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 |  موضوع: كتاب The Finite Element Method - Volume 2 : Solid Mechanics الجمعة 20 ديسمبر 2013, 2:44 pm | |
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The Finite Element Method - Volume 2 : Solid Mechanics
Fifth Edition
O.C. Zienkiewicz, CBE, FRS, FREng
UNESCO Professor of Numerical Methods in Engineering
International Centre for Numerical Methods in Engineering, Barcelona
Emeritus Professor of Civil Engineering and Director of the Institute for
Numerical Methods in Engineering, University of Wales, Swansea
R.L. Taylor
Professor in the Graduate School
Department of Civil and Environmental Engineering
University of California at Berkeley
Berkeley, California
و المحتوى كما يلي :
Preface to Volume 2
General problems in solid mechanics and
non-linearity
Introduction
Small deformation non-linear solid mechanics
problems
Non-linear quasi-harmonic field problems
Some typical examples of transient
non-linear calculations
Concluding remarks
Solution of non-linear algebraic equations
Introduction
Iterative techniques
Inelastic and non-linear materials
Introduction
Viscoelasticity - history dependence of
deformation
Classical time-independent plasticity theory
Computation of stress increments
Isotropic plasticity models
Generalized plasticity - non-associative case
Some examples of plastic computation
Basic formulation of creep problems
Viscoplasticity - a generalization
Some special problems of brittle materials
Non-uniqueness and localization in
elasto-plastic deformations
Adaptive refinement and localization
(slip-line) capture
Non-linear quasi-harmonic field problemsPlate bending approximation: thin
(Kirchhoff) plates and C1 continuity
requirements
Introduction
The plate problem: thick and thin
formulations
Rectangular element with corner nodes (12
degrees of freedom)
Quadrilateral and parallelograpm elements
Triangular element with corner nodes (9
degrees of freedom)
Triangular element of the simplest form (6
degrees of freedom)
The patch test - an analytical requirement
Numerical examples
General remarks
Singular shape functions for the simple
triangular element
An 18 degree-of-freedom triangular element
with conforming shape functions
Compatible quadrilateral elements
Quasi-conforming elements
Hermitian rectangle shape function
The 21 and 18 degree-of-freedom triangle
Mixed formulations - general remarks
Hybrid plate elements
Discrete Kirchhoff constraints
Rotation-free elements
Inelastic material behaviour
Concluding remarks - which elements?
Thick’ Reissner - Mindlin plates - irreducible
and mixed formulations
Introduction
The irreducible formulation - reduced
integrationMixed formulation for thick plates
The patch test for plate bending elements
Elements with discrete collocation constraints
Elements with rotational bubble or enhanced
modes
Linked interpolation - an improvement of
accuracy
Discrete ’exact’ thin plate limit
Performance of various ’thick’ plate elements
- limitations of twin plate theory
Forms without rotation parameters
Inelastic material behaviour
Concluding remarks - adaptive refinement
Shells as an assembly of flat elements
Introduction
Stiffness of a plane element in local
coordinates
Transformation to global coordinates and
assembly of elements
Local direction cosines
’Drilling’ rotational stiffness - 6
degree-of-freedom assembly
Elements with mid-side slope connections
only
Choice of element
Practical examples
Axisymmetric shells
Introduction
Straight element
Curved elements
Independent slope - displacement
interpolation with penalty functions (thick or
thin shell formulations)Shells as a special case of
three-dimensional analysis -
Reissner-Mindlin assumptions
Introduction
Shell element with displacement and rotation
parameters
Special case of axisymmetric, curved, thick
shells
Special case of thick plates
Convergence
Inelastic behaviour
Some shell examples
Concluding remarks
Semi-analytical finite element processes -
use of orthogonal functions and ’finite strip’
methods
Introduction
Prismatic bar
Thin membrane box structures
Plates and boxes and flexure
Axisymmetric solids with non-symmetrical
load
Axisymmetric shells with non-symmetrical
load
Finite strip method - incomplete decoupling
Concluding remarks
Geometrically non-linear problems - finite
deformation
Introduction
Governing equations.
Variational description for finitite deformation
A three-field mixed finite deformation
forumationA mixed-enhanced finite deformation
forumation
Forces dependent on deformation - pressure
loads
Material constitution for finite deformation
Contact problems
Numerical examples
Concluding remarks
Non-linear structural problems - large
displacement and instability
Introduction
Large displacement theory of beams
Elastic stability - energy interpretation
Large displacement theory of thick plates
Large displacement theory of thin plates
Solution of large deflection problems
Shells
Concluding remarks
Pseudo-rigid and rigid-flexible bodies
Introduction
Pseudo-rigid motions
Rigid motions
Connecting a rigid body to a flexible body
Multibody coupling by joints
Numerical examples
Computer procedures for finite element
analysis
Introduction
Description of additional program features
Solution of non-linear problems
Restart option
Solution of example problems
Concluding remarks
Appendix AA1 Principal invariants
A2 Moment invariants
A3 derivatives of invariants
Author index
Subject indexAuthor index
Page numbers in bold refer to the list of references at the end of each chapter.
Abramowitz, M. 165, 172
Adams, M. 35, 37
Adini, A. 124, 169
Agelet de Saracibar, C. 355, 363
Ahmad, S. 173, 177, 188, 212; 217, 224, 241,
242; 244, 264; 266, 270, 274, 275, 280, 284,
Bathe, K.-J. 28, 36; 144, 169; 183, 185, 188, 189,
191, 196, 213, 214; 286, 287; 347, 355, 362,
363; 386, 390, 394; 415, 425, 426, 431
Batoz, J.L. 31, 37; 144, 162, 169, 170, 171; 196,
214; 231, 236, 242; 386, 393
Bauchau, O.A. 396, 411
Bauer, J. 257, 258, 259, 260, 261, 262, 265
Bayless, A. 90, 109
Bazant, Z.P. 90, 91, 92, 93, 109
Bazeley, G.P. 123, 124, 139, 144, 148, 167
Beisinger, Z.E. 217, 241
Bell, K. 123, 154, 168
Belytschko, T. 90, 91, 109; 217, 241; 286, 287;
347, 362; 390, 394
Benson, D.J. 347, 362; 396, 404, 407, 410
Benson, P.R. 297, 310
Bergan, P.G. 31, 32, 35, 37; 124, 132, 169; 226,
242; 384, 388, 393
Besseling, J.F. 53, 105
Best, B. 88, 108
Betsch, P. 210, 215; 286, 287; 386, 394; 404, 411
Bicanic, N. 24, 36; 53, 70, 84, 90, 105, 106, 108,
109; 179, 212
Biezeno, C.B. 388, 394
Bingham, E.C. 79, 107
Birkhoff, G. 154, 170
Bischoff, M. 210, 215; 218, 242; 286, 287, 288;
332, 361; 386, 394
Bittencourt, E. 347, 362
Bjorck, A. 24, 36
Blaauwcndraad, J. 84, 108
Bogner, F.K. 123, 144, 168; 217, 240; 384, 393
Bonet, J. 314, 317, 328, 333, 338, 345, 360; 398, 411
Bonnes, G. 217, 240
Booker, J.R. 89, 90, 109
Boot, J.C. 156, 170
Boresi, A.P. 3, 20
Boroomand, B. 94, 110
286
Ahmed, H . 101, 110
A1 Mikdad, M. 367, 392; 401, 411
Alart, P. 347, 355, 363
Albasiny, E.L. 234, 243
Alfrey, T. 48, 104
Allman, D.J. 157, 158, 171; 226, 229, 242
Allwood, R.J. 157, 171
