有限元方法固体力学和结构力学

作者：(英国)监凯维奇 (Zienkiewicz.O.C)

Preface

1. General problems in solid mechanics and non-linearity

1.1 Introduction

1.2 Small deformation solid mechanics problems

1.3 Variational forms for non-linear elasticity

1.4 Weak forms of governing equations

1.5 Concluding remarks

References

2. Galerkin method of approximation - irreducible and mixed forms

2.1 Introduction

2.2 Finite element approximation - Galerkin method

2.3 Numerical integration - quadrature

2.4 Non-linear transient and steady-state problems

2.5 Boundary conditions: non-linear problems

2.6 Mixed or irreducible forms

2.7 Non-linear quasi-harmonic field problems

2.8 Typical examples of transient non-linear calculations

2.9 Concluding remarks

References

3. Solution of non-linear algebraic equations

3.1 Introduction

3.2 Iterative techniques

3.3 General remarks - incremental and rate methods

References

4. Inelastic and non-linear materials

4.1 Introduction

4.2 Viscoelasticity - history dependence of deformation

4.3 Classical time-independent plasticity theory

4.4 Computation of stress increments

4.5 Isotropic plasticity models

4.6 Generalized plasticity

4.7 Some examples of plastic computation

4.8 Basic formulation of creep problems

4.9 Viscoplasticity - a generalization

4.10 Some special problems of brittle materials

4.11 Non-uniqueness and localization in elasto-plastic deformations

4.12 Non-linear quasi-harmonic field problems

4.13 Concluding remarks

References

5. Geometrically non-linear problems - finite deformation

5.1 Introduction

5.2 Governing equations

5.3 Variational description for finite deformation

5.4 Two-dimensional forms

5.5 A three-field, mixed finite deformation formulation

5.6 A mixed-enhanced finite deformation formulation

5.7 Forces dependent on deformation - pressure loads

5.8 Concluding remarks

References

6. Material constitution for finite deformation

6.1 Introduction

6.2 Isotropic elasticity

6.3 Isotropic viscoelasticity

6.4 Plasticity models

6.5 Incremental formulations

6.6 Rate constitutive models

6.7 Numerical examples

6.8 Concluding remarks

References

7. Treatment of constraints - contact and tied interfaces

7.1 Introduction

7.2 Node-node contact: Hertzian contact

7.3 Tied interfaces

7.4 Node-surface contact

7.5 Surface-surface contact

7.6 Numerical examples

7.7 Concluding remarks

References

8. Pseudo-rigid and rigid-flexible bodies

8.1 Introduction

8.2 Pseudo-rigid motions

8.3 Rigid motions

8.4 Connecting a rigid body to a flexible body

8.5 Multibody coupling by joints

8.6 Numerical examples　References

References

9. Discrete element methods

9.1 Introduction

9.2 Early DEM formulations

9.3 Contact detection

9.4 Contact constraints and boundary conditions

9.5 Block deformability

9.6 Time integration for discrete element methods

9.7 Associated discontinuous modelling methodologies

9.8 Unifying aspects of discrete element methods

9.9 Concluding remarks

References

10. Structural mechanics problems in one dimension - rods

10.1 Introduction

10.2 Governing equations

10.3 Weak (Gaierkin) forms for rods

10.4 Finite element solution: Euler-Bernoulli rods

10.5 Finite element solution: Timoshenko rods

10.6 Forms without rotation parameters

10.7 Moment resisting frames

10.8 Concluding remarks

References

11. Plate bending approximation: thin (Kirchhoff) plates and C1 continuity requirements

11.1 Introduction

11.2 The plate problem: thick and thin formulations

11.3 Rectangular element with corner nodes (12 degrees of freedom)

11.4 Quadrilateral and parallelogram elements

11.5 Triangular element with corner nodes (9 degrees of freedom)

11.6 Triangular element of the simplest form (6 degrees of freedom)

