Finite Element Method for Solid and Structural Mechanics (eBook)

R. L. Taylor, O. C. Zienkiewicz (Autoren)

eBook Download: PDF

2005 | 6. Auflage
736 Seiten
Elsevier Science (Verlag)
978-0-08-045558-7 (ISBN)

Infos

This is the key text and reference for engineers, researchers and senior students dealing with the analysis and modelling of structures - from large civil engineering projects such as dams, to aircraft structures, through to small engineered components. Covering small and large deformation behaviour of solids and structures, it is an essential book for engineers and mathematicians. The new edition is a complete solids and structures text and reference in its own right and forms part of the world-renowned Finite Element Method series by Zienkiewicz and Taylor.

New material in this edition includes separate coverage of solid continua and structural theories of rods, plates and shells, extended coverage of plasticity (isotropic and anisotropic), node-to-surface and 'mortar' method treatments, problems involving solids and rigid and pseudo-rigid bodies, and multi-scale modelling.

* Dedicated coverage of solid and structural mechanics by world-renowned authors, Zienkiewicz and Taylor
* New material including separate coverage of solid continua and structural theories of rods, plates and shells, extended coverage for small and finite deformation, elastic and inelastic material constitution, contact modelling, problems involving solids, rigid and discrete elements, and multi-scale modelling
* Accompanied by online downloadable software

