

• Sensitivity analysis

• Weak form of influence functions

in the hope that these additional topics will also attract the readers’ interest.

Kassel Friedel Hartmann

Munich October 2006 Casimir Katz

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