Ambrosio, J.A.C. 396, 411
Andelfmger, U. 286, 287; 332, 360
Anderson, C.A. 15, 21; 102, 103, 110; 386, 392
Anderson, R.G. 385, 393
Ando, Y. 132, 169
Argyris, J.H. 123, 124, 129, 154, 168; 217, 240;
390, 395; 401, 411
Arlctt, P.L. 302, 310
Armero, F. 91, 109; 332, 358, 360
Armstrong, P.J. 53, 105
Arnold, 186, 197, 198, 213
Arulanandan, K. 20, 21
Ashwell, D.G. 217, 241; 388, 394
Atluri, S.N. 396, 411
Auricchio, F. 53, 66, 71, 105; 185, 199, 200, 203,
213, 214; 344, 361
Babuska, I. 120, 145, 167; 183, 208, 213, 214
Bagchi, D.K. 385, 393
Bahrani, A.K. 302, 310
Bakhrebah, S.A. 283, 287
Baldwin, J.T. 162, 171
Ballesteros, P. 139, 169
Barut, A. 390, 394, 395438 Author index
Borri, M. 396, 411
Bosshard, W. 123, 154, 168
Bottasso, C.L. 396, 411
Bouzinov, P.A. 347, 362
Braess, D. 332, 361; 386, 394
Braun, M. 210, 215; 286, 287
Brebbia, C.A. 217, 240; 373, 376, 383, 386, 390,
Cilia, M.A. 286, 287
Cimento, A.P. 28, 36
Clark, H.T. 396, 411
Clough, R.W. 123, 124, 144, 149, 167, 168, 169;
179, 212; 217, 226, 232, 240, 242; 267, 280,
286; 384, 388, 393
Cohen, H. 396, 397, 410
Cohen, M. 179, 182, 184, 185, 212; 286, 287
Collatz, L. 24, 36; 415, 431
Comini, G. 14, 21
Connor, J. 217, 240, 241; 373, 376, 383, 386, 390,
392
Brekke, T. 88, 108
Brczzi, F. 188, 213, 214; 226, 229, 242
Brogan, F.A. 390, 394
Bron, J. 156, 170
Brown, T.G. 297, 310
Broyden, C.G. 34, 37
Bucalem, M.L. 188, 214
Bucciarelly, L. I l l, 167
Bucco, D. 308, 310
Biichter, N. 210, 215; 286, 287
Bushnell, D. 286, 287
Butlin, G.A. 123, 154, 168
392
Cook, R.D. 157, 171; 179, 212; 226, 242; 284,
286, 287
Cormeau, I.C. 79, 81, 82, 91, 107, 108
Cornes, G.M.M . 157, 171
Cowper, G.R. 123, 154, 168; 217, 241
Cozzarelli, F.A. 3, 20; 59, 106; 220, 242; 314, 317,
328, 338, 339, 341, 360; 433, 436
Cramer, H. 308, 311
Creus, G.J. 347, 362
Crisfield, M.A. 28, 29, 31, 34, 36, 37; 162, 171;
200, 214; 359, 364; 390, 395
Cross, D.K. 162, 171
Cuomo, M. 347, 363
Curnier, A. 347, 355, 362, 363
Cusens, A.R. 297, 309, 310
Cwertny, A.J.(Jr.) 308, 311
Cyr, N.A. 78, 107
Cyrus, N.J. 124, 169
Cantin, G. 217, 240
Cardona, A. 396, 410
Carpenter, N. 217, 241
Carr, A.J. 217, 226, 240
Carson, W.G. 385, 393
Cassel, E. 17, 21; 34, 37
Cazzani, A. 396, 411
Cervera, M. 91, 109
Chaboche, J.L. 53, 105
Chadwick, P . 314, 360
Chan, A.H.C. 19, 20, 21; 70, 82, 106, 108; 124,
128, 133, 169; 182, 183, 212
Chan, A.S.L. 244, 257, 258, 259, 264
Chan, H.C. 297, 308, 310
Chan, S.K. 347, 361
Chan, Y.K. 385, 393
Chang, C.T. 53, 105
Chari, M.V.K. 101, 110
Chaterjee, A. 156, 170
Chattapadhyay, A. 386, 393
Chaudhary, A.B . 188, 189, 191, 213; 347, 355,
362, 363
Chawla, V. 347, 359, 362
Chen, A.J. 407, 412
Chen, W.F. 51, 53, 104
Cheung, M.S. 297, 309
Cheung, Y.K. 48, 77, 104, 107; 123, 124, 126,
132, 139, 144, 148, 167, 168, 169; 217, 231,
240; 297, 305, 306, 307, 308, 309, 310, 311
Chiang, M.Y.M. 188, 213, 214
Chong, K.P. 3, 20
Chou, P.C. 3, 20
Christensen, R.M. 39, 104
Church, K. 157, 171
Ciarlet, P.G. 216, 240
da Deppo, D.A. 371, 392
Dahlquist, G. 24, 36
Damilano, G. 396, 411
Darve, F. 68, 106
Davidon, W.C. 28, 36
Davies, J.D. 297, 310
Dawe, D.J. 124, 128, 168; 217, 230, 231, 241; 308,
310
De Borst, R. 84, 91, 93, 108, 109
DeAndrade, J.C. 308, 311
Defalias, Y. 70, 106
Del Guidice, S. 14, 21
Delcourt, C. 308, 310
Delpalc, R . 244, 252, 254, 258, 259, 260, 264
Demmel, J. 24, 36; 413, 430
Dennis, J.E. 28, 36
Desai, C.S. 82, 108
Dhalla, A.K. 72, 107
Dhatt, G. 31, 37; 156, 162, 170, 171; 217, 240;
386, 393
Dhatt, G.S. 144, 170, 196, 214
Dhillon, B.S. 200, 214
Dill, E.H. 384, 393
Dinno, K.S. 75, 107
Doan, D.B. 396, 410Author index 439
Doblare, M. 367, 392
Dong, S.B . 200, 214; 308, 311
Draper, J.K. 123, 167
Drucker, C.D. 51, 62, 104, 106
Duncan, W. 123, 168
Dupuis, G. 217, 241
Duvaut, G. 79, 80, 107
Dvorkin, E.N . 188, 189, 191, 213; 286, 287
Dworsky, N. Ill, 167
Gonzalez, O. 359, 364
Goodier, J.N. 3, 20; 302, 310
Goodman, R.E. 88, 108
Goudreau, G.L. 36; 39, 45, 46, 104; 347, 362
Gould, P.L. 244, 255, 264
Govindjee, S. 347, 355, 362; 430, 431
Grafton, P.E. 244, 248, 250, 251, 264; 303, 304,
310
Gray, N.G. 286, 287
Greenbaum, G.A. 77, 107
Greene, B.E. 157, 171; 217, 240, 241
Griemann, L.F. 200, 214
Gross, B. 39, 104
Gruttmann, F. 210, 215; 286, 287; 386, 394; 404,
Edwards, G. 157, 171; 217, 241
Elias, Z.M. 244, 265
Elsawaf, A.F. 34, 37
Ericksen, J.L. 433, 434, 436
411
Falk, R.S. 186, 197, 198, 213
Felippa, C.A. 123, 124, 132, 144, 149, 154, 168,
169, 170; 226, 242
Feshbach, H. 292, 309
Finnie, I. 81, 108
Firmin, A. 244, 257, 258, 259, 264
Fish, J. 90, 109
Fletcher, R. 34, 37
Fltigge, W. 216, 240
Foo, O. 297, 306, 310
Ford, R . 123, 154, 168
Fox, D.D. 218, 241; 286, 287; 386, 393, 394
Fox, R.L. 123, 144, 168; 217, 240; 384, 393
Fraeijis de Veubeke, B. 123, 132, 149, 150, 156,
167, 168, 170; 183, 200, 213; 330, 360; 373,
Guex, L. 144, 157, 158, 170
Gunderson, K. 144, 162, 170
Guo, D.J. 308, 311
Gurtin, M.E. 314, 317, 338, 360; 398, 411
Haisler, W.E. 72, 107; 144, 162, 170; 255, 265
Hallquist, J.O. 347, 362; 396, 404, 407, 410
Hanssen, L 124, 132, 169
Harou, M. 179, 212
Harter, R.H. 226, 227, 242
Hartz, BJ. 385, 393
Harvey, J.W. 156, 157, 170
Haug, E.J. 396, 410
Heegaard, J.-H. 347, 351, 362
Heege, A. 355, 363
Hellan, K. 157, 170
Heller, W.R. 81, 108
Henshell, R.D. 124, 157, 169, 171
Herrmann, L.R. 45, 104; 156, 157, 170; 217, 241
Hestenes, M. 34, 37
Hibbitt, H.D. 14, 21; 336, 361
Hildebrand, F.B. 57, 105
Hill, R. 51, 89, 104
Hilton, H.H. 48, 104
Hinton, E. 34, 37; 53, 57, 105; 179, 185, 188, 189,
190, 191, 212, 213; 286, 287; 297, 310
Hirschberg, M.H. 77, 107
Ho, L.W. 144, 169; 185, 196, 213, 214
Hobbs, R.E. 17, 21; 34, 37
Hoffstetter, G. 84, 108
Hogge, M. 28, 36
Hrabok, M.M. 144, 169
Hrudey, T.M. 144, 169
Hsiao, K.-M 390, 394
Huang, H.C. 93, 96, 109, 110; 188, 189, 190, 191,
213; 286, 287
Hughes, T.J.R . 11, 21; 49, 51, 53, 56, 59, 66, 68,
79, 80, 89, 104, 107; 124. 169; 179, 180, 182,
184, 185, 188, 200, 212, 213, 214; 226, 229,
242; 261, 265; 286, 287; 320, 344, 346, 347,
358, 360, 361, 362
392
Francavilla, A. 347, 361
Frederick, C.O. 53, 105
Frey, F. 217, 241
Fried, I. 123, 154, 168
Fulton, R.E. 124, 169
Gallagher, R.H. 72, 82, 107, 108; 217, 240, 241;
244, 265; 386, 393
Galvanetto, U. 359, 364
Garcia Orden, J.C. 398, 411
Gelder, D. 101, 110
Gellately, R.A. 386, 393
Geradin, M. 28, 36; 396, 410
Gere, J.M. 375, 392
Ghali, A. 297, 309, 310
Ghionis, P. 34, 37
Giannini, M. 244, 255, 257, 258, 259, 264
GiD, CIMNE 430, 431
Gill, S.S. 75, 107
Giroux, Y.M. 217, 240
Glaser, S. 332, 360
Goel, J.J. 154, 170; 217, 241
Goicolea, J.M. 398, 411
Goldstein, H. 404, 412
Golub, G.H. 69, 106; 407, 412; 413, 430440 Author index
Huhlhaus, H.B. 91, 93, 109
Hulbert, G.M. 396, 411
Humpheson, C. 82, 108
Hung, H.-C 390, 394
Huston, R.L. 396, 411
Ladkany, S.G. 157, 171
Landers, J.A. 347, 362
Langhaar, H.L. 373, 392
Lardeur, P. 196, 214
Larsson, R. 93, 110
Laug, E.J. 396, 410
Laursen, T.A. 347, 355, 359, 362, 363
Lawson, C.L. 154, 170
Leckie, F.A. 81, 108
Ledesma, A. 70, 106
Lee, E.H. 344, 361
Lee, S.-H 390, 394
Lee, S.L. 139, 169
Lees, M. 14, 21
Lefebvre, D. 124, 156, 169; 182, 183, 186, 196,
