有限元方法基础理论
2008-9
世界图书出版公司
监凯维奇
733
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it is thirty-eight years since the The Finite Element Method in Structural and ContinuumMechanics was first published. This book， which was the first dealing with the finiteelement method， provided the basis from which many further developments occurred.
This book is dedicated to our wives Helen, Mary Lou and Song and our families for their support and patience during the preparation of this book, and also to all of our students and colleagues who over the years have contributed to our knowledge of the finite element method. In particular we would like to mention Professor Eugenio Oniate and his group at CIMNE for their help, encouragement and support during the preparation process.
Preface1 The standard discrete system and origins of the finite element method 1.1 Introduction 1.2 The structural 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 Problems2 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 Problems3 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 Vitual work as the 'weak form' of equilibrium equations for analysis of solids or fluids 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, differentaal 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 3.13 Least squares approximations 3.14 Concluding remarks - finite difference and boundary methods 3.15 Problems4 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 dements - '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 dements 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 Problems5 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 ε, η, ζ coordinates 5.6 Evaluation of element matrices. Transformation in area and volumecoordinates 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 Problems6 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 Problems7 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 Problems8 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 Problems9 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 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 dements 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 Problems10 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-fidd 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 Problems11 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-~o 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 Problems12 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 Problems13 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 us? 13.11 Problems14 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 Problems15 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 Problems16 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 Problems17 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 Problems18 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 remarks19 Computer procedures for finite dement analysis 19.1 Introduction 19.2 Pre-processing module: mesh creation 19.3 Solution module 19.4 Post-processor module 19.5 User modulesAppendix A: Matrix algebraAppendix B: Tensor-indicial notation in the approximation of elasticity problemsAppendix C: Solution of simultaneous linear algebraic equationsAppendix D: Some integration formulae for a triangleAppendix E: Some integration formulae for a tetrahedronAppendix F: Some vector algebraAppendix G: Integration by parts in two or three dimensions (Green's theorem)Appendix H: Solutions exact at nodesAppendix I: Matrix diagonalization or lumpingAuthor indexSubject index
《有限元方法基础论第6版》适合的读者对象为计算力学、力学、土木、水利、机械、航天航空等领域的专家、教授、工程技术人员和研究生。
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这本书是有限元鼻祖写的纯有关有限元理论的书，值得收藏
这本书是纯有关有限元的数学理论的书，阅读时英语要好，因此，正在学习中。
有限元的经典理论著作，等待已久，书拿到还没来得及看，不第一版增加了很多内容。
有限元法鼻祖写的经典教程 很赞
经典有限元书籍，字再大些就好了。
昨天刚拿到书，当当的包装很一般。但打开一看，书完整无缺。大致地看了一下目录，感觉这就是我要买的有限元书。从今天开始要好好研读一下这本。
有限元中的经典三部曲啊~~
不是很大的一本书，但挺厚的，纸张还可以，挺清晰的，就是字小了点，看的有点累~~
前辈推荐的，看样子要花不少时间研读，如果能学习到对于有限元那是非常有帮助的。
监科维奇的这本书，是有限元的经典大作，通俗易懂，学习有限元的好教材！
我是跟第5版对照看看
最基础的教材，适合入门学习和研究
大师的书籍，如果英语基础好的话还是很推荐看下。
这个书不用说了，大师级的著作。
送货迅速,质量很不错
正版书籍，印刷质量很好！送货速度快
好书，英文经典就是不一样。但是希望当当网多留点时间给我们。这种专业书，不可能5天就看完的。反馈的时间要求太紧了。
有限元鼻祖写的,这本书是纯有关有限元理论的书，值得收藏
英文版，顺便可以学习一些专业词汇，书的质量很不错
属于部头比较大的书目~用下心读应该会有不小的收获
期待很久，附录H有误
经典名著，值得收藏，值得细读
收藏级
专业经典著作
经典专著，必学
书籍不错，值得收藏的好书
工具书应该是正规出版社的，包装很严实，书没受到任何损伤。很满意，下次需要购书时，还会光临的。
看书就要看原版的
很经典的一本书，值得拥有
刚收到，很喜欢，希望有用。
看过第五版，第六版的电子版也有，国外图书太贵，没买纸质版，现在国内出了影版，很不错，有限元鼻祖写的书，从事计算力学的都值得一看！
还在学习有限元知识，工科的，这本书纯理论，看起来很不舒服~
影印版，书质量着实一般，但关键在于经典~~
唯一的缺点是字体有点小 纸张不薄
书没细看，感觉不错，值得收藏
英文的虽然经典，但是看起来确实很费时间。
非常不错，很经典，收藏了
非常经典，需要慢慢细读……封面有折皱，不知道这次送货出什么状况？
字体有点小！其他还行。
刚刚收到这本书，很高兴，不是想象中的字很小、纸张很差什么的，字的大小我可以接受，纸张质量很不错了，只是书的一角有些折了，总体上还是不错的。
这本书总体上说还挺好的，值得推荐。缺点就是就是字迹太小，有点累眼睛，希望以后能得到改善，谢谢当当呵呵。
这本书挺好,不过字体很小!
内容不错，但是版面太小，字迹很小，伤眼睛啊
拿到Zienkiewiczandtaylor有限元方法基出理论第六版和拿到前几给我的感觉有点不一样，我从这本书的第三版读了第六版，书越来越厚，内容截越来越详实，同样价格也越来越高。第六版式的印发不好，有些页面没有公式印的看不清楚。只希望原版书引进来再印发的时候，能提高印发质量。
内容不错，影印版，纸张很差
没详细询问书的质量，应该还可以
在网上买书，确实是图方便，但却不想书的质量不好。在图片中可以看到封面的别致精美，但是到手后，发现纸张质量与盗版无异。给人的感觉是买了盗版。并且无疑这会影响阅读者的心情。如果没有改进，我不会再买这一类影印书！
今天刚收到书，印刷的字迹还是比较清楚，就是纸质太烂，让人感觉很不爽。这本书绝对是经典。
这些书是不是存货，脏的不行，完全看不出是新书。