Fundamental Principles and Numerical Methods of the Finite Element Method (Second Edition)

Author: Wang Xucheng, Shao Min (editors)
Publisher:
Publish Date: 1997-03-01
Features: The purpose of this book is to enable readers to grasp the fundamental principles and numerical methods of the finite element method and to effectively utilize and improve existing unit and numerical methods, as well as develop new ones. This book is a revised and expanded edition of the original 1988 version, reflecting the latest advancements in the finite element method and the authors' new teaching experiences in this course. It has undergone significant revisions compared to the original edition. The book is divided into two parts. The first part is the fundamental section, consisting of seven chapters, including the weighted residual method and variational principles as the theoretical foundation of the finite element method, the general principles and formulations of the finite element method for elastodynamics problems, the construction of units and interpolation functions, isoparametric units and numerical integration, practical considerations in the application of the finite element method, solution methods for linear equations, and the structure and characteristics of finite element method programs. The second part is the specialized section, consisting of nine chapters, including further theoretical foundations of the finite element method—generalized variational principles—as well as the finite element methods for eight specialized problems: bar structures, plate bending, axisymmetric shells, general shells, heat conduction, dynamics, material nonlinearity, and geometric nonlinearity. Each chapter is followed by exercises and discussion questions, and some chapters also include typical computational programs or subroutines. The first part and the second part are suitable for the basic teaching requirements of undergraduate and graduate students, respectively. The focus of the writing is on the establishment of the fundamental principles and formulations of the finite element method, the construction of unit interpolation functions and characteristic matrices, and the comparison of different unit characteristics. The principles, analysis, comparison, and computational implementation of various numerical methods are also emphasized. This book can serve as a textbook for undergraduate and graduate students in fields such as mechanics, mechanical engineering, civil engineering, and hydraulic engineering, as well as a reference for engineering professionals and teachers in these disciplines.