197, 198, 207, 210, 212
Leroy, Y. 90, 93, 109
Leung, K.H. 69, 106
Lewis, R.W. 14, 21; 63, 82, 106, 108
Li, W.Y. 307, 308, 310, 311
Liepins, A. 257, 259, 265
Lin, F.B. 90, 91, 92, 93, 109
Lin, J.I. 390, 394
Lindberg, G.M. 123, 154, 168; 217, 241
Ling, W. 355, 363
Lions, J.-L. 79, 80, 107
Liu, D.T. 344, 361
Liu, W.K. 185, 213; 286, 287
Liu, Z.A. 244, 264
Lo, K.S. 234, 243; 283, 286
Loden, W.A. 217, 240
Lohner, R. 34, 37
Loo, Y.C. 297, 309, 310
Lubliner, J.L. 49, 51, 53, 71, 104, 105
Lyness, J.F. 101, 110
Lynn, P.P. 200, 214
Lyons, L.P.R. 162, 171
Ibrahimbegovic, A. 226, 230, 242; 367, 392; 401,
411
Idelsohn, S. 28, 36
Irons, B.M. 34, 37; 123, 124, 139, 144, 148, 149,
150, 154, 158, 162, 167, 168, 171; 173, 177,
179, 188, 212; 217, 224, 230, 241, 242; 244,
264; 266, 274, 275, 280, 284, 286; 385, 386,
393
Isenberg, J. 84, 108
Ishihera, K. 70, 107
Jean, M. 355, 363
Jetteur, P. 217, 226, 229, 241, 242
Jirousek, J. 144, 157, 158, 170, 171
Johnson, C.P. 157, 171; 217, 232, 240
Johnson, K.W. 24, 36; 51, 53, 104
Jones, R.E. 157, 171; 217, 241; 244, 264; 347, 362
Joo, T. 396, 411
Jordan, F.F. 257, 259, 265
Jourdan, F. 355, 363
Ju, J.-W. 355, 363
Kabaila, A.P. 385, 393
Kalker, J.J. 347, 361, 362
Kanchi, M B. 78, 81, 107
Kane, C. 347, 363
Kang, D.S. 396, 411
Kanoknukulchai, W. 179, 185, 212; 261, 265
Kapania, R.K. 286, 288
Kapur, K.K. 124, 136, 139, 169; 385, 393
Kasper, E.P. 334, 336, 361
Kawai, T. 384, 393
Kelsey, S. 156, 157, 170
Key, S.W. 217, 241
Khachaturian, W. 84, 108
Khojasteh-Bakht, M. 244, 255, 264
Kikuchi, F. 132, 169
Kikuchi, N. 347, 362
King, I.P. 39, 56, 73, 84, 104, 105, 107, 108; 124,
132, 169; 217, 226, 227, 232, 240
Kirchoff, G. I l l, 167
Klapka, I . 396, 411
Klein, S. 244, 248, 264
Koiter, W.T. 51, 56, 80, 104, 108
Kosko, E. 123, 154, 168
Kotanchik, J.J. 244, 264
Krahl, N.W. 84, 108
Kraus, H. 257, 260, 265
Krieg, D.N 57, 105
Krieg, R.D. 57, 105
McHenry, D. 48, 104
Mackerle, J. 347, 362
McLay, R.M . 157, 171; 217, 241
McMeeking, R.M. 72, 107
MacNeal, R . H. 226, 227, 242
Madenci, E. 390, 394, 395
Maenchen, G. 58, 105
Malkus, D.S. 182, 212
Mallett, R.H. 384, 386, 393
Malvern, L.E. 3, 20; 220, 242; 345, 361; 398, 411
Mandel, J. 53, 89, 105, 109; 344, 361
Mang, H.A. 84, 108
Mansfield, L. 154, 170
Manson, S.S. 77, 107
Manzoli, O. 91, 109
Marcal, P.V. 14, 21; 73, 78, 107; 336, 361; 384,
390, 391, 395
Marcotte, L. 162, 171Author index 441
Needleman, A. 90, 93, 109
Nelson, R .B . 308, 311
Newton, R.E. 385, 393
Nguyen, Q.A. 79, 107
Noll, W. 345, 361
Noor, A.K. 390, 395
Norris, V.A. 63, 106
Novozhilov, V.V. 244, 245, 252, 265; 303, 310
Nygard, M.K. 124, 132, 169
Marcus, H . 139, 169
Marguerre, K. 373, 392
Mark, R. 237, 243
Marketos, E. 73, 107
Marsden, J.E. 345, 347, 361, 363
Martin, D.W. 234, 243
Martin, H.C. 384, 385, 393
Martin, J .B. 81, 108
Martins, R.A.F. 162, 171
Mason, W.E. 217, 241
Masud, A. 286, 288
Matsui, T. 386, 390, 393
Matsuoka, O. 386, 390, 393
Matte, Y. 162, 171
Matthies, H. 28, 29, 31, 34, 36; 415, 416, 430
Mawenya, A.S. 297, 310
Mazars, J. 90, 109
Mazumdax, J. 308, 310
Meek, J.L. 390, 395
Mellor, P.W. 51, 53, 104
Melosh, R .J. 124, 126, 169; 384, 393
Mendelson, A. 77, 107
Mescall, J.F. 388, 394
Meschke, G. 84, 108
Meyer, C. 308, 311
Miles, G.A. 244, 255, 258, 259, 264
Milford, R.V. 286, 287
Mindlin, R.D. I l l , 167
Mira, R. 93, 110
Moita, G.F. 390, 395
Mooney, M. 341, 361
More, J. 28, 36
Morgan, K. 14, 21; 96, 110; 257, 258, 259, 260,
261, 262, 265
Morley, L.S.D. 124, 133, 134, 157, 168, 169; 207,
Oancea, V.G. 355, 363
Obrecht, H. 308, 311
Oden, J.T. 162, 171; 336, 347, 361, 362
Ogden, R.W. 341, 342, 343, 361
Oliver, J. 91, 109
Olson, M.D. 123, 154, 168; 217, 241
Onate, E. 162, 163, 164, 172; 188, 191, 194,
195, 213, 214; 257, 258, 259, 260, 261, 262,
265
Ortiz, M. 90, 93, 109; 347, 363
Otter, J.H.R. 17, 21; 34, 37
Ottoscn, N.S. 93, 110
Owen, D.R.J. 54, 57, 78, 81, 84, 93, 101, 105,
107, 108, 110; 162, 171
Pacoste, C. 390, 395
Paczelt, I. 347, 363
Padlog, J. 386, 393
Pagano, N.J. 3, 20
Pamin, J. 91, 93, 109
Pande, G.N. 63, 82, 88, 91, 106, 108, 109
Papadopoulos, P. 188, 191, 195, 196, 200, 211,
213, 214, 215; 347, 355, 362, 363; 396, 397,
410
Papadrakakis, M. 34, 37
Parekh, CJ. 217, 226, 227, 231, 232, 240, 242
Parisch, H. 286, 287; 347, 362; 386, 393, 394
Parks, D.M. 72, 107
Parlett, B.N. 373, 392; 426, 431
Pastor, M. 19, 20, 21; 69, 70, 82, 93, 96, 106, 108,
109, 110
Paul, D.K. 70, 106
Pawsey, S.F. 179, 212; 267, 280, 283, 286
Peano, A. 154, 170
Penzien, J. 244, 264
Peraire, J. 93, 96, 110
Percy J.H. 244, 248, 264
Peric, D. 93, 110
Perzyna, P. 79, 83, 107
Peterson, F.E. 45, 104
Petocz, E.G. 397, 411
Phillips, D.V. 84, 108
Pian, T.H.H. 31, 36; 157, 171; 244, 248, 255, 264;
334, 361; 391, 395
Pica, A. 34, 37
Pietruszczak, S.T. 89, 90, 91, 109
214
Morse, P.M. 292, 309
Mroz, Z. 53, 69, 89, 90, 105, 106, 109
Mullen, R . 390, 394
Muncaster, R.G. 396, 397, 410
Murray, D.W. 384, 385, 393
Muscat, M. 101, 110
Naghdi, P.M. 262, 265
Nagtegaal, J.C. 72, 107
Nakazawa, S. 69, 106; 124, 169; 182, 183, 212
Narasimhan, R. 183, 213
Narayanaswami, R . 124, 168
Nath, P . 84, 96, 108
Navaratna, D.R. 244, 248, 255, 264
Nay, R.A. 162, 163, 171
Nayak, G.C. 51, 54, 57, 62, 104, 105; 388, 394;
434, 436
Naylor, D.J. 63, 106
Neal, M.O. 347, 362
Neale, B.K. 157, 171442 Author index
Pietrzak, G. 355, 363
Pijaudier-Cabot, G. 90, 91, 92, 93, 109
Pister, K.S. 4, 21; 39, 45, 46, 104
Pnezien, J. 244, 264
Polak, E, 34, 37
Popov, E.P. 70, 106; 244, 264
Poster, K.S. 4, 21
Prager, W. 51, 52, 53, 62, 104, 106
Prakash, A. 54, 105
Pramono, E. 90, 109
Pratt, C. 217, 241
Press, W.H. 413, 430; 433, 436
Pugh, E.D.L. 179, 185, 188, 212
Schmit, L A. 72, 107; 123, 144, 168; 217, 240;
384, 393
Schnabel, F. 308, 311
Schnobrich, W.C. 283, 286, 287
Schoenberg, IJ. 306, 310
Schrefler, B.A. 19, 20, 21; 70, 82, 106, 108
Schwarz, H . R. 24, 36
Schweizerhof, K. 337, 347, 361, 362; 373, 392
Scordelis, A.C. 234, 243; 283, 286; 308, 311
Scott, R.F. 20, 21
Seiler, C. 308, 311
Seiss, C.P. 84, 108
Sen, S.K. 244, 255, 264
Setlur, A.V. 156, 170
Shabana, A.A. 396, 407, 410
Shames, I .H . 3, 20; 59, 106; 220, 242; 314, 317,
328, 338, 339, 341, 360; 433, 436
Shapiro, G.S. 166. 172
Sharma, K.G. 88, 109
Shewchuk, J. 430, 431
Shi, G.-H . 397, 411
Shi, J. 359, 364; 390, 395
Shiomi, T. 70, 106
Silvester, P. 101, 110
Simo, J.C. 4, 11, 21; 25, 36; 49, 51, 53, 56, 58, 59,
66, 68, 80, 89, 90, 91, 104, 105, 106, 109;
124, 128, 133, 169; 182, 183, 212; 218, 226,
241, 242; 286, 287; 320, 328, 332, 337, 338,
341, 342, 343, 344, 346, 347, 355, 358, 359,
360, 361, 362, 363, 364; 366, 367, 373, 386,
392, 393, 394; 396, 399, 401, 404, 410, 411
Sloan, S.W. 89, 90, 109
Sluys, L.J. 91, 93, 109
Smith, I.M. 123, 168
Sokolnikoff, I.S. 3, 20; 276, 286; 299, 304, 310
Solberg, J.M. 347, 362; 396, 397, 410
Southwell, R.V. 124, 169
Specht, B. 124, 132, 169
Stebbins, F.J. 308, 311
Stegun, I.A. 165, 172; 386, 393
Stein, E. 210, 215; 286, 287; 355, 363; 386, 394;
404, 411
Steinmann, P. 93, 110
Stiefel, E. 34, 37
Stolarski, H. 217, 241; 286, 287; 390, 394
Stolarski, H.K. 188, 213, 214; 355, 363
Strang, G. 28, 29, 31, 34, 36; 415, 416, 430
