《工程有限元分析》由崔德渝、徐元铭编著。

This textbook presents the necessary concepts，principles and general procedure of Finite Element Method(FEM) which are primarily applied for linearly elastic structural analysis including plane problems，axisymmetric problems，space problems，plates and shells and fracture mechanics.The FEM of heat transfer in brief is also incorporated.Some straightforward examples are introduced to demonstrate a complete and detailed finite element procedure.

《工程有限元分析》由崔德渝、徐元铭编著。

《工程有限元分析》内容简介：

This textbook presents the necessary concepts，principles and general procedure of Finite Element Method(FEM) which are primarily applied for linearly elastic structural analysis including plane problems，axisymmetric problems，space problems，plates and shells and fracture mechanics.The FEM of heat transfer in brief is also incorporated.Some straightforward examples are introduced to demonstrate a complete and detailed finite element procedure.The aim of the text is to provide the fundamental theories and numerical methodology in finite element analysis.It focuses on the derivation of key governing equations of the FEM and its engineering application.

This text can be regarded as a text or reference book for the university under and postgraduate students or engineers whose majors are related to mechanics,aerospace，mechanical and civil engineering,heat transfer and so on.

Chapter 1 Introduction to Finite Element Method

 1.1 Basic Concept of Finite Element Method

 1.2 General Description of Finite Element Method

1.2.1 Finite Element Technique in Structure Analysis

1.2.2 Finite Element Technique in Heat Conduction

1.2.3 Summary

 1.3 Engineering Applications of Finite Element Analysis

 1.4 Principle of Virtual Displacements and Variational Approach

1.4.1 Principle of Virtual Displacements (PVD)

1.4.2 Variational Formulation

 Problem Set 1

Chapter 2 General Procedure of Finite Element Method

 2. i Interpolation Functions

 2.2 Strain- displacement Relations

 2.3 Stress - strain Relations (Constitutive Relations)

 2.4 Governing Equations in Finite Element Analysis

 2.5 Stiffness Matrices

2.5.1 Element Stiffness Matrix

2.5.2 Global Stiffness Matrix

 2.6 Equivalent Nodal Force Vectors

2.6.1 Element Equivalent Nodal Force Vector

2.6.2 Global Equivalent Nodal Force Vector

 2.7 Imposition of Boundary Condition

 2.8 Numerical Examples

 2.9 Area Coordinates

 2.10 Six-node Triangular Elements

 2.11 Linear Rectangular Elements

 Problem Set 2

Chapter 3 Formulation of Isoparametric Finite Element Matrices

 3.1 Isoparametric Concepts

 3.2 Construction of Interpolation Functions

3.2.1 The Pascal Triangle

3.2.2 Lagrange Polynomials

3.2.3 Lagrange Polynomials in Dimensionless Form

 3.3 Family of Two-dimensional Isoparametric Elements

 3.4 Formulation of Isoparametrie Finite Element Matrices for Plane Elasticity

3.4.1 Interpolation Functions

3.4.2 Strain- displacement Transformation Matrix

3.4.3 Constitutive Relations

3.4.4 Element Stiffness Matrix

3.4.5 Element Load Vector

 3.5 Isoparametric Triangular Elements in Terms of Area Coordinates

 Problem Set 3

Chapter 4 Stress Analysis of Axisymmetric Problems

 4.1 Interpolation Functions

 4.2 Strain- displacement Relations

 4.3 Stress- strain Relations

 4.4 Element Stiffness Matrix

 4.5 Element Equivalent Nodal Force Vector

 4.6 Four-node Rectangular Ring Element

 4.7 A Numerical Example

 Problem Set 4

Chapter 5 Analysis of Three-dimensional Problems

 5.1 Convergence Considerations

 5.2 Shape Functions for Three-dimensional Elements

5.2.1 Shape Functions for Tetrahedron Elements

5.2.2 Shape Functions for Three-dimensional Hexahedral Elements

 5.3 Formulation of Three-dimensional Isoparametrie Element Matrices

5.3.1 Interpolation Functions

5.3.2 Strain- displacement Relations

5.3.3 Constitutive Relations

5.3.4 Element Stiffness Matrix

5.3.5 Element Load Vector

 5.4 Formulation and Calculation of Tetrahedron Element Matrices

5.4.1 Displacement Functions

5.4.2 Strain- displacement Transformation

5.4.3 Stress- strain Relations

5.4.4 Element Stiffness Matrix

5.4.5 Element Load Vector

5.4.6 Degeneration of Eight-node Brick Element to Tetrahedral Element

 5.5 Numerical Examples

 Problem Set 5

Chapter 6 Finite Element Analysis for Plates and Shells

 6.1 Introduction

 6.2 Thin Plate Elements

6.2.1 Thin Plate Theory

6.2.2 Interpolation Functions for a Rectangular Thin Plate Element

6.2.3 Stiffness Matrix of a Rectangular Plate Element

6.2.4 Equivalent Nodal Force Vector and Internal Moments

 6.3 Mindlin Plate Elements

6.3.1 Formulation with Mindlin Model

6.3.2 Governing Equations of Equilibrium

6.3.3 Interpolation Functions for a Mindlin Plate Element

6.3.4 Plate Element Stiffness Matrix and Equivalent Nodal Force Vector

 6.4 Shell Elements

6.4.1 Geometric Description of a Curved Shell Element

6.4.2 Interpolation Functions for a Curved Shell Element

6.4.3 Strain- displacement Transformation Relations

6.4.4 Transformed Elasticity and Stress Matrices

6.4.5 Element Stiffness Matrix and Load Vectors

 6.5 Mindlin Laminated Plate Element

6.5.1 Element Displacement and Coordinate Interpolation

6.5.2 Strain- displacement Relations

6.5.3 Constitutive Relations

6.5.4 Element Stiffness Matrix

6.5.5 Governing Equations in Finite Element Analysis

6.5.6 Calculation of Displacements and Stresses for Composite Laminates

6.5.7 A Numerical Example

 Problem Set 6

Chapter 7 Finite Element Analysis in Fracture Mechanics

 7.1 Displacement and Stress Fields in the Vicinity of Crack Tip

 7.2 Finite Element Analysis with Conventional Elements for Determination of SIF

7.2.1 Fine Mesh-extrapolation Method

7.2.2 Coarse Mesh-J-integral Method

7.2.3 Coarse Mesh-stiffness Derivative Method

 7.3 Finite Element Analysis with Singular Elements for Determination of SIF

7.3.1 Isoparametric Element Method

7.3.2 Global-local Finite Element Method

 Problem Set 7

Chapter 8 Heat Transfer

 8.1 Governing Equations of Heat Transfer

8.1.1 Rate Equations in Heat Transfer

8.1.2 Governing Differential Equation of Temperature Field

8.1.3 Variational Formulation of Field Problems

 8.2 Finite Element Formulation for Field Problems

  8.3 One-dimensional Heat Transfer

8.3.1 One-dimensional Linear Element

8.3.2 One-dimensional Quadratic Element

  8.4 Two-dimensional Heat Transfer

8.4.1 Three-node Triangular Element

8.4.2 Higher-order Two-dimensional Elements

  8.5 Three-dimensional Heat Transfer

  8.6 Radiation Heat Transfer

  Problem Set 8

References