工程有限元分析

Chapter 1 Introduction to Finite Element Method

1.1 Basic Concept of Finite Element Method

1.2 General Description of Finite Element Method

1.3 Engineering Applications of Finite Element Analysis

1.4 Principle of Virtual Displacements and Variational

Approach

Problem Set 1

Chapter 2 General Procedure of Finite Element Method

2.1 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

2.6 Equivalent Nodal Force Vectors

2.7 Imposition of Boundary Condition

2.8 Numerical Examples

Chapter 1 Introduction to Finite Element Method

1.1 Basic Concept of Finite Element Method

1.2 General Description of Finite Element Method

1.3 Engineering Applications of Finite Element Analysis

1.4 Principle of Virtual Displacements and Variational

Approach

Problem Set 1

Chapter 2 General Procedure of Finite Element Method

2.1 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

2.6 Equivalent Nodal Force Vectors

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

3.3 Family of Two-dimensional Isoparametric Elements

3.4 Formulation of Isoparametric Finite Element Matrices for Plane

Elasticity

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

5.3 Formulation of Three-dimensional Isoparametric Element

Matrices

……

Chapter 6 Finite Element Analysis for Plates and Shells

Chapter 7 Finite Element Analysis in Fracture Mechanics

Chapter 8 Heat Transfer

References

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 post-graduate students or engineers whose
majors are related to mechanics， aerospace， mechanical and civil
engineering， heat transfer and so on.