Finite element methods for engineering sciences: theoretical approach and problem solving techniques

Joel Chaskalovic (auth.)3540763422, 9783540763420

This self-tutorial offers a concise yet thorough grounding in the mathematics necessary for successfully applying FEMs to practical problems in science and engineering. The unique approach first summarizes and outlines the finite-element mathematics in general and then, in the second and major part, formulates problem examples that clearly demonstrate the techniques of functional analysis via numerous and diverse exercises. The solutions of the problems are given directly afterwards. Using this approach, the author motivates and encourages the reader to actively acquire the knowledge of finite- element methods instead of passively absorbing the material, as in most standard textbooks. The enlarged English-language edition, based on the original French, also contains a chapter on the approximation steps derived from the description of nature with differential equations and then applied to the specific model to be used. Furthermore, an introduction to tensor calculus using distribution theory offers further insight for readers with different mathematical backgrounds.

Table of contents :
Front Matter….Pages i-xii
Summary of Courses on Finite Elements….Pages 1-38
Some Fundamental Classes of Finite Elements….Pages 39-61
Variational Formulations….Pages 63-111
Finite Elements in Deformable Solid Body Mechanics….Pages 113-146
Finite Elements Applied to Strength of Materials….Pages 147-210
Finite Elements Applied to Non Linear Problems….Pages 211-249
Back Matter….Pages 251-255