Inhalt

Front Cover 1
The Finite Element Method for Solid and Structural Mechanics 4
Copyright Page 5
Contents 8
Preface 14
Chapter 1. General problems in solid mechanics and non-linearity 18
1.1 Introduction 18
1.2 Small deformation solid mechanics problems 21
1.3 Variational forms for non-linear elasticity 29
1.4 Weak forms of governing equations 31
1.5 Concluding remarks 32
References 32
Chapter 2. Galerkin method of approximation –irreducible and mixed forms 34
2.1 Introduction 34
2.2 Finite element approximation – Galerkin method 34
2.3 Numerical integration – quadrature 39
2.4 Non-linear transient and steady-state problems 41
2.5 Boundary conditions: non-linear problems 45
2.6 Mixed or irreducible forms 50
2.7 Non-linear quasi-harmonic field problems 54
2.8 Typical examples of transient non-linear calculations 55
2.9 Concluding remarks 60
References 61
Chapter 3. Solution of non-linear algebraic equations 63
3.1 Introduction 63
3.2 Iterative techniques 64
3.3 General remarks – incremental and rate methods 75
References 77
Chapter 4. Inelastic and non-linear materials 79
4.1 Introduction 79
4.2 Viscoelasticity – history dependence of deformation 80
4.3 Classical time-independent plasticity theory 89
4.4 Computation of stress increments 97
4.5 Isotropic plasticity models 102
4.6 Generalized plasticity 109
4.7 Some examples of plastic computation 112
4.8 Basic formulation of creep problems 117
4.9 Viscoplasticity – a generalization 119
4.10 Some special problems of brittle materials 124
4.11 Non-uniqueness and localization in elasto-plastic deformations 129
4.12 Non-linear quasi-harmonic field problems 133
4.13 Concluding remarks 135
References 137
Chapter 5. Geometrically non-linear problems – finite deformation 144
5.1 Introduction 144
5.2 Governing equations 145
5.3 Variational description for finite deformation 152
5.4 Two-dimensional forms 160
5.5 A three-field, mixed finite deformation formulation 162
5.6 A mixed–enhanced finite deformation formulation 167
5.7 Forces dependent on deformation– pressure loads 171
5.8 Concluding remarks 172
References 173
Chapter 6. Material constitution for finite deformation 175
6.1 Introduction 175
6.2 Isotropic elasticity 175
6.3 Isotropic viscoelasticity 189
6.4 Plasticity models 190
6.5 Incremental formulations 191
6.6 Rate constitutive models 193
6.7 Numerical examples 195
6.8 Concluding remarks 202
References 206
Chapter 7. Treatment of constraints – contact and tied interfaces 208
7.1 Introduction 208
7.2 Node–node contact: Hertzian contact 210
7.3 Tied interfaces 214
7.4 Node–surface contact 217
7.5 Surface–surface contact 235
7.6 Numerical examples 236
7.7 Concluding remarks 241
References 241
Chapter 8. Pseudo-rigid and rigid–flexible bodies 245
8.1 Introduction 245
8.2 Pseudo-rigid motions 245
8.3 Rigid motions 247
8.4 Connecting a rigid body to a flexible body 251
8.5 Multibody coupling by joints 254
8.6 Numerical examples 257
References 259
Chapter 9. Discrete element methods 262
9.1 Introduction 262
9.2 Early DEM formulations 264
9.3 Contact detection 267
9.4 Contact constraints and boundary conditions 273
9.5 Block deformability 277
9.6 Time integration for discrete element methods 284
9.7 Associated discontinuous modelling methodologies 287
9.8 Unifying aspects of discrete element methods 288
9.9 Concluding remarks 289
References 290
Chapter 10. Structural mechanics problems in one dimension– rods 295
10.1 Introduction 295
10.2 Governing equations 296
10.3 Weak (Galerkin) forms for rods 302
10.4 Finite element solution: Euler–Bernoulli rods 307
10.5 Finite element solution: Timoshenko rods 322
10.6 Forms without rotation parameters 334
10.7 Moment resisting frames 336
10.8 Concluding remarks 337
References 337
Chapter 11. Plate bending approximation: thin (Kirchhoff) plates and C1 continuity requirements 340
11.1 Introduction 340
11.2 The plate problem: thick and thin formulations 342
11.3 Rectangular element with corner nodes (12 degrees of freedom) 353
11.4 Quadrilateral and parallelogram elements 357
11.5 Triangular element with corner nodes (9 degrees of freedom) 357
11.6 Triangular element of the simplest form (6 degrees of freedom) 362
11.7 The patch test– an analytical requirement 363
11.8 Numerical examples 365
11.9 General remarks 374
11.10 Singular shape functions for the simple triangular element 374
11.11 An 18 degree-of-freedom triangular element with conforming shape functions 377
11.12 Compatible quadrilateral elements 378
11.13 Quasi-conforming elements 379
11.14 Hermitian rectangle shape function 380
11.15 The 21 and 18 degree-of-freedom triangle 381
11.16 Mixed formulations – general remarks 383
11.17 Hybrid plate elements 385
11.18 Discrete Kirchhoff constraints 386
11.19 Rotation-free elements 388
11.20 Inelastic material behaviour 391
11.21 Concluding remarks – which elements? 393
References 393
Chapter 12. 'Thick' Reissner-Mindlin plates – irreducible and mixed formulations 399
12.1 Introduction 399
12.2 The irreducible formulation– reduced integration 402
12.3 Mixed formulation for thick plates 407
12.4 The patch test for plate bending elements 409
12.5 Elements with discrete collocation constraints 414
12.6 Elements with rotational bubble or enhanced modes 422
12.7 Linked interpolation– an improvement of accuracy 425
12.8 Discrete 'exact' thin plate limit 430
12.9 Performance of various 'thick' plate elements – limitations of thin plate theory 432
12.10 Inelastic material behaviour 436
12.11 Concluding remarks – adaptive refinement 437
References 438
Chapter 13. Shells as an assembly of flat elements 443
13.1 Introduction 443
13.2 Stiffness of a plane element in local coordinates 445
13.3 Transformation to global coordinates and assembly of elements 446
13.4 Local direction cosines 448
13.5 'Drilling' rotational stiffness – 6 degree-of-freedom assembly 452
13.6 Elements with mid-side slope connections only 457
13.7 Choice of element 457
13.8 Practical examples 458
References 467
Chapter 14. Curved rods and axisymmetric shells 471
14.1 Introduction 471
14.2 Straight element 471
14.3 Curved elements 478
14.4 Independent slope–displacement interpolation with penalty functions (thick or thin shell formulations) 485
References 490
Chapter 15. Shells as a special case of three-dimensional analysis – Reissner–Mindlin assumptions 492
15.1 Introduction 492
15.2 Shell element with displacement and rotation parameters 492
15.3 Special case of axisymmetric, curved, thick shells 501
15.4 Special case of thick plates 504
15.5 Convergence 504
15.6 Inelastic behaviour 505
15.7 Some shell examples 505
15.8 Concluding remarks 510
References 512
Chapter 16. Semi-analytical finite element processes – use of orthogonal functions and 'finite strip' methods 515
16.1 Introduction 515
16.2 Prismatic bar 518
16.3 Thin membrane box structures 521
16.4 Plates and boxes with flexure 522
16.5 Axisymmetric solids with non-symmetrical load 524
16.6 Axisymmetric shells with non-symmetrical load 527
16.7 Concluding remarks 531
References 532
Chapter 17. Non-linear structural problems – large displacement and instability 534
17.1 Introduction 534
17.2 Large displacement theory of beams 534
17.3 Elastic stability – energy interpretation 540
17.4 Large displacement theory of thick plates 543
17.5 Large displacement theory of thin plates 549
17.6 Solution of large deflection problems 551
17.7 Shells 554
17.8 Concluding remarks 559
References 560
Chapter 18. Multiscale modelling 564
18.1 Introduction 564
18.2 Asymptotic analysis 566
18.3 Statement of the problem and assumptions 567
18.4 Formalism of the homogenization procedure 569
18.5 Global solution 570
18.6 Local approximation of the stress vector 571
18.7 Finite element analysis applied to the local problem 572
18.8 The non-linear case and bridging over several scales 577
18.9 Asymptotic homogenization at three levels: micro, meso and macro 578
18.10 Recovery of the micro description of the variables of the problem 579
18.11 Material characteristics and homogenization results 582
18.12 Multilevel procedures which use homogenization as an ingredient 584
18.13 General first-order and second-order procedures 587
18.14 Discrete-to-continuum linkage 589
18.15 Local analysis of a unit cell 595
18.16 Homogenization procedure – definition of successive yield surfaces 595
18.17 Numerically developed global self-consistent elastic–plastic constitutive law 597
18.18 Global solution and stress-recovery procedure 598
18.19 Concluding remarks 603
References 604
Chapter 19. Computer procedures for finite element analysis 607
19.1 Introduction 607
19.2 Solution of non-linear problems 608
19.3 Eigensolutions 609
19.4 Restart option 611
19.5 Concluding remarks 612
References 612
Appendix A. Isoparametric finite element approximations 614
Appendix B. Invariants of second-order tensors 621
Author index 626
Subject index 636
Colour Plates 650

Produkt-Details

• Erscheint lt. Verlag: 9.8.2005
• Sprache: englisch
• Themenwelt: Sachbuch/Ratgeber
• Themenwelt: Mathematik / Informatik ► Mathematik ► Analysis
• Themenwelt: Technik ► Bauwesen
• Themenwelt: Technik ► Maschinenbau
• ISBN-10: 0-08-045558-1 / 0080455581
• ISBN-13: 978-0-08-045558-7 / 9780080455587