Non-linear finite element analysis of solids and structures

Library	Item Barcode	Call Number	Material Type	Item Category 1	Status
Searching... PSZ JB	30000010306141	TA647 N66 2012	Open Access Book	Book	Searching... Unknown
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Built upon the two original books by Mike Crisfield and their own lecture notes, renowned scientist René de Borst and his team offer a thoroughly updated yet condensed edition that retains and builds upon the excellent reputation and appeal amongst students and engineers alike for which Crisfield's first edition is acclaimed.

Together with numerous additions and updates, the new authors have retained the core content of the original publication, while bringing an improved focus on new developments and ideas. This edition offers the latest insights in non-linear finite element technology, including non-linear solution strategies, computational plasticity, damage mechanics, time-dependent effects, hyperelasticity and large-strain elasto-plasticity.

The authors' integrated and consistent style and unrivalled engineering approach assures this book's unique position within the computational mechanics literature.

Key features:

Combines the two previous volumes into one heavily revised text with obsolete material removed, an improved layout and updated references and notations Extensive new material on more recent developments in computational mechanics Easily readable, engineering oriented, with no more details in the main text than necessary to understand the concepts. Pseudo-code throughout makes the link between theory and algorithms, and the actual implementation. Accompanied by a website (www.wiley.com/go/deborst) with a Python code, based on the pseudo-code within the book and suitable for solving small-size problems.

Non-linear Finite Element Analysis of Solids and Structures, 2nd Edition is an essential reference for practising engineers and researchers that can also be used as a text for undergraduate and graduate students within computational mechanics.

Author Notes

Mike Crisfield (deceased), Imperial College, London; René de Borst, Joris Remmers & Clemens Verhoosel, TU Eindhoven, Netherlands

Professor Mike Crisfield (deceased) joined the Transport & Road Research Laboratory (TRRL) in 1971, where he rose to the rank of Deputy Chief Scientific Officer. In 1989 he was appointed as first holder of the FEA Chair in Computational Mechanics in the aeronautics department at Imperial College, London, the department that had pioneered FEA in the 1950s and 1960s. Shortly before he died, a list of the most cited engineering researchers in the UK was published included Mike in the top 20, and he received an IACM Research Achievement Award in recognition of his extraordinary achievements in the field of non-linear computational mechanics. An eminent researcher and a scholar, he was reputed as an innovative thinker who adopted a 'hands-on' approach.

René de Borst was appointed Dean and Distinguished University Professor of the Faculty of Mechanical Engineering of TU Eindhoven in May 2007 after a long tenure as Professor and deputy Dean at TU Delft. He is Editor for the International Journal for Numerical Methods in Engineering and International Journal for Numerical and Analytical Methods in Geomechanics and Editor for the Encyclopedia of Computational Mechanics. His many awards and the outstanding assessment of his work by the scientific community attest to his reputation as a world leading scientist and researcher within the field of computational mechanics.

Joris Remmers is an assistant professor within René de Borst's group at TU Eindhoven.

Clemens Verhoosel is an assistant professor within René de Borst's group at TU Eindhoven.

