該書綜述了有限元方法的基礎，包括讀者在解決各自存在的工程問題以及理解該知識點更先進的應用所必須了解詳細的基礎理論和工作室實例。為了讓讀者更清晰地了解有限元的研究進展，該版本在內容上作了明顯的重排，將兩個新章節放在前面：弱式；變分形式；多維場問題；網格自動生成；平板彎曲和殼理論；無網格技術的進展。 O.C.Zienkiewicz是有限元數值方法研究的先驅者之一，長期處於世界前沿，對現代數值計算中的有限元法作出了系統性和創造性的開拓和發展，在有限元法許多具方向性的重大進展上都作出了重要貢獻

List of FiguresList of TablesPrefaceCHAPTER 1 The Standard Discrete System and Origins of the Finite Element Method1.1 Introduction1.2 The structural element and the structural system1.3 Assembly and analysis of a structure1.4 The boundary conditions1.5 Electrical and fluid networks1，6 The general pattern1.7 The standard discrete system1.8 Transformation of coordinates1.9 ProblemsReferencesCHAPTER 2 Problems in Linear Elasticity and Fields2.1 Introduction2.2 Elasticity equations2.2.1 Displacement function2.2.2 Strain matrix2.2.3 Stress matrix2.2.4 Equilibrium equations2.2.5 Boundary conditions2.2.6 Initial conditions2.2.7 Transformation of stress and strain2.2.8 Stress—strain relations：Elasticity matrix2.3 General quasi—harmonic equation2.3.1 Governing equations：Flux and continuity2.3.2 Boundary conditions2.3.3 Initial condition2.3.4 Constitutive behavior2.3.5 Irreducible form in φ2.3.6 Anisotropic and isotropic forms for k：Transformations2.3.7 Two—dimensional problems2.4 Concluding remarks2.5 ProblemsReferencesCHAPTER 3 Weak Forms and Finite ElementApproximation：1—D Problems3.1 Weak forms3.2 One—dimensional form of elasticity3.2.1 Weak form of equilibrium equation3.3 Approximation to integral and weak forms：The weighted residual （Galerkin） method3.3.1 Galerkin solution of elasticity equation3.4 Finite element solution3.4.1 Requirements for finite element approximations3.5 Isoparametric form3.5.1 Higher order elements：Lagrange interpolation3.5.2 Integrals on the parent element：Numerical integration3.6 Hierarchical interpolation3.7 Axisymmetric one—dimensional problem3.7.1 Weak form for axisymmetric problem3.7.2 A variational notation3.7.3 Irreducible form for axisymmetric problem3.7.4 Finite element solution3.8 Transient problems3.8.1 Discrete time methods3.8.2 Semi—discretization of the problem3.9 Weak form for one—dimensional quasi—harmonic equation3.9.1 Weak form3.9.2 Finite element solution of quasi—harmonic problem3.9.3 Transient problems3.10 Concluding remarks3.11 ProblemsReferencesCHAPTER 4 Variational Forms and Finite Element Approximation：1—D Problems4.1 Variational principles4.2 ”Natural” variational principles and their relation to governing differential equations4.2.1 Euler equations4.3 Establishment of natural variational principles for linear，self—adjoint differential equations4.4 Maximum，minimum，or a saddle point？4.5 Constrained variational principles4.5.1 Lagrange multipliers4.5.2 Identification of Lagrange multipliers：Forced boundary conditions and modified variational principles4.6 Constrained variational principles：Penalty function and perturbed Lagrangian methods4.6.1 Penalty functions4.6.2 Perturbed Lagrangian4.7 Least squares approximations4.8 Concluding remarks：Finite difference and boundary methods4.9 ProblemsReferencesCHAPTER 5 Field Problems：A Multidimensional Finite Element Method5.1 Field problems：Quasi—harmonic equation5.1.1 Irreducible form5.1.2 Finite element discretization5.1.3 Shape functions for triangle，rectangle，and tetrahedron5.2 Partial discretization：Transient problems5.3 Numerical examples：An assessment of accuracy5.3.1 Torsion of prismatic bars5.3.2 Transient heat conduction5.3.3 Anisotropic seepage5.3.4 Electrostatic and magnetostatic problems5.3.5 Lubrication problems5.3.6 Irrotational and free surface flows5.4 ProblemsReferencesCHAPTER 6 Shape Functions，Derivatives，and Integration6.1 Introduction6.2 Two—dimensional shape functions6.2.1 Shape functions for triangles6.2.2 Shape functions for quadrilaterals6.3 Three—dimensional shape functions6.3.1 Tetrahedral elements6.3.2 Hexagon elements：Brick family6.4 Other simple three—dimensional elements6.5 Mapping：Parametric forms6.6 Order of convergence for mapped elements6.7 Computation of global derivatives6.7.1 Placement of element coordinates6.8 Numerical integration6.8.1 Quadrilateral elements6.8.2 Brick elements6.8.3 Triangular elements6.8.4 Tetrahedral elements6.8.5 Required order of numerical integration6.8.6 Matrix singularity due to numerical integration6.9 Shape functions by degeneration6.9.1 Higher order degenerate elements6.10 Generation of finite element meshes by mapping6.10.1 Blending functions6.10.2 Bezier functions6.11 Computational advantage of numerically integrated finite elements6.12 ProblemsReferencesCHAPTER 7 Elasticity：Two—and Three—Dimensional Finite Elements7.1 Introduction7.2 Elasticity problems：Weak form for equilibrium7.2.1 Displacement method：Irreducible form7.3 Finite element approximation by the Galerkin method7.4 Boundary conditions7.5 Numerical integration and alternate forms7.6 Infinite domains and infinite elements7.6.1 The mapping function7.7 Singular elements by mapping：Use in fracture mechanics，etc7.8 Reporting results：Displacements，strains，and stresses7.9 Discretization error and convergence rate7.10 Minimization of total potential energy7.10.1 Bound on strain energy in a displacement formulation7.10.2 Direct minimization7.11 Finite element solution process7.12 Numerical examples7.12.1 Practical examples7.13 Concluding remarks7.14 ProblemsReferences……CHAPTER 8 The Patch Test，Reduced Integration，and Nonconforming ElementsCHAPTER 9 Mixed Formulation and Constraints：Complete Field MethodsCHAPTER 10 Incompressible Problems，Mixed Methods，and Other Procedures of SolutionCHAPTER 11 Multidomain Mixed ApproximationsCHAPTER 12 The Time Dimension：Semi—Discretization of Field and Dynamic ProblemsCHAPTER 13 Plate Bending Approximation：Thin and Thick PlatesCHAPTER 14 Shells as a Special Case of Three—Dimensional AnalysisCHAPTER 15 Errors，Recovery Processes，and Error EstimatesCHAPTER 16 Adaptive Finite Element RefinementCHAPTER 17 Automatic Mesh GenerationCHAPTER 18 Computer Procedures for Finite Element AnalysisAppendix AAppendix BAppendix CAppendix DAppendix EAppendix FAppendix GAppendix HAuthor IndexSubject Index