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图书信息

书名：有限元方法基础论第6版

出版社: 世界图书出版公司; 第6版 (2008年9月1日)

外文书名: finite element method

平装: 733页

正文语种: 英语

开本: 24

isbn: 9787506292542

条形码: 9787506292542

商品尺寸: 22.4 x 14.8 x 3.8 cm

商品重量: 898 g

品牌: 世界图书出版公司北京公司

内容简介

《有限元方法基础论第6版》是一套在国际上颇具权威性的经典著作（共三卷）,由有限元法的创始人Zienkiewicz教授和美国加州大学Taylor教授合作撰写,初版于1967年,多次修订再版,深受力学界和工程界科技人员的欢迎。《有限元方法基础论第6版》的特点是理论可靠，内容全面，既有基础理论，又有其具体应用。第1卷目次：标准的离散系统和有限元方法的起源；弹性力学问题的直接方法；有限元概念的推广，Galerkin加权残数和变分法；‘标准的’和‘晋级的’单元形函数：Co连续性单元族；映射单元和数值积分—无限元和奇异元；线性弹性问题；场问题—热传导、电磁势、流体流动；自动网格生成；拼法试验，简缩积分和非协调元；混合公式和约束—完全场方法；不可压缩材料，混合方法和其它解法；多区域混合逼近-区域分解和“框架”方法；误差、恢复过程和误差估计；自适应有限元细分；以点为基础和单元分割的近似，扩展的有限元方法；时间维-场的半离散化、动力学问题以及分析解方法；时间维—时间的离散化近似；耦合系统；有限元分析和计算机处理。

目录

Preface

1 The standard discrete system and origins of the finite element method

1.1 Introduction

1.2 The struraal element and the structural system

1.3 Assembly and analysis of a structure

1.4 The boundary conditions

1.5 Electrical and fluid networks

1.6 The general pattern

1.7 The standard discrete system

1.8 Transformation of coordinates

1.9 Problems

2 A direct physical approach to problems in elasticity: plane stress

2.1 Introduction

2.2 Direct formulation of finite element characteristics

2.3 Generalization to the whole region - internal nodal force concept abandoned

2.4 Displacement approach as a minimization of total potential energy

2.5 Convergence criteria

2.6 Discretization error and convergence rate

2.7 Displacement functions with discontinuity between elements non-conforming elements and the patch test

2.8 Finite element solution process

2.9 Numerical examples

2.10 Concluding remarks

2.11 Problems

3 Generalization of the finite element concepts. Galerkin-weighted residual and variational approaches

3.1 Introduction

3.2 Integral or 'weak' statements equivalent to the differential equations

3.3 Approximation to integral formulations: the weighted residual Galerkin method

3.4 Virtual work as the 'weak form' of equilibrium equations for analysis of solids or fluids

69

3.5 Partial discretization

3.6 Convergence

3.7 What are 'variational principles'？

3.8 'Natural' variational principles and their relation to governing differential equations

3.9 Establishment of natural variational principles for linear, self-adjoint, differential equations

3.10 Maximum, minimum, or a saddle point？

3.11 Constrained variational principles. Lagrange multipliers

3.12 Constrained variational principles. Penalty function and perturbed lagrangian methods

88

3.13 Least squares approximations

3.14 Concluding remarks - finite difference and boundary methods

3.15 Problems

4 'Standard' and 'hierarchical' element shape functions: some general families of Co continuity