Part 1 Basic Concepts and Solution Techniques	p. 21
1 Preliminaries	p. 23
1.1 A simple example of non-linear behaviour	p. 23
1.2 A review of concepts from linear algebra	p. 25
1.3 Vectors and tensors	p. 32
1.4 Stress and strain tensors	p. 36
1.5 Elasticity	p. 42
1.6 The PYFEM finite element library 44 Bibliography	p. 48
2 Non-linear finite element analysis	p. 49
2.1 Equilibrium and virtual work	p. 49
2.2 Spatial discretisation by finite elements	p. 51
2.3 PyFEM: Shape function utilities	p. 55
2.4 Incremental-iterative analysis	p. 59
2.5 Load vs displacement control	p. 68
2.6 PyFEM: A linear finite element code with displacement control 71 Bibliography	p. 80
3 Geometrically non-linear analysis	p. 81
3.1 Truss elements	p. 82
3.1.1 Total Lagrange formulation	p. 85
3.1.2 Updated Lagrange formulation	p. 88
3.1.3 Corotational formulation	p. 89
3.2 PyFEM: The shallow truss problem	p. 94
3.3 Stress and deformation measures in continua	p. 103
3.4 Geometrically non-linear formulation of continuum elements	p. 109
3.4.1 Total and Updated Lagrange formulations	p. 109
3.4.2 Corotational formulation	p. 113
3.5 Linear buckling analysis	p. 117
3.6 PyFEM: A geometrically non-linear continuum element 119 Bibliography	p. 127
4 Solution techniques in quasi-static analysis	p. 129
4.1 Line searches 129 2 Contents
4.2 Path-following or arc-length methods	p. 132
4.3 PYFEM: Implementation of Riks' arc-length solver	p. 140
4.4 Stability and uniqueness in discretised systems	p. 145
4.4.1 Stability of a discrete system	p. 145
4.4.2 Uniqueness and bifurcation in a discrete system	p. 146
4.4.3 Branch switching	p. 150
4.5 Load stepping and convergence criteria	p. 150
4.6 Quasi-Newton methods 153 Bibliography	p. 156
5 Solution techniques for non-linear dynamics	p. 157
5.1 The semi-discrete equations	p. 157
5.2 Explicit time integration	p. 159
5.3 PYFEM: Implementation of an explicit solver	p. 162
5.4 Implicit time integration	p. 167
5.4.1 The Newmark family	p. 167
5.4.2 The HHT _-method	p. 168
5.4.3 Alternative implicit methods for time integration	p. 169
5.5 Stability and accuracy in the presence of non-linearities	p. 171
5.6 Energy-conserving algorithms	p. 175
5.7 Time step size control and element technology 178 Bibliography	p. 179
Part 2 Material Non-linearities	p. 181
6 Damage mechanics	p. 183
6.1 The concept of damage	p. 183
6.2 Isotropic elasticity-based damage	p. 185
6.3 PYFEM: A plane-strain damage model	p. 188
6.4 Stability, ellipticity, and mesh sensitivity	p. 192
6.4.1 Stability, ellipticity, and mesh sensitivity	p. 192
6.4.2 Mesh sensitivity	p. 195
6.5 Cohesive-zone models	p. 198
6.6 Element technology: Embedded discontinuities	p. 203
6.7 Complex damage models	p. 211
6.7.1 Anisotropic damage models	p. 211
6.7.2 Microplane models	p. 212
6.8 Crack models for concrete and other quasi-brittle materials	p. 214
6.8.1 Elasticity-based smeared crack models	p. 214
6.8.2 Reinforcement and tension stiffening	p. 219
6.9 Regularised damage models	p. 223
6.9.1 Non-local damage models	p. 223
6.9.2 Gradient damage models 224 Bibliography	p. 227
7 Plasticity 231 Contents	p. 3
7.1 A simple slip model	p. 231
7.2 Flow theory of plasticity	p. 235
7.2.1 Yield function	p. 235
7.2.2 Flow rule	p. 240
7.2.3 Hardening behaviour	p. 244
7.3 Integration of the stress-strain relation	p. 250
7.4 Tangent stiffness operators	p. 261
7.5 Multi-surface plasticity	p. 264
7.5.1 Koiter's generalisation	p. 264
7.5.2 Rankine plasticity for concrete	p. 267
7.5.3 Tresca and Mohr-Coulomb plasticity	p. 272
7.6 Soil plasticity: Cam-clay model	p. 279
7.7 Coupled damage-plasticity models	p. 282
7.8 Element technology: volumetric locking 283 Bibliography	p. 289