Strickland, G.E. 217, 240
Stricklin, J.A. 72, 107; 144, 162, 170; 244, 255,
264, 265; 308, 311
Strome, D.R. 157, 171; 217, 240; 244, 248, 250,
251, 264; 303, 304, 310
Sture, S. 90, 109
Suarez, B. 188, 194, 214
Sumihara, K. 334, 361
Suneda, D.K . 101, 110
Qu, S. 69, 106; 124, 169; 182, 183, 212
Ralston, A. 24, 29, 36
Ramm, E. 31, 37; 210, 215; 218, 242; 286, 287,
288; 332, 337, 360, 361; 386, 393, 394
Rankin, C.C. 390, 394
Rao, R.S. 188, 214
Razzaque, A. 124, 144, 150, 159, 162, 168, 170,
171; 231, 242; 384, 393
Reeves, C.M . 34, 37
Reinsch, C. 415, 425, 430
Reissner, E. 111, 167; 229, 242; 366, 388, 392,
394
Repetto, E.A. 347, 363
Rice, J.R. 72, 89, 90, 107, 109; 336, 361
Riesa, J.D. 237, 243
Rifai, M.S. 218, 241; 286, 287; 386, 394
Riks, E. 31, 36
Ristic, S. 390, 395
Roberts, T.M. 388, 394
Robichaud, L.P.A. 217, 240
Rockey, K.C. 385, 393
Roehl, D. 210, 215; 286, 287; 332, 360
Rots, J.G. 84, 108
Rubinstein, M.F. 77, 107
Rubio, C. 93, 110
Rudnicki, J.W. 89, 90, 109
Runcsson, K. 93, 110
Russell, H.G. 48, 104
Rybicki, E.F. 72, 107
Sabir, A. 217, 241
Sackman, J.L. 347, 362
Sacks, S. 58, 105
Saigal, S. 286, 288
Sakurai, T. 56, 105
Samuelsson, A. 124, 132, 169
Sander, G. 123, 149, 157, 167
Sanders, J.L.(Jr.) 257, 259, 265
Scapolla, T. 120, 145, 167; 208, 214
Scharpf, D.W. 123, 154, 168; 401, 411
Schmidt, R. 371, 392Author index 443
Sved, G. 308, 310
Swaddiwudhipong, S. 308, 310
Szabo, B.A. 347, 363
Szabo, T. 347, 363
Szilard, R . 376, 392
von Mises, R. 51, 104
von Reisman, W. 72, 107
Vu Van, T. 355, 363
Vu-Quoc, L. 25, 36; 367, 392
Walters, D. 124, 169
Walz, J.E. 124, 169
Warburton, G.B. 124, 169
Wasfy, T.M. 390, 395
Washizu, K. 4, 21; 244, 245, 262, 265
Watson, M. 39, 48, 104
Webster, JJ. 217, 241; 244, 256, 264
Wehage, R.A. 396, 410
Weikel, R.C. 217, 240
Wempner, G.A. 162, 171
Westergaard, H.M. 433, 436
White, J.L. 39, 104
Wilkins, M.L. 58, 105
Wilkinson, J.H. 415, 425, 430
Will, G. 217, 241
Wiliam, K.J. 90, 93, 109, 110
Wilson, E.L. 149, 170; 203, 214; 226, 242; 249,
265; 302, 310; 336, 361; 384, 385, 393; 415,
425, 431
Winnicki, L.A. 63, 106; 308, 311
Winslow, A.M. 101, 102, 110
Withum, D. 154, 170
Witmer, E.A. 244, 264
Wittaker, E.T. 401, 411
Woinowski-Krieger, S. I l l, 113, 121, 167; 216,
240; 244, 245, 252, 257, 265
Wong, K. 396, 399, 401, 410
Wood, R.D. 124, 134, 168; 314, 317, 320, 328,
333, 338, 339, 345, 360; 372, 384, 388, 392;
398, 411
Wriggers, P. 332, 337, 338, 347, 350, 351, 355,
360, 361, 362, 363; 373, 392
Wu, J. 96, 110
Wunderlich, W. 308, 311
Tabbara, M. 91, 109
Tadros, G.S. 297, 310
Tahar, M.B. 144, 170; 231, 236, 242
Tarnow, N. 359, 363, 364; 367, 386, 392, 394
Tatsueka, T. 70, 107
Taylor, R.L. 3, 4, 20, 21; 39, 45, 46, 53, 58, 59,
66, 68, 69, 71, 73, 79, 88, 104, 105, 106, 107,
108; 124, 128, 133, 169; 179, 182, 183, 185,
188, 191, 194, 195, 196, 199, 200, 203, 211,
212, 213, 214, 215; 226, 229, 242; 261, 265;
267, 270, 274, 278, 280, 283, 286; 328, 329,
332, 334, 336, 337, 338, 341, 342, 344, 347,
355, 360, 361, 362, 363; 373, 392; 413, 430;
434, 436
Tessler, A. 200, 214; 390, 395
Teter, R.D. 78, 107
Tezduyar, T. 188, 213
Tham, L.G. 307, 308, 310, 311
Theocaris, P.S. 73, 107
Theron, NJ. 396, 411
Thomas, G.R. 217, 241
Timoshenko, S.P. 3, 20; 111, 113, 121, 167; 216,
240; 244, 245, 252, 257, 265; 302, 310; 375,
392
Tisdale, P. 144, 162, 170
Tocher, J.L. 123, 124, 136, 139, 144, 167, 169;
217, 240
Tong, P. 31, 36; 157, 171; 391, 395
Tong, R. 157, 171
Too, J . 179, 185, 212; 267, 270, 274, 278, 280,
283, 286; 295, 308, 309
Torbe, I. 157, 171
Toyoshima, S. 182, 212
Truesdell, C. 345, 361
Tsay, C.-S. 390, 394
Tu, T. 198, 214
Tuba, I.S. 347, 361
Turner, M.J. 384, 393
Xie, Y.M. 70, 106
Xu, Z. 185, 186, 197, 198, 200, 206, 213, 214
Yamada, Y. 56, 105
Yang, H.T.Y. 286, 288; 386, 393
Yang, T.Y. 388, 394
Yishimura, N. 56, 105
Yoshimura, N. 384, 393
Yu, J. 93, 110
Utku, S. 162, 163, 171; 217, 240
Vahdati, M. 96, 110
Valliappan, S. 56, 73, 84, 86, 105, 108
Van Loan, C.F. 69, 106; 407, 412; 413, 430
van Randen, Y. 347, 361
Ventura, G. 347, 363
Vilotte, J.P. 182, 212
Visser, W. 123, 154, 156, 168, 170
Vlachoutsis, S. 286, 287
Volker, R.E. 101, 110
Zanisek, A . 154, 170
Zarate, F. 162, 163, 164, 172
Zarka, J. 79, 107
Zavarise, G. 332, 351, 360, 363
Zeng, L.F. 185, 198, 200, 206, 213
Zhong, H.G. 390, 395444 Author index
Zhong, W.X. 183, 213
Zhong, Z. 347, 362
Zhu, D.S. 308, 311
Zhu, J.Z. 94, 110; 211, 215
Ziegler, H. 52, 104
Zienkiewicz, O.C. 3, 4, 14, 15, 19, 20, 20, 21; 31,
34, 36, 37; 39, 48, 51, 53, 56, 57, 62, 63, 69,
70, 73, 77, 78, 79, 81, 82, 84, 88, 91, 93, 94,
96, 101, 102, 103, 104, 105, 106, 107, 108,
109, 110; 123, 124, 126, 128, 132, 133, 139,
144, 148, 156, 167, 168, 169, 170; 173, 177,
179, 182, 183, 185, 186, 188, 191, 194, 195,
196, 197, 198, 200, 207, 210, 211, 212, 213,
214
, 215; 217, 224, 226, 227, 231, 232, 240,
242; 244, 257, 258, 259, 260, 261, 262, 264,
265; 266, 267, 270, 274, 275, 278, 280, 283,
284, 286; 295, 297, 302, 308, 309, 310, 311;
347, 361; 371, 385, 386, 388, 392, 393, 394;
413, 430; 434, 436Subject index
Acceleration of convergence 30
Accuracy, axisymmetric shells 244
Adaptive analysis, plastic flow deformation 97
Adaptive refinement 93, 211
based on energy norm error estimates 93
Additional enhanced mode 248
Additional plastic potentials 88
Aerospace structures 244
Ageing effects 42
Algebraic non-linear solutions, use of 8
Algorithms:
BFGS 414, 419
GN22 13, 419, 424
line search computer programs 414
line-search 414
Newton-type 415, 416, 417
return map 58
return map implicit 80
Almansi strain tensor 316
Alternative refinement using error indicators 95
Analogies:
McHenry-Alfrey 48
solution by 48
Angular momentum 399
balance of 4
Approximations:
curved shells, polygonal shape 249
displacement approximation, plates 121
finite element 163, 322
finite element virtual displacements 5
finite elements displacements 5
Galerkin 156
Galerkin weighting 156
Herrmann 156
pressure 11
quadratic displacement 162
shells, flat element 217
thick plates 180
volumetric strain 11
Arc-length controls 31
Arch, clamped-hinged 371
Arch dam , analysis example 231
Associative plasticity 52, 60
Assumptions:
Kirchhoff'-Love 245
Reissner-Mindlin 266
thick and thin plates 114, 115
Asymptotic rates 34
Augmented Lagrangian form 351
Axisymmetric body, torsion problem 300
Axisymmetric shells 217, 244, 387
curved , thick 275
with non-symmetrical load 303
Axisymmetric solids, with non-symmetrical load
297
Barrel vaults:
analysis example 234
problem 230
Beams:
with attached mass, numerical example 409
beam functions 153
definition 1
deformed configuration 367
large displacement theory of 365
one-dimensional example 159
stress resultants 113
two-dimensional theory of 366
Behaviour:
deformation of solids 137
elasto-plastic 343
geometric non-linearity 1
inelastic material 164, 210
inelastic shells 279
laminates 88
limit loads 74
material non-linearity 1
non-linear elastic 48
path dependent 35
plastic 48446 Subject index
Behaviour - emit.
softening behaviour 31
soil 83
solids, non-linear:
geometric 1
material non-linearity 1
small deformation problems 3
symmetric stress 164
