有限元方法固体力学和结构力学 第6版2025|PDF|Epub|mobi|kindle电子书版本百度云盘下载

有限元方法固体力学和结构力学 第6版PDF格式电子书版下载

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1．General problems in solid mechanics and non-linearity1

1.1 Introduction1

1.2 Small deformation solid mechanics problems4

1.3 Variational forms for non-linear elasticity12

1.4 Weak forms of governing equations14

1.5 Concluding remarks15

References15

2．Galerkin method of approximation-irreducible and mixed forms17

2.1 Introduction17

2.2 Finite element approximation-Galerkin method17

2.3 Numerical integration-quadrature22

2.4 Non-linear transient and steady-state problems24

2.5 Boundary conditions:non-linear problems28

2.6 Mixed or irreducible forms33

2.7 Non-linear quasi-harmonic field problems37

2.8 Typical examples of transient non-linear calculations38

2.9 Concluding remarks43

References44

3．Solution of non-linear algebraic equations46

3.1 Introduction46

3.2 Iterative techniques47

3.3 General remarks-incremental and rate methods58

References60

4．Inelastic and non-linear materials62

4.1 Introduction62

4.2 Viscoelasticity-history dependence of deformation63

4.3 Classical time-independent plasticity theory72

4.4 Computation of stress increments80

4.5 Isotxopic plasticity models85

4.6 Generalized plasticity92

4.7 Some examples of plastic computation95

4.8 Basic formulation of creep problems100

4.9 Viscoplasticity-a generalization102

4.10 Some special problems of brittle materials107

4.11 Non-uniqueness and localization in elasto-plastic deformations112

4.12 Non-linear quasi-harmonic field problems116

4.13 Concluding remarks118

References120

5．Geometrically non-linear problems-finite deformation127

5.1 Introduction127

5.2 Governing equations128

5.3 Variational description for finite deformation135

5.4 Two-dimensional forms143

5.5 A three-field,mixed finite deformation formulation145

5.6 A mixed-enhanced finite deformation formulation150

5.7 Forces dependent on deformation-pressure loads154

5.8 Concluding remarks155

References156

6．Material constitution for finite deformation158

6.1 Introduction158

6.2 Isotropic elasticity158

6.3 Isotropic viscoelasticity172

6.4 Plasticity models173

6.5 Incremental formulations174

6.6 Rate constitutive models176

6.7 Numerical examples178

6.8 Concluding remarks185

References189

7．Treatment of constraints-contact and tied interfaces191

7.1 Introduction191

7.2 Node-node contact:Hertzian contact193

7.3 Tied interfaces197

7.4 Node-surface contact200

7.5 Surface-surface contact218

7.6 Numerical examples219

7.7 Concluding remarks224

References224

8．Pseudo-rigid and rigid-flexible bodies228

8.1 Introduction228

8.2 Pseudo-rigid motions228

8.3 Rigid motions230

8.4 Connecting a rigid body to a flexible body234

8.5 Multibody coupling by joints237

8.6 Numerical examples240

References242

9．Discrete element methods245

9.1 Introduction245

9.2 Early DEM formulations247

9.3 Contact detection250

9.4 Contact constraints and boundary conditions256

9.5 Block deformability260

9.6 Time integration for discrete element methods267

9.7 Associated discontinuous modelling methodologies270

9.8 Unifying aspects of discrete element methods271

9.9 Concluding remarks272

References273

10．Structural mechanics problems in one dimension-rods278

10.1 Introduction278

10.2 Governing equations279

10.3 Weak(Galerkin)forms for rods285

10.4 Finite element solution:Euler-Bernoulli rods290

10.5 Finite element solution:Timoshenko rods305

10.6 Forms without rotation parameters317

10.7 Moment resisting frames319

10.8 Concluding remarks320

References320

11．Plate bending approximation:thin(Kirchhoff)plates and C1 continuity requirements323

