工程有限元分析

出版时间:2013-1  出版社:北京航空航天大学出版社  作者:崔德渝,徐元铭 著  页数:323  

内容概要

  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.

书籍目录

Chapter 1 Introduction to Finite Element Method1.1 Basic Concept of Finite Element Method1.2 General Description of Finite Element Method1.2.1 Finite Element Technique in Structure Analysis1.2.2 Finite Element Technique in Heat Conduction1.2.3 Summary1.3 Engineering Applications of Finite Element Analysis1.4 Principle of Virtual Displacements and Variational Approach1.4.1 Principle of Virtual Displacements (PVD)1.4.2 Variational FormulationProblem Set 1Chapter 2 General Procedure of Finite Element Method2.1 Interpolation Functions2.2 Strain-displacement Relations2.3 Stress-strain Relations (Constitutive Relations)2.4 Governing Equations in Finite Element Analysis2.5 Stiffness Matrices2.5.1 Element Stiffness Matrix2.5.2 Global Stiffness Matrix2.6 Equivalent Nodal Force Vectors2.6.1 Element Equivalent Nodal Force Vector2.6.2 Global Equivalent Nodal Force Vector2.7 Imposition of Boundary Condition2.8 Numerical Examples2.9 Area Coordinates2.10 Six-node Triangular Elements2.11 Linear Rectangular ElementsProblem Set 2Chapter 3 Formulation of Isoparametric Finite Element Matrices3.1 Isoparametric Concepts3.2 Construction of Interpolation Functions3.2.1 The Pascal Triangle3.2.2 Lagrange Polynomials3.2.3 Lagrange Polynomials in Dimensionless Form3.3 Family of Two-dimensional Isoparametric Elements3.4 Formulation of Isoparametric Finite Element Matrices for Plane Elasticity3.4.1 Interpolation Functions3.4.2 Strain-displacement Transformation Matrix3.4.3 Constitutive Relations3.4.4 Element Stiffness Matrix3.4.5 Element Load Vector3.5 Isoparametric Triangular Elements in Terms of Area CoordinatesProblem Set 3Chapter 4 Stress Analysis of Axisymmetric Problems4.1 Interpolation Functions4.2 Strain-displacement Relations4.3 Stress-strain Relations4.4 Element Stiffness Matrix4.5 Element Equivalent Nodal Force Vector4.6 Four-node Rectangular Ring Element4.7 A Numerical ExampleProblem Set 4Chapter 5 Analysis of Three-dimensional Problems5.1 Convergence Considerations5.2 Shape Functions for Three-dimensional Elements5.2.1 Shape Functions for Tetrahedron Elements5.2.2 Shape Functions for Three-dimensional Hexahedral Elements5.3 Formulation of Three-dimensional Isoparametric Element Matrices5.3.1 Interpolation Functions……Chapter 6 Finite Element Analysis for Plates and ShellsChapter 7 Finite Element Analysis in Fracture MechanicsChapter 8 Heat TransferReferences

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