有限元方法固体力学和结构力学 第6版PDF电子书下载

1．General problems in solid mechanics and non-linearity 1

1.1 Introduction 1

1.2 Small deformation solid mechanics problems 4

1.3 Variational forms for non-linear elasticity 12

1.4 Weak forms of governing equations 14

1.5 Concluding remarks 15

References 15

2．Galerkin method of approximation-irreducible and mixed forms 17

2.1 Introduction 17

2.2 Finite element approximation-Galerkin method 17

2.3 Numerical integration-quadrature 22

2.4 Non-linear transient and steady-state problems 24

2.5 Boundary conditions:non-linear problems 28

2.6 Mixed or irreducible forms 33

2.7 Non-linear quasi-harmonic field problems 37

2.8 Typical examples of transient non-linear calculations 38

2.9 Concluding remarks 43

References 44

3．Solution of non-linear algebraic equations 46

3.1 Introduction 46

3.2 Iterative techniques 47

3.3 General remarks-incremental and rate methods 58

References 60

4．Inelastic and non-linear materials 62

4.1 Introduction 62

4.2 Viscoelasticity-history dependence of deformation 63

4.3 Classical time-independent plasticity theory 72

4.4 Computation of stress increments 80

4.5 Isotxopic plasticity models 85

4.6 Generalized plasticity 92

4.7 Some examples of plastic computation 95

4.8 Basic formulation of creep problems 100

4.9 Viscoplasticity-a generalization 102

4.10 Some special problems of brittle materials 107

4.11 Non-uniqueness and localization in elasto-plastic deformations 112

4.12 Non-linear quasi-harmonic field problems 116

4.13 Concluding remarks 118

References 120

5．Geometrically non-linear problems-finite deformation 127

5.1 Introduction 127

5.2 Governing equations 128

5.3 Variational description for finite deformation 135

5.4 Two-dimensional forms 143

5.5 A three-field,mixed finite deformation formulation 145

5.6 A mixed-enhanced finite deformation formulation 150

5.7 Forces dependent on deformation-pressure loads 154

5.8 Concluding remarks 155

References 156

6．Material constitution for finite deformation 158

6.1 Introduction 158

6.2 Isotropic elasticity 158

6.3 Isotropic viscoelasticity 172

6.4 Plasticity models 173

6.5 Incremental formulations 174

6.6 Rate constitutive models 176

6.7 Numerical examples 178

6.8 Concluding remarks 185

References 189

7．Treatment of constraints-contact and tied interfaces 191

7.1 Introduction 191

7.2 Node-node contact:Hertzian contact 193

7.3 Tied interfaces 197

7.4 Node-surface contact 200

7.5 Surface-surface contact 218

7.6 Numerical examples 219

7.7 Concluding remarks 224

References 224

8．Pseudo-rigid and rigid-flexible bodies 228

8.1 Introduction 228

8.2 Pseudo-rigid motions 228

8.3 Rigid motions 230

8.4 Connecting a rigid body to a flexible body 234

8.5 Multibody coupling by joints 237

8.6 Numerical examples 240

References 242

9．Discrete element methods 245

9.1 Introduction 245

9.2 Early DEM formulations 247

9.3 Contact detection 250

9.4 Contact constraints and boundary conditions 256

9.5 Block deformability 260

9.6 Time integration for discrete element methods 267

9.7 Associated discontinuous modelling methodologies 270

9.8 Unifying aspects of discrete element methods 271

9.9 Concluding remarks 272

References 273

10．Structural mechanics problems in one dimension-rods 278

10.1 Introduction 278

10.2 Governing equations 279

10.3 Weak(Galerkin)forms for rods 285

10.4 Finite element solution:Euler-Bernoulli rods 290

10.5 Finite element solution:Timoshenko rods 305

10.6 Forms without rotation parameters 317

10.7 Moment resisting frames 319

10.8 Concluding remarks 320

References 320

11．Plate bending approximation:thin(Kirchhoff)plates and C1 continuity requirements 323