Bending strains, plates 117
Bergan mcthod/proccdurc 32
BFGS computer program algorithm 414, 419
BFGS update 28
Bifurcation 22
instability 384
Bilinear elements 179
Blending function mesh generation 358
Boundary conditions 291
constrained 184
displacement 318
fixed 119
mixed 120
plates 116
simply supported prism 295
Boundary constraints 187
Boundary integral terms 132
Boundary layers 250
Boundary traction 120
Bounding surface plasticity models 70
Box structures, thin membrane 295, 297
Boxes, with flexure 296
Branching shell 260
Bridge, railway 138
Bridge with beams, skewed, curved 137
Brittle materials, special problems of 84
Broyden method 34
Bubble modes 187. 196, 198
Buckling 1
Euler 374
with large deflections 385
relation to discrete Kirchhoff formulation 159,
194
for triangular elements 194
Components, skew-symmetric stress 229
Composites, plates 118
Computed central deflection, square plates 136
Computer contour plot 139
Computer procedures, finite element analysis 413
Computer programs:
FEAPpv 413, 418, 425, 428, 429
GID 430
Concentrated discontinuities 91
Condensation, static 249
Condensation process 203
Conical frustra 246, 247
Conservation of linear momentum 399
Consistency tests, irreducible forms 186
Consistent tangent matrix 66
Constant isotropic hardening modulus 52
Constant strain 132
Constitutive law 84
Constitutive models 9, 166, 333
Constitutive relations, plates 118
Constrained boundary conditions 184
Constrained elements 155
Constraints:
boundary 187
discrete collocation 187, 192
discrete Kirchhoff 162
Kirchhoff 158
Kuhn —Tucker form 51
Lagrange multiplier 405
patch count and discrete collocation 188
rotational 406, 407
translation 405
triangles/triangular elements 194
see also Collocation constraints: Joints
Contact:
frictionless 352
Hertzian 348
node-node 348
Contact problems 313, 347
Continuity:
Cu requirements, plates 156, 159, 177, 182, 188,
262
Ci requirements, plates 111, 122, 145, 261
cross derivatives 123
difficulty avoidance 155
patch tests 135
Continuum problems 314
Continuum rate formulation 55
Convective heat transfer coefficient 14
Convergence:
criteria for 8, 33
with Newton-Raphson method 25
non-conforming elements 124
Cantilever, propped, Euler buckling 374
Cartesian and curvilinear coordinates 269
Cartesian tensor form 3, 4
Cauchy stress 316, 325, 329, 339, 342, 345
Cauchy-Green deformation tensor 316, 338, 342
Circular bar, necking of 357
Circular plate, bending 262
Clamped edges, spherical dome 257
Clamped hinged-arch 371
Clamped plates 136, 139, 175
Classical time-dependent plasticity theory 48
Closed loops, and joints 407
Clough and Toucher triangles 148
Collocation constraints:
element matrices 192
quadrilaterals 187Subject index 447
and plate and shell problems 278
rate of 145
study 263
Cooling tower, analysis example 233
Coordinates:
cartesian and curvilinear relation 269
curvilinear 128, 244, 268
local and global 220
use of 3
Corner nodes 124
Comer supported square plate 136
Cosines:
direction 221, 224
normal direction 225
Crash analysis 18
Creep, in metals 80
Creep compliance 40
Creep law, Norton-Soderberg 81
Creep problems:
basic formulation of 75
fully explicit solutions 77
Creep strain 78
Criterion, constant strain 132
Cross derivatives 123
Cubic axisymmetric shell elements 277
Cubic elements 179
Cubic expansion 129
Cubic functions 130
Cubic Hermitian interpolations 296
Cubic interpolation 161
Cubic lagrangian interpolation 188, 286
Current configuration 312
Current configuration formulation 324
Current deformed configuration 314
Current stiffness parameter 35
Curved dams 283
Curved elements 244, 251
properties 254
shape functions for 252
strain expressions for 254
Curved, isoparametric hexahedra 267
Curved shells 267
polygonal shape approximation 249
Curvilinear coordinates 128, 244, 268
relation with cartesian 269
Curvilinear elements 262
Cylinder:
edge loaded 282
thick-walled, subject to internal pressure 46
Cylindrical billet, upsetting of 356
Cylindrical shells 250, 281
Cylindrical vault 282
Definitions, strains and stresses 271
Deformation:
behaviour of solids 137
deformation analysis 349
deformation gradient 315, 316, 321, 332. 344
polar decomposition of 398
deformation tensors 316, 328
Cauchy-Green 338
equations for 314
finite 312
process of 319
thin case axisymmetric shell 303
thin plates 112
Deformed configuration 312
Degrees of freedom see DOF
Delpak elements 260
Delta weighting, Dirac 189
Deviatoric term 42
Differential equations:
forth order 112
model 41
Dirac delta weighting 189
Direct elimination 159
Direct iteration 29
Direct iterative methods 34
Direction cosines 221, 224
Discontinuity capture 95
Discontinuity and slip lines 95
Discontinuous deformation analysis (DDA) 397
Discontinuous S interpolation 182
Discrete collocation constraints 1S7, 192
Discrete exact thin plate limit 202
Discrete Kirchhoff constraints 158
Discrete Kirchhoff theory ( DKT) elements 161,
188, 194. 196
Discretization 4, 71, 121, 176, 202
error of 33, 216
Discretized equilibrium equation 77
Displacement approximation equations, plates
121
Displacement boundary conditions 318
Displacement boundary restraints 73
Displacement control 31
Displacement field 270
Displacement formulation:
plates 122
use of 9
Displacement functions 124, 305
multiplicative type 305
Displacement increment 166
Displacement-based finite element models 327
Displacements:
finite element approximations to 5
global 276
global nodal 254
tangential 256
D’Alembert principle 323
Damping effects, with GN22 algorithm 424
Dams, curved 283448 Subject index
Distributed loads 294
DKT (discrete KirchholT theory) elements 161,
188, 194, 196
Delpak 260
discrete collocation constraints 187, 192
discrete KirchholT triangular plate element 226
eight-node serendipity 286
enhanced mode 196
equilibrium 157
failure of 183
finite 251, 329
matrix notation 334
method for shells 217
geometric definition of 268
heterosis 180
Hinton-Huang 191
hybrid 157
integration 184
isoparametric quadratic 75
isoparametric three dimensional 174
joints 86
Kelvin 40
linear beam and plate 261
linear triangular 198
with mid-side slope connections only 230
mixed 155
use of 72
parabolic-type 297
parallelogram 128
Pian-Sumihara 199, 334
plane element stiffness 218
plate 157
plate bending 183
quadratic fully integrated (QS) 179
quadratic of Huang and Hinton 189
quadratic T6S3B3 196, 369
quadrilateral 128, 148, 201
quadrilateral mixed 185
quartic and quintic 154
quasi-conforming 150
rectangular with collocational constraints 192
rectangular quadrilateral 209
rotation-free 162
rotational bubble modes 196
serendipity eight-node 286
serendipity quadratic 179
shell properties and transformations 272
shells with displacement and rotation 266
smoothed 150
strain and virtual strain in 10
superparametric 271
thick plate theory limitations 203
transformation to global coordinates 219
Trefftz-hybrid 158
see also Finite clement; Triangles/triangular
elements
ELMTnn computer element module 413
Elongation strain 91
Embankment under gravity 83
DOF:
6 133, 225
9 128, 144
12 124, 144
16 144
18 148, 153
21 124, 144, 153
