This web page is a companion to the book
by Friedel Hartmann and Casimir Katz
published by Springer-Verlag Berlin Heidelberg New York in February 2007
About the book
It develops the foundations and applications of the finite element method in structural analysis in a language which is familiar to structural engineers.
It provides a new foundation for the finite element method that enables structural engineers to address key questions that arise in computer modeling of structures with finite elements.
It uncovers the structural mechanics behind the finite element method. It explores and explains issues such as:
Why finite element results are 'wrong'.
Why support reactions are relatively accurate.
Why stresses at midpoints are more reliable.
Why averaging the stresses sometimes may not help.
Why the equilibrium conditions are violated.
An additional chapter treats the boundary element method, and related software is available at this side.
For a continuation of the ideas developed in this book see our new title
by Friedel Hartmann
published by Springer-Verlag Berlin Heidelberg New York in March 2012
About the book
Key words: Green's functions, influence functions, finite elements, stiffness matrices, duality, goal-oriented refinement, nonlinear problems p-method, model adaptivity, error analysis, solid mechanics, frames, trusses
Green's functions are the physical basis functions of a problem domain and in the finite element method these functions are approximated with nodal basis functions. These discrete Green's functions produce the output the engineer sees on the screen.
This book is devoted to the study of these Green's functions and how finite element codes can best approximate these functions, an issue which is central for the quality of engineering analysis with finite elements as testified by the fact that the discretization error, the modeling error as well as the pollution error strongly depend on the error in the Green's functions.
The success of goal-oriented refinement techniques is proof of the close connection between Green's functions and finite elements and also questions of verification as well as validation all hinge on the same issue: the choice of the correct Green's function (validation) and the best possible approximation of this function (verification).
The book follows this path by a detailed analysis of the engineering and numerical aspects of Green's functions in the finite element context and in particular how questions of modeling the mechanics in a problem with finite elements must focus on the choice and the approx- imability of the Green's functions. Many engineering examples illustrate the basic concepts and the relevance of the results for practical engineering analysis with finite elements.