The Finite Element Method for Solid and Structural Mechanics, Sixth Edition

✍ Scribed by O. C. Zienkiewicz, R. L. Taylor

• Publisher: Butterworth-Heinemann
• Year: 2005
• Tongue: English
• Leaves: 648
• Edition: 6
• Category: Library

✦ Synopsis

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

✦ Table of Contents

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