Automated Solution of Differential Equations by The Finite Element Method 1264258828

by Zhilin Li (Author),‎ Zhonghua Qiao (Author),‎ Tao Tang (Author)

This book presents important contributions to modern theories concerning the distribution theory applied to convex analysis (convex functions, functions of lower semicontinuity, the subdifferential of a convex function).

The basic idea of this introduction to the finite element method is based on the concept of explaining the complex method using only one-dimensional elements. Thus, the mathematical description remains largely simple and straightforward. The emphasis in each chapter is on explaining the method and understanding it itself. The reader learns to understand the assumptions and derivations in various physical problems in structural mechanics and to critically assess the possibilities and limitations of the finite element method.

Based on simple examples, this book offers a short introduction to the general-purpose finite element program MSC Marc, a specialized program for non-linear problems (implicit solver) distributed by the MSC Software Corporation, which is commonly used in academia and industry. Today the documentation of all finite element programs includes a variety of step-by-step examples of differing complexity, and in addition, all software companies offer professional workshops on different topics. As such, rather than competing with these, the book focuses on providing simple examples, often single-element problems, which can easily be related to the theory that is discussed in finite element lectures. This makes it an ideal companion book to classical introductory courses on the finite element method.