11.1 Introduction323

11.2 The plate problem:thick and thin formulations325

11.3 Rectangular element with corner nodes(12 degrees of freedom)336

11.4 Quadrilateral and parallelogram elements340

11.5 Triangular element with corner nodes(9 degrees of freedom)340

11.6 Triangular element of the simplest form(6 degrees of freedom)345

11.7 The patch test-ananalytical requirement346

11.8 Numerical examples348

11.9 General remarks357

11.10 Singular shape functions for the simple triangular element357

11.11 An 18 degree-of-freedom triangular element with conforming shape functions360

11.12 Compatible quadrilateral elements361

11.13 Quasi-conforming elements362

11.14 Hermitian rectangle shape function363

11.15 The 21 and 18 degree-of-freedom triangle364

11.16 Mixed formulations-general remarks366

11.17 Hybrid plate elements368

11.18 Discrete Kirchhoff constraints369

11.19 Rotation-free elements371

11.20 Inelastic material behaviour374

11.21 Concluding remarks-which elements?376

References376

12．'Thick'Reissner-Mindlin plates-irreducible and mixed formulations382

12.1 Introduction382

12.2 The irreducible formulation-reduced integration385

12.3 Mixed formulation for thick plates390

12.4 The patch test for plate bending elements392

12.5 Elements with discrete collocation constraints397

12.6 Elements with rotational bubble or enhanced modes405

12.7 Linked interpolation-an improvement of accuracy408

12.8 Discrete'exact'thin plate limit413

12.9 Pefformance of various'thick'plate elements-limitations of thin plate theory415

12.10 Inelastic material behaviour419

12.11 Concluding remarks-adaptive refinement420

References421

13．Shells as an assembly of flat elements426

13.1 Introduction426

13.2 Stiffness of a plane element in local coordinates428

13.3 Transformation to global coordinates and assembly of elements429

13.4 Local direction cosines431

13.5 'Drilling'rotational stiffness-6 degree-of-freedom assembly435

13.6 Elements with mid-side slope connections only440

13.7 Choice of element440

13.8 Practical examples441

References450

14．Curved rods and axisymmetric shells454

14.1 Introduction454

14.2 Straight element454

14.3 Curved elements461

14.4 Independent slope-displacement interpolation with penalty functions(thick or thin shell formulations)468

References473

15．Shells as a special case of three-dimensional analysis-Reissner-Mindlin assumptions475

15.1 Introduction475

15.2 Shell element with displacement and rotation paranrters475

15.3 Special case of axisymmetric,curved,thick shells484

15.4 Special case of thick plates487

15.5 Convergence487

15.6 Inelastic behaviour488

15.7 Some shell examples488

15.8 Concluding remarks493

References495

16．Semi-analytical finite element processes-use of orthogonal functions and'finite strip'methods498

16.1 Introduction498

16.2 Prismatic bar501

16.3 Thin membrane box structures504

16.4 Plates and boxes with flexure505

16.5 Axisymmetric solids with non-symmetrical load507

16.6 Axisymmetric shells with non-symmetrical load510

16.7 Concluding remarks514

References515

17．Non-linear structural problems-large displacement and instability517

17.1 Introduction517

17.2 Large displacement theory of beams517

17.3 Elastic stability-energy interpretation523

17.4 Large displacement theory of thick plates526

17.5 Large displacement theory of thin plates532

17.6 Solution of large deflection problems534

17.7 Shells537

17.8 Concluding remarks542

References543

18．Multiscale modelling547

18.1 Introduction547

18.2 Asymptotic analysis549

18.3 Statement of the problem and assumptions550

18.4 Formalism of the homogenization procedure552

18.5 Global solution553

18.6 Local approximation of the stress vector554

18.7 Finite element analysis applied to the local problem555

18.8 The non-linear case and bridging over several scales560

18.9 Asymptotic homogenization at three levels:micro,meso and macro561

18.10 Recovery of the micro description of the variables of the problem562

18.11 Material characteristics and homogenization results565

18.12 Multilevel procedures which use homogenization as an ingredient567

18.13 General first-order and second-order procedures570

18.14 Discrete-to-continuum linkage572

18.15 Local analysis of a unit cell578

18.16 Homogenization procedure-definition of successive yield surfaces578

18.17 Numerically developed global self-consistent elastic-plastic constitutive law580

18.18 Global solution and stress-recovery procedure581

18.19 Concluding remarks586

References587

19．Computer procedures for finite element analysis590

19.1 Introduction590

19.2 Solution of non-linear problems591

19.3 Eigensolutions592

19.4 Restart option594

19.5 Concluding remarks595

References595

Appendix A Isoparametric finite element approximations597

Appendix B Invariants of second-order tensors604

Author index609

Subject index619