书名：有限元法基础理论
定价：79.0
ISBN：9787030752918
版次：1
出版时间：2023-03

内容提要：
本书主要阐述有限元法基础理论，通过介绍有限元法的基本概念和关键技术，使读者建立该方法的知识体系。本书主要内容包括：有限元法概述、弹性力学基本理论、等效积分弱形式、单元和形函数、等参单元和数值积分、弹性力学问题的有限元求解格式、线性代数方程组的解法、误差估计和自适应分析、有限元法程序。为便于教与学，书中加入了与知识点配套的课后习题、编程作业、参考答案和计算程序。另外，本书配有电子课件，读者可直接联系作者索取。



目录：
Contents
Chapter 1　Introduction of Finite Element Method　1
1.1　Development Process of Finite Element Method　1
1.2　Computation Procedure of Finite Element Method　3
1.3　Main Contents of the Book　4
1.4　Exercises　5
Chapter 2　Fundamentals of Elasticity Mechanics　6
2.1　Displacements　7
2.2　Strains　8
2.3　Stresses　8
2.4　Geometric Equations　9
2.5　Constitutive Equations　10
2.6　Equilibrium Equations　12
2.6.1　Three-Dimensional Problems　12
2.6.2　Two-Dimensional Plane Stress and Strain Problems　13
2.6.3　Two-Dimensional Axisymmetric Problems　13
2.7　Boundary Conditions　13
2.8　Exercises　14
Chapter 3　Weak Form of Equivalent Integration　15
3.1　Weak Form of Equivalent Integration for Differential Equations　15
3.2　Weak Form of One-Dimensional Elasticity Problems　15
3.3　Finite Element Computation Based on Weak Form　17
3.3.1　Galerkin Method　17
3.3.2　Finite Element Computation　20
3.4　Global Assembly from One-Dimensional Elements　23
3.5　Treatments on Boundary Conditions　24
3.6　Exercises　28
Chapter 4　Elements and Shape Functions　29
4.1　One-Dimensional Lagrange Element　29
4.1.1　Linear Element with Two Nodes　29
4.1.2　Higher-Order Lagrange Element　29
4.1.3　Quadratic Lagrange Element　31
4.2　Two-Dimensional Triangle Element　32
4.2.1　Triangle with Three Nodes　32
4.2.2　Higher-Order Triangle Element　35
4.2.3　Quadratic Triangle Element　37
4.2.4　Cubic Triangle Element　37
4.3　Two-Dimensional Rectangle Element　37
4.3.1　Linear Rectangle Element with Four Nodes　37
4.3.2　Higher-Order Rectangle Element　39
4.3.3　Quadratic Rectangle Element　40
4.4　Three-Dimensional Tetrahedron Element　41
4.4.1　Linear Tetrahedron Element with Four Nodes　41
4.4.2　Higher-Order Tetrahedron Element　44
4.4.3　Quadratic Tetrahedron Element　44
4.4.4　Cubic Tetrahedron Element　44
4.5　Three-Dimensional Hexahedron Element　45
4.5.1　Hexahedron with Eight Nodes　45
4.5.2　Higher-Order Hexahedron Element　46
4.5.3　Quadratic Hexahedron Element　47
4.6　Exercises　48
Chapter 5　Isoparametric Element and Numerical Integration　50
5.1　Isoparametric Element　50
5.1.1　One-Dimensional Isoparametric Lagrange Element　50
5.1.2　Two-Dimensional Isoparametric Triangle Element　51
5.1.3　Two-Dimensional Isoparametric Rectangle Element　53
5.1.4　Three-Dimensional Isoparametric Tetrahedron Element　54
5.1.5　Three-Dimensional Isoparametric Hexahedron Element　56
5.1.6　Requirements of Isoparametric Element　58
5.2　Numerical Integration　59
5.2.1　One-Dimensional Integration for Lagrange Element　59
5.2.2　Two-Dimensional Integration for Triangle Element　62
5.2.3　Two-Dimensional Integration for Rectangle Element　63
5.2.4　Three-Dimensional Integration for Tetrahedron Element　64
5.2.5　Three-Dimensional Integration for Hexahedron Element　65
5.2.6　Required Order of Numerical Integration　66
5.3　Exercises　67
Chapter 6　Finite Element Computation Scheme of Elasticity Problems　68
6.1　Weak Form for General Elasticity Problems　68
6.2　Finite Element Method for Solving Elasticity Problems　71
6.3　Global Assembly from High-Dimensional Elements　72
6.4　Treatments on Boundary Conditions　78
6.5　Exercises　82
Chapter 7　Solutions of Linear Algebraic Equations　83
7.1　LU Decomposition Method　83
7.2　Exercises　87
Chapter 8　Error Estimation and Adaptive Analysis　88
8.1　Error Estimation of Finite Element Solutions　88
8.1.1　Error of Finite Element Solutions　88
8.1.2　Superconvergent Patch Recovery Method　88
8.2　Adaptive Finite Element Method　90
8.2.1　Categories of Adaptive Finite Element Method　90
8.2.2　h-Version Adaptive Finite Element Method　91
8.2.3　hp-Version Adaptive Finite Element Method　92
8.3　Exercises　94
Chapter 9　Programs of Finite Element Method　95
9.1　One-Dimensional Program of Beam Deformation　95
9.1.1　Main Program　96
9.1.2　Numerical Example　98
9.1.3　Interactive Interface　98
9.2　Two-Dimensional Program of Plane Strain Problem　108
9.2.1　Main Program　108
9.2.2　Numerical Example　112
9.2.3　Interactive Interface　114
9.3　Three-Dimensional Program of Solid Compression　124
9.3.1　Main Program　124
9.3.2　Numerical Example　128
9.3.3　Interactive Interface　131
9.4　Exercises　141
Appendix A. Keyword Index　143
Appendix B. Matrix Calculation　145
B.1　Definition　145
B.2　Matrix Addition or Subtraction　146
B.3　Transpose　146
B.4　Transpose of a Product　147
B.5　Inverse　147
B.6　Symmetric Matrices　148
B.7　Partitioning　148
Appendix C. Summary of Elements and Shape Functions　150
C.1　One-Dimensional Lagrange Element　150
C.2　Two-Dimensional Triangle Element　150
C.3　Two-Dimensional Rectangle Element　151
C.4　Three-Dimensional Tetrahedron Element　151
C.5　Three-Dimensional Hexahedron Element　152
Appendix D. Gaussian Integration Points and Weights　154
Appendix E. Exercise Solutions　158
References　174