11.7 The patch test - an analytical requirement

11.8 Numerical examples

11.9 General remarks

11.10 Singular shape functions for the simple triangular element

11.11 An I8 degree-of-freedom triangular element with conforming shape functions

11.12 Compatible quadrilateral elements

11.13 Quasi-conforming elemems

11.14 Hermitian rectangle shape function

11.15 The 21 and 18 degree-of-freedom triangle

11.16 Mixed formulations - general remarks

11.17 Hybrid plate elements

11.18 Discrete Kirchhoff constraints

11.19 Rotation-free elements

11.20 Inelastic material behaviour

11.21 Concluding remarks - which elements"para" label-module="para">

References

12. 'Thick' Reissner-Mindlin plates - irreducible and mixed formulations

12.1 Introduction

12.2 The irreducible formulation - reduced integration

12.3 Mixed formulation for thick plates

12.4 The patch test for plate bending elements

12.5 Elements with discrete collocation constraints

12.6 Elements with rotational bubble or enhanced modes

12.7 Linked interpolation - an improvement of accuracy

12.8 Discrete 'exact' thin plate limit

12.9 Performance of various 'thick' plate elements - limitations of thin plate theory

12.10 Inelastic material behaviour

12.11 Concluding remarks-adaptive refinement

References

13. Shells as an assembly of flat elements

13.1 Introduction

13.2 Stiffness of a plane element in local coordinates

13.3 Transformation to global coordinates and assembly of elements

13.4 Local direction cosines

13.5 'Drilling' rotational stiffness - 6 degree-of-freedom assembly

13.6 Elements with mid-side slope connections only

13.7 Choice of element

13.8 Practical examples

References

14. Curved rods and axisymmetric shells

14.1 Introduction

14.2 Straight element

14.3 Curved elements

14.4 Independent slope——displacement interpolation with penalty functions (thick or thin shell formulations)

References

15. Shells as a special case of three-dimensional analysis - Reissner-Mindlin assumptions

15.1 Introduction

15.2 Shell element with displacement and rotation parameters

15.3 Special case of axisymmetric, curved, thick shells

15.4 Special case of thick plates

……

16. Semi-analytical finite element processes - use of orthogonal functions

17. Non-linear structural problems - large displacement and instability

18. Multiscale modelling

19. Computer procedures for finite element analysis

Appendix A Isoparametric finite element approximations

Appendix B Invariants of second-order tensors

Author index

Subject index2100433B

出版社: 世界图书出版公司; 第6版 (2009年1月1日)

平装: 631页

正文语种: 英语

开本: 24

ISBN: 9787506292559

条形码: 9787506292559

尺寸: 22.4 x 14.8 x 3 cm

重量: 821 g

《有限元方法固体力学和结构力学(第6版)》is dedicated to our wives Helen and Mary Lou 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 Onate and his group at CIMNE for their help, encouragement and support during the preparation process。

结构力学是一门古老的学科，又是一门迅速发展的学科。新型工程材料和新型工程结构的大量出现，向结构力学提供了新的研究内容并提出新的要求。计算机的发展，又为结构力学提供了有力的计算工具。另一方面，结构力学对数学及其他学科的发展也起了推动作用。有限元法这一数学方法的出现和发展就和结构力学的研究有密切关系。在固体力学领域中，材料力学给结构力学提供了必要的基本知识，弹性力学和塑性力学是结构力学的理论基础。另外，结构力学与流体力学相结合形成边缘学科——结构流体弹性力学。

评定结构的优劣，从力学角度看，主要是结构的强度和刚度。工程结构设计既要保证结构有足够的强度，又要保证它有足够的刚度。强度不够，结构容易破坏；刚度不够，结构容易皱损，或出现较大的振动，或产生较大的变形。皱损能够导致结构的变形破坏，振动能够缩短结构的使用寿命，皱损、振动、变形都会影响结构的使用性能，例如，降低机床的加工精度或减低控制系统的效率等。

观察自然界中的天然结构，如植物的根、茎和叶，动物的骨骼，蛋类的外壳，可以发现它们的强度和刚度不仅与材料有关，而且和它们的造型有密切的关系。很多工程结构是受到天然结构的启发而创制出来的。人们在结构力学研究的基础上，不断创造出新的结构造型。加劲结构(见加劲板壳)、夹层结构(见夹层板壳)等都是强度和刚度比较高的结构。结构设计不仅要考虑结构的强度和刚度，还要做到用料省、重量轻。减轻重量对某些工程尤为重要，如减轻飞机的重量就可以使飞机航程远、上升快、速度大、能耗低。

结构力学——静定结构力学课程定位

结构力学——静定结构力学课程是一门理论与实践相结合的课程，通过对几何构造分析、静定结构的受力分析、虚功原理与结构位移计算等内容的学习，使学习者具备对静定结构进行内力和位移计算的能力，以及自学和阅读结构力学教学参考书的能力。

结构力学——静定结构力学适应专业

结构力学——静定结构力学课程适合土木工程、水利类工程等专业学习。

2019年1月8日，结构力学——静定结构力学课程被中华人民共和国教育部认定为“国家精品在线开放课程”。