11.1 Introduction 323

11.2 The plate problem:thick and thin formulations 325

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

11.4 Quadrilateral and parallelogram elements 340

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 requirement 346

11.8 Numerical examples 348

11.9 General remarks 357

11.10 Singular shape functions for the simple triangular element 357

11.11 An 18 degree-of-freedom triangular element with conforming shape functions 360

11.12 Compatible quadrilateral elements 361

11.13 Quasi-conforming elements 362

11.14 Hermitian rectangle shape function 363

11.15 The 21 and 18 degree-of-freedom triangle 364

11.16 Mixed formulations-general remarks 366

11.17 Hybrid plate elements 368

11.18 Discrete Kirchhoff constraints 369

11.19 Rotation-free elements 371

11.20 Inelastic material behaviour 374

11.21 Concluding remarks-which elements? 376

References 376

12．'Thick'Reissner-Mindlin plates-irreducible and mixed formulations 382

12.1 Introduction 382

12.2 The irreducible formulation-reduced integration 385

12.3 Mixed formulation for thick plates 390

12.4 The patch test for plate bending elements 392

12.5 Elements with discrete collocation constraints 397

12.6 Elements with rotational bubble or enhanced modes 405

12.7 Linked interpolation-an improvement of accuracy 408

12.8 Discrete'exact'thin plate limit 413

12.9 Pefformance of various'thick'plate elements-limitations of thin plate theory 415

12.10 Inelastic material behaviour 419

12.11 Concluding remarks-adaptive refinement 420

References 421

13．Shells as an assembly of flat elements 426

13.1 Introduction 426

13.2 Stiffness of a plane element in local coordinates 428

13.3 Transformation to global coordinates and assembly of elements 429

13.4 Local direction cosines 431

13.5 'Drilling'rotational stiffness-6 degree-of-freedom assembly 435

13.6 Elements with mid-side slope connections only 440

13.7 Choice of element 440

13.8 Practical examples 441

References 450

14．Curved rods and axisymmetric shells 454

14.1 Introduction 454

14.2 Straight element 454

14.3 Curved elements 461

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

References 473

15．Shells as a special case of three-dimensional analysis-Reissner-Mindlin assumptions 475

15.1 Introduction 475

15.2 Shell element with displacement and rotation paranrters 475

15.3 Special case of axisymmetric,curved,thick shells 484

15.4 Special case of thick plates 487

15.5 Convergence 487

15.6 Inelastic behaviour 488

15.7 Some shell examples 488

15.8 Concluding remarks 493

References 495

16．Semi-analytical finite element processes-use of orthogonal functions and'finite strip'methods 498

16.1 Introduction 498

16.2 Prismatic bar 501

16.3 Thin membrane box structures 504

16.4 Plates and boxes with flexure 505

16.5 Axisymmetric solids with non-symmetrical load 507

16.6 Axisymmetric shells with non-symmetrical load 510

16.7 Concluding remarks 514

References 515

17．Non-linear structural problems-large displacement and instability 517

17.1 Introduction 517

17.2 Large displacement theory of beams 517

17.3 Elastic stability-energy interpretation 523

17.4 Large displacement theory of thick plates 526

17.5 Large displacement theory of thin plates 532

17.6 Solution of large deflection problems 534

17.7 Shells 537

17.8 Concluding remarks 542

References 543

18．Multiscale modelling 547

18.1 Introduction 547

18.2 Asymptotic analysis 549

18.3 Statement of the problem and assumptions 550

18.4 Formalism of the homogenization procedure 552

18.5 Global solution 553

18.6 Local approximation of the stress vector 554

18.7 Finite element analysis applied to the local problem 555

18.8 The non-linear case and bridging over several scales 560

18.9 Asymptotic homogenization at three levels:micro,meso and macro 561

18.10 Recovery of the micro description of the variables of the problem 562

18.11 Material characteristics and homogenization results 565

18.12 Multilevel procedures which use homogenization as an ingredient 567

18.13 General first-order and second-order procedures 570

18.14 Discrete-to-continuum linkage 572

18.15 Local analysis of a unit cell 578

18.16 Homogenization procedure-definition of successive yield surfaces 578

18.17 Numerically developed global self-consistent elastic-plastic constitutive law 580

18.18 Global solution and stress-recovery procedure 581

18.19 Concluding remarks 586

References 587

19．Computer procedures for finite element analysis 590

19.1 Introduction 590

19.2 Solution of non-linear problems 591

19.3 Eigensolutions 592

19.4 Restart option 594

19.5 Concluding remarks 595

References 595

Appendix A Isoparametric finite element approximations 597

Appendix B Invariants of second-order tensors 604

Author index 609

Subject index 619