Preface |
|
xi | |
|
|
xv | |
|
|
1 | (18) |
|
Nonlinear finite elements in design |
|
|
1 | (3) |
|
Related books and a brief history of nonlinear finite elements |
|
|
4 | (3) |
|
|
7 | (2) |
|
|
9 | (4) |
|
Classification of partial differential equations |
|
|
13 | (5) |
|
|
18 | (1) |
|
Lagrangian and Eulerian finite elements in one dimension |
|
|
19 | (56) |
|
|
19 | (1) |
|
Governing equations for total Lagrangian formulation |
|
|
20 | (7) |
|
Weak form for total Lagrangian formulation |
|
|
27 | (6) |
|
Finite element discretization in total Lagrangian formulation |
|
|
33 | (5) |
|
Element and global matrices |
|
|
38 | (10) |
|
Governing equations for updated Lagrangian formulation |
|
|
48 | (3) |
|
Weak form for updated Lagrangian formulation |
|
|
51 | (1) |
|
Element equations for updated Lagrangian formulation |
|
|
52 | (12) |
|
Governing equations for Eulerian formulation |
|
|
64 | (1) |
|
Weak forms for Eulerian mesh equations |
|
|
65 | (1) |
|
|
66 | (4) |
|
|
70 | (2) |
|
|
72 | (1) |
|
|
72 | (3) |
|
|
75 | (66) |
|
|
75 | (1) |
|
|
76 | (16) |
|
|
92 | (9) |
|
|
101 | (7) |
|
|
108 | (11) |
|
Lagrangian conservation equations |
|
|
119 | (6) |
|
Polar decomposition and frame-invariance |
|
|
125 | (12) |
|
|
137 | (4) |
|
|
141 | (74) |
|
|
141 | (1) |
|
|
142 | (3) |
|
Weak form: principle of virtual power |
|
|
145 | (7) |
|
Updated Lagrangian finite element discretization |
|
|
152 | (10) |
|
|
162 | (23) |
|
Corotational formulations |
|
|
185 | (8) |
|
Total Lagrangian formulation |
|
|
193 | (3) |
|
Total Lagrangian weak form |
|
|
196 | (2) |
|
Finite element semidiscretization |
|
|
198 | (15) |
|
|
213 | (2) |
|
|
215 | (94) |
|
|
215 | (1) |
|
|
216 | (5) |
|
One-dimensional elasticity |
|
|
221 | (4) |
|
|
225 | (15) |
|
One-dimensional plasticity |
|
|
240 | (7) |
|
|
247 | (17) |
|
Hyperelastic-plastic models |
|
|
264 | (10) |
|
|
274 | (3) |
|
|
277 | (17) |
|
Continuum mechanics and constitutive models |
|
|
294 | (14) |
|
|
308 | (1) |
|
Solution methods and stability |
|
|
309 | (84) |
|
|
309 | (1) |
|
|
310 | (7) |
|
Equilibrium solutions and implicit time integration |
|
|
317 | (20) |
|
|
337 | (16) |
|
Stability and continuation methods |
|
|
353 | (16) |
|
|
369 | (15) |
|
|
384 | (8) |
|
|
392 | (1) |
|
Arbitrary Lagrangian Eulerian formulations |
|
|
393 | (58) |
|
|
393 | (2) |
|
|
395 | (7) |
|
Conservation laws in ALE description |
|
|
402 | (1) |
|
|
403 | (1) |
|
|
404 | (4) |
|
Introduction to the Petrov-Galerkin method |
|
|
408 | (9) |
|
Petrov-Galerkin formulation of momentum equation |
|
|
417 | (3) |
|
|
420 | (12) |
|
Linearization of the discrete equations |
|
|
432 | (3) |
|
|
435 | (7) |
|
Numerical example: an elastic-plastic wave propagation problem |
|
|
442 | (1) |
|
|
443 | (8) |
|
|
451 | (58) |
|
|
451 | (2) |
|
|
453 | (8) |
|
Element properties and patch tests |
|
|
461 | (8) |
|
Q4 and volumetric locking |
|
|
469 | (5) |
|
Multi-field weak forms and elements |
|
|
474 | (13) |
|
Multi-field quadrilaterals |
|
|
487 | (4) |
|
One-point quadrature elements |
|
|
491 | (9) |
|
|
500 | (4) |
|
|
504 | (3) |
|
|
507 | (2) |
|
|
509 | (60) |
|
|
509 | (2) |
|
|
511 | (3) |
|
|
514 | (10) |
|
|
524 | (12) |
|
Continuum-based shell implementation |
|
|
536 | (14) |
|
|
550 | (5) |
|
Shear and membrane locking |
|
|
555 | (5) |
|
|
560 | (3) |
|
One-point quadrature elements |
|
|
563 | (3) |
|
|
566 | (3) |
|
|
569 | (46) |
|
|
569 | (1) |
|
Contact interface equations |
|
|
570 | (10) |
|
|
580 | (5) |
|
|
585 | (10) |
|
Finite element discretization |
|
|
595 | (14) |
|
|
609 | (6) |
Appendix 1 Voigt notation |
|
615 | (4) |
Appendix 2 Norms |
|
619 | (3) |
Appendix 3 Element shape functions |
|
622 | (5) |
Glossary |
|
627 | (4) |
References |
|
631 | (10) |
Index |
|
641 | |