Basic Theory of Finite Element Method 9787030752918 王永亮

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書名：Basic Theory of Finite Element Method
ISBN：9787030752918
出版社：科學
著編譯者：王永亮
頁數：176
所在地：中國大陸 *此為代購商品
書號：1508405
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【台灣高等教育出版社簡體書】 Basic Theory of Finite Element Method 787030752918 王永亮

內容簡介

本書主要闡述有限元法基礎理論，通過介紹有限元法的基本概念和關鍵技術，使讀者建立該方法的知識體系。本書主要內容包括：有限元法概述、彈性力學基本理論、等效積分弱形式、單元和形函數、等參單元和數值積分、彈性力學問題的有限元求解格式、線性代數方程組的解法、誤差估計和自適應分析、有限元法程序。為便於教與學，書中加入了與知識點配套的課後習題、編程作業、參考答案和計算程序。另外，本書配有電子課件，讀者可直接聯繫作者索取（wangyl@cumtb edu cn）。 本書可作為工程力學、土木工程、採礦工程等專業本科生和研究生的教材，亦可作為相關領域研究人員的參考書。

目錄

Chapter 1 Introduction of Finite Element Method
1 1 Development Process of Finite Element Method
1 2 Computation Procedure of Finite Element Method
1 3 Main Contents of the Book
1 4 Exercises
Chapter 2 Fundamentals of Elasticity Mechanics
2 1 Displacements
2 2 Strains
2 3 Stresses
2 4 Geometric Equations
2 5 Constitutive Equations
2 6 Equilibrium Equations
2 6 1 Three-Dimensional Problems
2 6 2 Two-Dimensional Plane Stress and Strain Problems
2 6 3 Two-Dimensional Axisymmetric Problems
2 7 Boundary Conditions
2 8 Exercises
Chapter 3 Weak Form of Equivalent Integration
3 1 Weak Form of Equivalent Integration for Differential Equations
3 2 Weak Form of One-Dimensional Elasticity Problems
3 3 Finite Element Computation Based on Weak Form
3 3 1 Galerkin Method
3 3 2 Finite Element Computation
3 4 Global Assembly from One-Dimensional Elements
3 5 Treatments on Boundary Conditions
3 6 Exercises
Chapter 4 Elements and Shape Functions
4 1 One-Dimensional Lagrange Element
4 1 1 Linear Element with Two Nodes
4 1 2 Higher-Order Lagrange Element
4 1 3 Quadratic Lagrange Element
4 2 Two-Dimensional Triangle Element
4 2 1 Triangle with Three Nodes
4 2 2 Higher-Order Triangle Element
4 2 3 Quadratic Triangle Element
4 2 4 Cubic Triangle Element
4 3 Two-Dimensional Rectangle Element
4 3 1 Linear Rectangle Element with Four Nodes
4 3 2 Higher-Order Rectangle Element
4 3 3 Quadratic Rectangle Element
4 4 Three-Dimensional Tetrahedron Element
4 4 1 Linear Tetrahedron Element with Four Nodes
4 4 2 Higher-Order Tetrahedron Element
4 4 3 Quadratic Tetrahedron Element
4 4 4 Cubic Tetrahedron Element
4 5 Three-Dimensional Hexahedron Element
4 5 1 Hexahedron with Eight Nodes
4 5 2 Higher-Order Hexahedron Element
4 5 3 Quadratic Hexahedron Element
4 6 Exercises
Chapter 5 Isoparametric Element and Numerical Integration
5 1 Isoparametric Element
5 1 1 One-Dimensional Isoparametric Lagrange Element
5 1 2 Two-Dimensional Isoparametric Triangle Element
5 1 3 Two-Dimensional Isoparametric Rectangle Element
5 1 4 Three-Dimensional Isoparametric Tetrahedron Element
5 1 5 Three-Dimensional Isoparametric Hexahedron Element
5 1 6 Requirements of Isoparametric Element
5 2 Numerical Integration
5 2 1 One-Dimensional Integration for Lagrange Element
5 2 2 Two-Dimensional Integration for Triangle Element
5 2 3 Two-Dimensional Integration for Rectangle Element
5 2 4 Three-Dimensional Integration for Tetrahedron Element
5 2 5 Three-Dimensional Integration for Hexahedron Element
5 2 6 Required Order of Numerical Integration
5 3 Exercises
Chapter 6 Finite Element Computation Scheme of Elasticity Problems
6 1 Weak Form for General Elasticity Problems
6 2 Finite Element Method for Solving Elasticity Problems
6 3 Global Assembly from High-Dimensional Elements
6 4 Treatments on Boundary Conditions
6 5 Exercises
Chapter 7 Solutions of Linear Algebraic Equations
7 1 LU Decomposition Method
7 2 Exercises
Chapter 8 Error Estimation and Adaptive Analysis
8 1 Error Estimation of Finite Element Solutions
8 1 1 Error of Finite Element Solutions
8 1 2 Superconvergent Patch Recovery Method
8 2 Adaptive Finite Element Method
8 2 1 Categories of Adaptive Finite Element Method
8 2 2 h-Version Adaptive Finite Element Method
8 2 3 hp-Version Adaptive Finite Element Method
8 3 Exercises
Chapter 9 Programs of Finite Element Method
9 1 One-Dimensional Program of Beam Deformation
9 1 1 Main Program
9 1 2 Numerical Example
9 1 3 Interactive Interface
9 2 Two-Dimensional Program of Plane Strain Problem
9 2 1 Main Program
9 2 2 Numerical Example
9 2 3 Interacti
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