Dome spherical 257
under uniform pressure 281
Drilling rotational stiffness 225
Drucker-Prager yield conditions 62
Dynamic buckling, computer programs for 428
Dynamic relaxation methods 34
Earthquake response, soil structures 19
Edge loaded cylinder 282
Eigenfunctions 306
Eigenproblem 342
Eigensolutions, computer programs for 425
Eight-node serendipity element 286
Elastic bulk modulus 41
Elastic calculations 87
Elastic constitutive equations, rate form 345
Elastic deformation in joints 407
Elastic material, isotropic 300
Elastic moduli, isotropic material 340
Elastic modulus matrix 61
Elastic shear modulus 42
Elastic stability, energy interpretation 373
Elasticity:
isotropic, and finite deformation 338
isotropic for plates 118
three-dimensional 155
as a variational problem 320
Elasticity matrix 55, 245, 272
Elasto-plastic behaviour 343
Elasto-plastic deformations:
localization in 88
non-uniqueness in 88
Elasto-plastic matrix 55
Elasto-plastic modulus matrix 56
Elasto-plastic slope 99
Elasto-plastic solutions 249
Elasto-viscoplastic material 78
Elements:
assembly of 219
axisymmetric shell 246
bilinear 179
choice of 230
constrained 155
cubic 179
curved 244, 251
curvilinear 262Subject index 449
Energy:
constrained potential principle 193
minimum potential 162
transverse shear 189
Energy function, stored, Saint-Venant-Kirchhoff
model 320
Energy interpretation , elastic stability 373
Energy norm 144
Energy norm error 95
estimates and adaptive refinement 93
Enhanced modes 196
Enhanced strain methods 332
Enhanced strain mode 248
Enthalpy 14
Equations:
deformation 314
differential 41, 112
discretized equilibrium 77
displacement approximation, plates 121
elastic constitutive, rate form 345
equilibrium 3, 6, 163, 225, 317, 371
Euler, for static equilibrium 321
finite element convergence 60
finite elements, plates 121
fourth-order differential 112
Galerkin (variational) 10
inelastic constitutive 12
integral model 43
kinematics and deformation 314
non-linear algebraic 22
plate equilibrium 115
plate problem 113
Prandtl-Reuss 63
of rigid body motion 399
singular systems 182
strain-displacement, mixed form 11
stress measures 316
tangent system 32
traction measures 317
virtual work 5
Equilibrating stress field 157
Equilibrium, weak form for 4
Equilibrium elements 157
Equilibrium equation 3, 163. 225, 317, 371
residual form 6
Equivalence, discontinuous S interpolation 182
Erratic yielding 249
Error indicators, alternative refinement using
FEAPpv computer program 413, 418
and eigensolutions 425
example problem solutions 429
restart option 428
and static and steady-state problems 418
Field, displacement 270
Field problems, non-linear quasi-harmonic 12
Fine element solution 377
Finite angle solution 373
Finite deformation 1, 312
material constitution for 338
mixed-enhanced 332
plasticity model 358
problems 313, 319
three-field mixed 328
variational description 319
Finite elasticity, variational theorem for 320
Finite element analysis, computer procedures
413
Finite element approximations 163, 322
Finite element contact 348
Finite element discretization 4
Finite element equation convergence 60
Finite element equations, plates 121
Finite element evaluation , strain-displacement
matrices 378
Finite element forms, use of 9
Finite element formulation 326
Finite element method 22
Finite element model, construction from 400
Finite element processes 289
Finite elements in hemispherical shells 251
Finite precision arithmetic 33
Finite strip method 289, 297
incomplete coupling 305
semi-analytical 305
spline finite strip 305
First order problem solution using GN11 420
Fixed boundary conditions 119
Flexible bodies, connected to a rigid body 402
Flow rule ( normality principle ) 51
Fluid dynamics, high speed 95
Folded plate structure, analysis example 237
Forces:
external 127
in-plane 244
membrane 244
nodal 127, 337
pressure load 336
Forces dependent on deformation-pressure loads
95
Errors, from incomplete solutions 33
Euler buckling, propped cantilever 374
Euler column 1
Euler equations, for static equilibrium 321
Euler ( explicit) method 79
Euler implicit schemes 36
Evaluation, tangent matrix 379
336
Formulae:
Gauss-Lobatto-type 165
Gaussian quadrature 274
recursion 46
Sherman-Morrison-Woodbury 69450 Subject index
Formulations:
continuum rate 55
current configuration 324
displacement, plates 9, 122
finite element 326
Saint-Venant-Kirchhoff model 320
stress 302
substitute shape 150
viscoelastic relaxation 46
yield 50
free of locking 330
irreducible 112, 173, 176
isoparametric 255
isotropic elasticity 338
Kirchhoff 194
large displacement with small rotations
Galerkin form 319, 353
Galerkin method 321
Galerkin procedures 13, 181
Galerkin Process 176
Galerkin statement, variational 137
Galerkin (variational) equations 10
Galerkin weighting approximations 156
Gauss points 183, 194, 204, 262, 278
quadrature 160, 248, 274
Gauss-Lobatto-type formulae 165
Gaussian integration 180
General constitutive models 9
Generalized Maxwell model 41, 43, 44
Generalized Maxwell solid 39
Generalized plasticity:
forms 69
J2 model 71
non-associative case 68
Geometric definition of elements 268
Geometric matrix 383
Geometric modelling 348
Geometric non-linearity behaviour 1
Geometric stiffness 3, 328
Geometric tangent 332, 371
Geometric vector algebra 223
Geometrically exact specialization 367
Geometrically non-linear problems 312
GID computer program 430
Global displacements 276
Global and local coordinates 220
Global nodal displacements 254
Global strains 276
GN 11 and Newmark (GN22 ) algorithms 13, 419
GN22 method 6, 13, 419, 424
Green strain matrices 321
Green strain tensor 316
Green-Lagrange strain 368, 369, 376, 381, 387
non-zero 370
370
mixed 155, 173, 180, 332
non-associated 89
non-linear 6, 379
plates displacement 122
reference configuration 320
reference configuration for 320
small rotations, large displacement 370
steady-state non-linear problems 6
thick plates 180
three-field mixed finite deformation 328
use of 9
Foundation with eccentric loading 100
Fourier components/series 290, 292, 294
Fourier expansion 297
Frames, definition 1
Freezing moist soil 14
Frictional materials, non-associative case 68
Frictionless conditions 348
Frictionless contact 352
Frustra, conical 246, 247
Functions:
beam 153
blending mesh generation 358
conforming shape 148
cubic 130
displacement 124, 305
eigenfunctions 306
energy, stored, Saint-Venant-Kirchhoff model
320
Hermitian rectangular shape 151
Huber—von Mises yield 62, 67
internal shape 256
least square substitute shape 151
linking, derivation of 200
mesh generation, blending 358
non-conforming shape 124
orthogonal 289
penalty 261, 350
serendipity 201
shape 112, 124, 129, 145, 208, 290
shape for curved elements 252
shear relaxation modulus 43
spline 306
stored energy 340
Hardening:
hardening/softening rules 52
isotropic 51, 52
kinematic 51, 52, 55
non-associative 53
plastic material 48
Heat conduction, transient 14
Hellinger-Reissner principle 156
Hemispherical shells 251
Hermitian interpolations 247, 253
Hermitian polynomials 296Subject index 451
Hermitian rectangular shape function 151