4.1 Introduction

4.2 Standard and hierarchical concepts

4.3 Rectangular elements - some preliminary considerations

4.4 Completeness of polynomials

4.5 Rectangular elements - Lagrange family

4.6 Rectangular elements - 'serendipity' family

4.7 Triangular element family

4.8 Line elements

4.9 Rectangular prisms - Lagrange family

4.10 Rectangular prisms - 'serendipity' family

4.11 Tetrahedral elements

4.12 Other simple three-dimensional elements

4.13 Hierarchic polynomials in one dimension

4.14 Two- and three-dimensional, hierarchical elements of the 'rectangle'or 'brick' type

4.15 Triangle and tetrahedron family

4.16 Improvement of conditioning with hierarchical forms

4.17 Global and local finite element approximation

4.18 Elimination of internal parameters before assembly - substructures

4.19 Concluding remarks

4.20 Problems

5 Mapped elements and numerical integration 'infinite' and singularity elements'

5.1 Introduction

5.2 Use of 'shape functions' in the establishment of coordinate transformations

5.3 Geometrical conformity of elements

5.4 Variation of the unknown function within distorted, curvilinear elements. Continuity requirements

5.5 Evaluation of element-matrices. Transformation in coordinates

5.6 Evaluation of element matrices. Transformation in area and volume coordinates

5.7 Order of convergence for mapped elements

5.8 Shape functions by degeneration

5.9 Numerical integration- one dimensional

5.10 Numerical integration - rectangular （2D） or brick regions （3D）

5.11 Numerical integration - triangular or tetrahedral regions

5.12 Required order of numerical integration

5.13 Generation of finite element meshes by mapping. Blending functions

5.14 Infinite domains and infinite elements

5.15 Singular elements by mapping - use in fracture mechanics, etc.

5.16 Computational advantage of numerically integrated finite elements

5.17 Problems

6 Problems in linear elasticity

6.1 Introduction

6.2 Governing equations

6.3 Finite element approximation

6.4 Reporting of results: displacements, strains and stresses

6.5 Numerical examples

6.6 Problems

7 Field problems - heat conduction, electric and magnetic potential and fluid flow

7.1 Introduction

7.2 General quasi-harmonic equation

7.3 Finite element solution process

7.4 Partial discretization - transient problems

7.5 Numerical examples - an assessment of accuracy

7.6 Concluding remarks

7.7 Problems

8 Automatic mesh generation

8.1 Introduction

8.2 Two-dimensional mesh generation - advancing front method

8.3 Surface mesh generation

8.4 Three-dimensional mesh generation- Delaunay triangulation

8.5 Concluding remarks

8.6 Problems

9 The patch test, reduced integration, and non-conforming elements

9.1 Introduction

9.2 Convergence requirements

9.3 The simple patch test （tests A and B） - a necessary condition for convergence

332

9.4 Generalized patch test （test C） and the single-element test

9.5 The generality of a numerical patch test

9.6 Higher order patch tests

9.7 Application of the patch test to plane elasticity elements with'standard' and 'reduced' quadrature

9.8 Application of the patch test to an incompatible element

9.9 Higher order patch test - assessment of robustness

9.10 Concluding remarks

9.11 Problems

10 Mixed formulation and constraints - complete field methods

10.1 Introduction

10.2 Discretization of mixed forms - some general remarks

10.3 Stability of mixed approximation. The patch test

10.4 Two-field mixed formulation in elasticity

10.5 Three-field mixed formulations in elasticity

10.6 Complementary forms with direct constraint

10.7 Concluding remarks - mixed formulation or a test of element'robustness'

10.8 Problems

11 Incompressible problems, mixed methods and other procedures of solution

11.1 Introduction

11.2 Deviatoric stress and strain, pressure and volume change

11.3 Two-field incompressible elasticity （up form）

11.4 Three-field nearly incompressible elasticity （u-p- form）

11.5 Reduced and selective integration and its equivalence to penalized mixed problems

11.6 A simple iterative solution process for mixed problems: Uzawa method

11.7 Stabilized methods for some mixed elements failing the incompressibility patch test

11.8 Concluding remarks

11.9 Problems

12 Multidomain mixed approximations - domain decomposition and 'frame' methods

12.1 Introduction

12.2 Linking of two or more subdomains by Lagrange multipliers

12.3 Linking of two or more subdomains by perturbed lagrangian and penalty methods

12.4 Interface displacement 'frame'

12.5 Linking of boundary （or Trefftz）-type solution by the 'frame' of specified displacements

12.6 Subdomains with 'standard' elements and global functions

12.7 Concluding remarks

12.8 Problems

13 Errors, recovery processes and error estimates

13.1 Definition of errors

13.2 Superconvergence and optimal sampling points

13.3 Recovery of gradients and stresses

13.4 Superconvergent patch recovery -= SPR

13.5 Recovery by equilibration of patches - REP

13.6 Error estimates by recovery

13.7 Residual-based methods

13.8 Asymptotic behaviour and robustness of error estimators - the Babuska patch test

13.9 Bounds on quantities of interest

13.10 Which errors should concern us7

13.11 Problems

14 Adaptive finite element refinement

14.1 Introduction

14.2 Adaptive h-refinement

14.3 p-refinement and hp-refinement

14.4 Concluding remarks

14.5 Problems

15 Point-based and partition of unity approximations. Extended finite element methods

15.1 Introduction

15.2 Function approximation

15.3 Moving least squares approximations - restoration of continuity of approximation

15.4 Hierarchical enhancement of moving least squares expansions

15.5 Point collocation - finite point methods

15.6 Galerkin weighting and finite volume methods

15.7 Use of hierarchic and special functions based on standard finite elements satisfying the partition of unity requirement

15.8 Concluding remarks

15.9 Problems

16 The time dimension - semi-discretization of field and dynamic problems and analytical solution procedures

16.1 Introduction

16.2 Direct formulation of time-dependent problems with spatial finite element subdivision

16.3 General classification

16.4 Free response - eigenvalues for second-order problems and dynamic vibration

16.5 Free response - eigenvalues for first-order problems and heat conduction, etc.

16.6 Free response - damped dynamic eigenvalues

16.7 Forced periodic response

16.8 Transient response by analytical procedures

16.9 Symmetry and repeatability

16.10 Problems

17 The time dimension - discrete approximation in time

17.1 Introduction

17.2 Simple time-step algorithms for the first-order equation

17.3 General single-step algorithms for first- and second-order equations

17.4 Stability of general algorithms

17.5 Multistep recurrence algorithms

17.6 Some remarks on general performance of numerical algorithms

17.7 Time discontinuous Galerkin approximation

17.8 Concluding remarks

17.9 Problems

18 Coupled systems

18.1 Coupled problems - definition and classification

18.2 Fluid-structure interaction （Class I problems）

18.3 Soil-pore fluid interaction （Class II problems）

18.4 Partitioned single-phase systems - implicit-explicit partitions （Class I problems）

18.5 Staggered solution processes

18.6 Concluding remarks

19 Computer procedures for finite element analysis

19.1 Introduction

19.2 Pre-processing module: mesh creation

19.3 Solution module

19.4 Post-processor module

19.5 User modules

Appendix A: Matrix algebra

Appendix B: Tensor-indicial notation in the approximation of elasticity problems

Appendix C: Solution of simultaneous linear algebraic equations

Appendix D: Some integration formulae for a triangle

Appendix E: Some integration formulae for a tetrahedron

Appendix F: Some vector algebra

Appendix G: Integration by parts in two or three dimensions （Green's theorem）

Appendix H: Solutions exact at nodes

Appendix I: Matrix diagonalization or lumping

Author index

Subject index