8 Time-dependent material models	p. 293
8.1 Linear visco-elasticity	p. 293
8.1.1 One-dimensional linear visco-elasticity	p. 293
8.1.2 Three-dimensional visco-elasticity	p. 296
8.1.3 Algorithmic aspects	p. 297
8.2 Creep models	p. 299
8.3 Visco-plasticity	p. 301
8.3.1 One-dimensional visco-plasticity	p. 302
8.3.2 Integration of the rate equations	p. 303
8.3.3 Perzyna visco-plasticity	p. 304
8.3.4 Duvaut-Lions visco-plasticity	p. 306
8.3.5 Consistency model	p. 308
8.3.6 Propagative or dynamic instabilities	p. 310
Bibliography	p. 315
Part 3 Structural Elements	p. 317
9 Beams and arches	p. 319
9.1 A shallow arch	p. 319
9.1.1 Kirchhoff formulation	p. 319
9.1.2 Including shear deformation: Timoshenko beam	p. 326
9.2 PYFEM: A Kirchhoff beam element	p. 329
9.3 Corotational elements	p. 333
9.3.1 Kirchhoff theory	p. 333
9.3.2 Timoshenko beam theory	p. 337
9.4 An isoparametric degenerate continuum 2D beam element	p. 339
9.5 An isoparametric degenerate continuum 3D beam element	p. 344
Bibliography	p. 352
10 Plates and shells	p. 355
4 Contents
10.1 Shallow-shell formulations	p. 356
10.2 An isoparametric degenerate continuum shell element	p. 363
10.3 Solid-like shell elements	p. 368
10.4 Shell plasticity: Ilyushin's criterion	p. 369
Bibliography	p. 373
Part 4 Large Strains	p. 375
11 Hyperelasticity	p. 377
11.1 More continuum mechanics	p. 377
11.1.1 Momentum balance and stress tensors	p. 377
11.1.2 Objective stress rates	p. 380
11.1.3 Principal stretches and invariants	p. 384
11.2 Strain-energy functions	p. 386
11.2.1 Incompressibility and near-incompressibility	p. 388
11.2.2 Strain energy as a function of stretch invariants	p. 390
11.2.3 Strain energy as a function of principal stretches	p. 394
11.2.4 Logarithmic extension of linear elasticity: Hencky model	p. 398
11.3 Element technology	p. 400
11.3.1 u/p formulation	p. 401
11.3.2 Enhanced Assumed Strain elements	p. 404
11.3.3 F-bar approach	p. 406
11.3.4 Corotational approach	p. 407
Bibliography	p. 409
12 Large-strain elastoplasticity	p. 411
12.1 Eulerian formulations	p. 412
12.2 Multiplicative elastoplasticity	p. 417
12.3 Multiplicative elastoplasticity vs rate formulations	p. 421
12.4 Integration of the rate equations	p. 424
12.5 Exponential return-mapping algorithms	p. 428
Bibliography	p. 432
Part 5 Advanced Discretisation Concepts	p. 435
13 Interfaces and discontinuities	p. 437
13.1 Interface elements	p. 437
13.2 Discontinuous Galerkin methods 446 Bibliography	p. 450
14 Meshless and partition-of-unity methods	p. 451
14.1 Meshless methods	p. 452
14.1.1 The element-free Galerkin method	p. 452
14.1.2 Application to fracture	p. 456
14.1.3 Higher-order damage mechanics 458 Contents	p. 5
14.1.4 Volumetric locking	p. 460
14.2 Partition-of-unity approaches	p. 461
14.2.1 Application to fracture	p. 465
14.2.2 Extension to large deformations	p. 470
14.2.3 Dynamic fracture	p. 476
14.2.4 Weak discontinuities	p. 479
Bibliography	p. 480
15 Isogeometric finite element analysis	p. 483
15.1 Basis functions in computer aided geometric design	p. 483
15.1.1 Univariate B-splines	p. 484
15.1.2 Univariate non-uniform rational B-splines	p. 487
15.1.3 Multivariate B-splines and NURBS patches	p. 488
15.1.4 T-splines	p. 490
15.2 Isogeometric finite elements	p. 493
15.2.1 B'ezier element representation	p. 493
15.2.2 B'ezier extraction	p. 495
15.3 PYFEM: Shape functions for isogeometric analysis	p. 497
15.4 Isogeometric analysis in non-linear solid mechanics	p. 500
15.4.1 Design-through-analysis of shell structures	p. 500
15.4.2 Higher-order damage models	p. 505
15.4.3 Cohesive-zone models	p. 510
Bibliography	p. 518

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