Herrmann, approximations 156
Hertzian contact 348
High-speed fluid dynamics 95
Hinton-Huang elements 191
History dependent paths 48
Homogeneous fields 157
Homogeneous motion 397
Homogeneous plates 158
Hoop stresses 284
Hu-Washizu functional 162
Huber-von Mises flow rule 72
Huber-von Mises yield conditions/function 62, 67
Huber-von Mises-type materials 166
Hybrid elements 157
Hyperelastic material 313
Hyperelasticity 338
linked 199, 229
membrane 227
Invariants:
first derivatives of 434
moment 433
second derivatives of 435
Invariants of second-order tensors 432
Irreducible forms:
consistency tests for 186
use of 9
Irreducible formulations 112, 173, 176
Irreducible systems 175
Isoparametric concepts 208
Isoparametric formulation 255
Isoparametric hexahedra, curved 267
Isoparametric mapping 203
Isoparametric quadratic elements 75
Isoparametric quadrilaterals 81
Isoparametric shell elements 285
Isoparametric three dimensional elements 174
Isoparametric transformations 262
Isotropic elasticity:
elastic material 300
formulation in invariants 338
formulation in principal stretches 338
plates 118
Isotropic elasto-plastic material forms 313
Isotropic hardening 51, 52, 54. 63
Isotropic homogeneous plate 380
Isotropic materials 61, 179, 272
Isotropic models 40
Isotropic plasticity models 61
Isotropic yield surfaces 61
Iteration:
direct (or Picard) 29
Newton-Raphson 166, 327, 351
use of 8
Iteration number 24
Iterative correction 24
Iterative processes, use of 7
Iterative solution scheme
, viscoelasticity 80
Iterative techniques 23
Identity matrix 28
Impenetrability condition 347
In-plane forces 244
In-plane stress action 218
Increment size 35
Incremental return map form 65
Incremental-secant method 26
Independent slope-displacement interpolation 261
Induction time 15
Inelastic behaviour, shells 279
Inelastic constitutive equations 12
Inelastic material behaviour 164, 210
Inelastic materials 38
Initial conditions 319
Initial stress matrix for plate bending 381
Initial stress method 26
Initial stress process 84
Initial stress stiffness 3
Instability, bifurcation 384
Integral equation model 43
Integration:
Gaussian 180
numerical 274
reduced (selective) 182
through-thickness 165
Integration elements 184
Integration order 278
Internal shape functions 256
Interpolations:
boundary-type 189
cubic 161
cubic Hermitian 296
cubic lagrangian 188, 286
four-term 199
Hermitian 247, 253
independent slope-displacement 261
Lagrangian 160
linear 247
Ji model:
with isotropic and kinematic hardening 63
and volumetric plastic strain 68
J2 plane stress 66
Jacobian matrix 26, 273
computer program for 416
Jacobian transformations 199
Jaumann-Zaremba stress rate form 346
Joint elements 86
Joints:
and closed loops 407
coupling multibodies 404
revolute 407452 Subject index
Joints - cont.
single rotational constraint 407
single translational constraint 407
spherical 407
with rotational constraints 406
with translation constraints 405
Linear viscoelasticity 39
model for 45
Linearization 327, 350, 354, 380
Linked interpolation 199, 229
Linking function, derivation of 200
load bifurcations 1
Load correction matrix 336
Load matrix 127, 133, 134
Loading, axisymmetric 245
Loading factor expansion 291
Local direction cosines 221
Local and global coordinates 220
Localization , in elasto-plastic deformations 88
Localization (slip line) capture 93
Kelvin element/model/solid 40
Kinematic boundary conditions 321
Kinematic hardening 51, 52, 55, 63
Kinematic hardening back stress 67
Kinematic hardening relations 66
Kinematics equations 314
Kirchhoff constraints 158
Kirchhoffplates 111
Kirchhoff stress 316, 317, 325, 329, 342, 343, 344,
345, 358
Kirchhoff triangular plate bending element 226
Kirchhoff—Love assumption 245
Koitr treatment for multi-surface plasticity 80
Kronecker delta quantities 315
Kuhn-Tucker constraint form 51
McHenry-Alfrey analogies 48
Magnetic response, and non-linear quasiharmonic field problems 101
Mapping, isoparametric 203
Martices, strain displacement 378
Master nodes 348, 351
Material:
behaviour of 1, 164.210
brittle 84
constitution for finite deformation 338
elasto-viscoplastic 78
finite deformation 338
frictional 68
Huber-von Mises-type 166
hyperelastic 313, 320
inelastic 38, 164, 210
isotropic 61, 179, 272, 300, 313, 340
laminar 86
Maxwell 43
neo-Hookean 341, 357
no-tension 84
non-linear 1 , 38
plastic, hardening/softening of 48
Matrices:
elastic modulus 61
elasticity 55, 245, 272
elasto-plastic modulus 56
element for discrete collocation constraints 192
finite elements notation 334
geometric 383
Green strain 321
identity 28
and index form 5
Jacobian 26, 273, 416
linear stiffness 6
load 127, 133, 134
load correction 336
Newton method 30. 31
orthogonal 366
Piola-Kirchhoff stress 321
plate bendinginitial stress 381
Lagrange multiplier constraint 405
Lagrange multiplier form 350, 353
perturb of 406
Lagrange multipliers 398, 402
Lagrangian form, augmented 351
Lagrangian interpolation 160, 188, 286
Lagrangian quadratics (QL ) 179
Lagrangian variables 113
Laminar behaviour 88
Laminar materials 86
Laminar structures 308
Laplace transform theory 40
Large deflection problems, solution of 383
Large displacement formulation with small
rotations 370
Large displacement theories:
beams 365
thick plates 375
thin plates 381
Least square substitute shape functions 151
Legendre polynomial 256
Limit load behaviour 74
Limit plastic state 71
Line search computer programs 416
algorithm for 414
Line search procedures 30
Linear axisymmetric shell elements 277
Linear elasticity 6
Linear interpolations 247
Linear momentum 399
balance of 4
Linear stiffness matrix 6
Linear triangular element (T3S1B1 ) 198, 200Subject index 453
stiffness 127, 128, 131, 133, 134, 219, 221, 248,
272, 293, 300
strain-displacement 5, 182, 378
substitute shear strain 194
tangent 66, 337, 379, 383, 416
velocity 399
Matrix form, relation with index form 5
Maximum plastic dissipation principle 53
Maxwell material 43
Maxwell model 39
generalized 41, 43, 44
Membrane box structures 295
Membrane forces 244
Membrane interpolations 227
Membrane locking 286
Membrane stresses 250
Mesh density 140, 142, 143
Mesh generation, blending function 358
Metals, creep of 80
Mid-side nodes 146
Minimum potential energy 162
Mixed elements 155
use of 72
Mixed forms, use of 9
Mixed formulations 155, 173
Mixed patch test 230
Mixed variational principle 162
Mixed-enhanced finite deformation formulation
Multiaxial stress 49
Multibodies, coupled by joints 404
Multiple branches 22
Multiple solutions 23
Multipliers, penalty 261
Necessary requirements 184
Necking of a circular bar 357
Neo-Hookean models/materials 341, 357
Neutral equilibrium, and stability 374
Newmark procedure 6, 419
Newton matrix method 30, 31
Newton-Raphson iteration 35, 59, 102, 166, 327,
351
Newton-Raphson method 24, 79
modified 26, 84
Newton-Raphson process 59, 336, 379, 392
negative features of 25
Newton-Raphson scheme 78, 331, 335, 346, 359
Newton-Raphson solution 313, 324, 326, 339,
345, 352, 354, 369, 403
Newton-type computer algorithms 415, 416, 417
Newton-type solution 46
strategy for 42
