有限元方法固體力學和結(jié)構(gòu)力學

作者：(英國)監(jiān)凱維奇 (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: 世界圖書出版公司; 第6版 (2009年1月1日)

平裝: 631頁

正文語種: 英語

開本: 24

ISBN: 9787506292559

條形碼: 9787506292559

尺寸: 22.4 x 14.8 x 3 cm

重量: 821 g

《有限元方法固體力學和結(jié)構(gòu)力學(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。

結(jié)構(gòu)力學是一門古老的學科，又是一門迅速發(fā)展的學科。新型工程材料和新型工程結(jié)構(gòu)的大量出現(xiàn)，向結(jié)構(gòu)力學提供了新的研究內(nèi)容并提出新的要求。計算機的發(fā)展，又為結(jié)構(gòu)力學提供了有力的計算工具。另一方面，結(jié)構(gòu)力學對數(shù)學及其他學科的發(fā)展也起了推動作用。有限元法這一數(shù)學方法的出現(xiàn)和發(fā)展就和結(jié)構(gòu)力學的研究有密切關(guān)系。在固體力學領(lǐng)域中，材料力學給結(jié)構(gòu)力學提供了必要的基本知識，彈性力學和塑性力學是結(jié)構(gòu)力學的理論基礎(chǔ)。另外，結(jié)構(gòu)力學與流體力學相結(jié)合形成邊緣學科——結(jié)構(gòu)流體彈性力學。

評定結(jié)構(gòu)的優(yōu)劣，從力學角度看，主要是結(jié)構(gòu)的強度和剛度。工程結(jié)構(gòu)設(shè)計既要保證結(jié)構(gòu)有足夠的強度，又要保證它有足夠的剛度。強度不夠，結(jié)構(gòu)容易破壞；剛度不夠，結(jié)構(gòu)容易皺損，或出現(xiàn)較大的振動，或產(chǎn)生較大的變形。皺損能夠?qū)е陆Y(jié)構(gòu)的變形破壞，振動能夠縮短結(jié)構(gòu)的使用壽命，皺損、振動、變形都會影響結(jié)構(gòu)的使用性能，例如，降低機床的加工精度或減低控制系統(tǒng)的效率等。

觀察自然界中的天然結(jié)構(gòu)，如植物的根、莖和葉，動物的骨骼，蛋類的外殼，可以發(fā)現(xiàn)它們的強度和剛度不僅與材料有關(guān)，而且和它們的造型有密切的關(guān)系。很多工程結(jié)構(gòu)是受到天然結(jié)構(gòu)的啟發(fā)而創(chuàng)制出來的。人們在結(jié)構(gòu)力學研究的基礎(chǔ)上，不斷創(chuàng)造出新的結(jié)構(gòu)造型。加勁結(jié)構(gòu)(見加勁板殼)、夾層結(jié)構(gòu)(見夾層板殼)等都是強度和剛度比較高的結(jié)構(gòu)。結(jié)構(gòu)設(shè)計不僅要考慮結(jié)構(gòu)的強度和剛度，還要做到用料省、重量輕。減輕重量對某些工程尤為重要，如減輕飛機的重量就可以使飛機航程遠、上升快、速度大、能耗低。

結(jié)構(gòu)力學——靜定結(jié)構(gòu)力學課程定位

結(jié)構(gòu)力學——靜定結(jié)構(gòu)力學課程是一門理論與實踐相結(jié)合的課程，通過對幾何構(gòu)造分析、靜定結(jié)構(gòu)的受力分析、虛功原理與結(jié)構(gòu)位移計算等內(nèi)容的學習，使學習者具備對靜定結(jié)構(gòu)進行內(nèi)力和位移計算的能力，以及自學和閱讀結(jié)構(gòu)力學教學參考書的能力。

結(jié)構(gòu)力學——靜定結(jié)構(gòu)力學適應(yīng)專業(yè)

結(jié)構(gòu)力學——靜定結(jié)構(gòu)力學課程適合土木工程、水利類工程等專業(yè)學習。

2019年1月8日，結(jié)構(gòu)力學——靜定結(jié)構(gòu)力學課程被中華人民共和國教育部認定為“國家精品在線開放課程”。