Newton’s method see Newton-Raphson method
No-tension material 84
Nodal circles 246
Nodal displacement 218
Nodal forces 127
and tangent matrix terms 337
Nodal load vector 127
Nodal parameters 123, 192
Nodal rotation 255
Nodal values 188
Nodal variables 134
Node transforms 220
Node-node contact 348
Node-surface contact/treatment 351
between discs 355
Nodeless variables 255
Nodes:
master 348, 351
slave 348, 351
Non-associated formulations 89
Non-associated plasticity 91
Non-associative case:
frictional materials 68
generalized plasticity 68
Non-associative hardening 53
Non-associative plasticity 52, 60
Non-linear algebraic equations 22
Non-linear behaviour of solids:
geometric non-linearity 1
material non-linearity 1
small deformation problems 3
Non-linear elastic behaviour 48
332
Modelling, geometric 348
Models:
neo-Hookean 341
resultant constitutive 166
Modes:
additional enhanced 248
bubble 187, 196, 198
enhanced 196
enhanced strain 248
rigid body 130
vibration 428
Modified modulus term 12
Modified Newton-Raphson method 26, 34, 84
Moduli:
direct elastic 114
shear elastic 114
Young’s 272
Mohr-Coulomb surface 56, 89
Mohr-Coulomb yield conditions 62
Moist soil, freezing 14
Moment invariants 433
Momentum, linear and angular 399
Motions:
pseudo-rigid 396
rigid 398
Multi-degree-of-freedom systems 30
Multi-surface plasticity, Koiter treatment 80454 Subject index
Non-linear formulation, transient and steadystate problems 6
Non-linear materials 38
Non-linear problems, computer program
solutions 415
Non-linear quasi-harmonic field problems 12, 101
Non-linear structural problems 365
Non-local approach 92
Non-uniqueness 23, 90
in elasto-plastic deformations 88
Normal direction cosines 225
Normal slopes 146
Normality principle (flow rule) 51
Norton-Soderberg creep law 81
Numerical integration 165, 274
Numerical patch tests 186
Picard iteration 29
Piola-Kirchhoff stress 317, 320, 328, 333, 339,
345, 368, 369
Piola-Kirchhoff stress matrix 321
Pipe penetration 284
Plane element stiffness 218
Plane strain solutions, perforated plate 73
Plane stress 165
J2 66
Plane stress solutions, perforated plate 72
Plastic behaviour 48
Plastic computation , examples of 71
Plastic correction 58
Plastic deformation, sustained 51
Plastic deviatoric strain rates 64
Plastic flow rule potential 51
Plastic localization calculation 96
Plastic material, hardening/softening of 48
Plastic mechanisms 93
Plastic potentials, additional 88
Plastic strain rate 51, 54
Plastic stress-strain relations 54
Plastic yield surfaces 87
Plasticity:
associative 52, 60
constitutive model construction 54
non-associated 91
non-associative 52, 60
rate form equations 64
time-independent theory 48
upper and lower bound theorems 52
Plasticity models 343
finite deformation 358
isotropic 61
Plate bending, initial stress matrix for 381
Plate elements 157
Plates:
bending 111
bending elements 183
bending stiffness 114
bending strains 117
bending triangles 151
boundary conditions 116
circular, bending 262
clamped 175, 384
composites 118
cylindrical bending 113, 114
definition 1
discrete exact thin limit 202
displacement formulation 122
equilibrium equations 115
with flexure 296
governing equations 113
homogeneous 158
hybrid 157
in-plate plate stiffness 114
One-dimensional beam example 159
Orthogonal functions 289
Orthogonal matrix 366
Orthogonal transformations 220
Overlay models 54
Parabolic axisymmetric shell elements 277
Parabolic-type elements 297
Parallelogram elements 128
Parameters:
forms without rotational 208
nodal 123. 192
rotational 208
Pascal triangle 154
Patch count, and discrete collocation constraints
188
Patch tests 131
an analytical requirement 134
and collocation constraints 195
continuity condition 135
curvilinear coordinates 128
numerical 186
plate bending elements 183
quadrilateral mixed elements 185
simple count 187
thick plate elements 203
triangular mixed elements 186
Patches:
four-element 190
single-element 190
Path dependent behaviour 35
Penalty functions 261, 350
Penalty multiplier 261
Penalty parameters 175
Perforated plate:
plane strain solutions 73
plane stress solutions 72
Perturbing a Lagrange multiplier form 406
Pian-Sumihara elements 199, 334Subject index 455
internal/external virtual work 121
isotropic elasticity 118
isotropic homogeneous 380
large deflection problems 383
non-homogeneous 158
non-linear formulation 379
point loads 176
rectangular 125
square with clamped edges 136, 139
square simply supported 278
strain components in 165
thick 173. 180, 203
large displacement theory 375
Reissner-Mindlin 173
and shells 277
thin 111, 112
irreducible approximation 120
transverse shear group strains 117
twisting moments 118
Point collocation of nodes 193
Point loads on plates 176
Point numbering 222
Poisson ratio operator 48
Poisson's ratio 67, 73, 114. 118, 272
Polar decomposition of the deformation gradient
static condensation 203, 336
Prony series 43
Properties, curved elements 254
Propped cantilever, Euler buckling 374
Pseudo-rigid motions 396
Push forward transformation 340
Quadratic displacement approximations 162
Quadratic fully integrated elements (QS) 179
Quadratic interpolation 194. 198
Quadratic triangles 135
Quadratics, lagrangian (QL ) 179, 190
Quadrature formulae 248, 274
Quadrilaterals:
and discrete collocation constraints 187
elements 128, 149, 183
linear 200
mixed elements, patch tests 185
Quartic and quintic elements 154
Quasi-conforming elements 150
Quasi-harmonic field problems, non-linear 12, 101
Quasi-harmonic problem 13
Quasi-Newton method 26, 31, 34
Quintic polynomials 153
Railway bridge 138
Rate constitutive models 345
Rates of convergence 145
Rayleigh quotient form 374
Rectangular element (12 DOF) 124
Rectangular quadrilateral elements 209
Recursion formula 46
Reduced (selective) integration 182
Reference configuration 312, 314
Reference configuration formulation 320
Regula falsi procedure 30
Reinforced concrete:
cracking of 86
as a no tension material 84
Reissner-Mindlin assumptions 266
Reissner-Mindlin postulates 111
Reissner-Mindlin thick plates 173
Relaxation moduli 39
Relaxation modulus function 43
Relaxation times 39, 41
REP methods 94
Restart option, FEAPpv computer program 428
Resultant constitutive models 166
Retaining wall, earthquake excitation of 19
Retardation time parameters 40
Return map algorithm 58, 80
Rcvolutc joint 407
Rigid bodies:
connected to a flexible body 402
equations of motion 399
modes 130
398
Polygonal shape approximation, to a curved shell
249
Polynomials:
area coordinate 130
complete linear 129
Hermitian 152, 296
Legendre 256
quintic 153
Postulates, Reissner-Mindlin 111
Potential energy principle 193
Power station , underground 84
Prandtl-Reuss equations 63
Prandtl-Reuss-strain relations 65
Pressure approximations 11
Pressure loads, and deformation dependent
forces 336
Principal stretches, logarithmic form 342
Principal tensile stresses, elimination of 84
Principles:
constrained potential energy 193
d'Alembert 323
Hellinger— Reissner 156
Prismatic bar 292
Procedures:
discretization 176
Galerkin 181
Processes:
Galerkin 176
Newton-Raphson 336
semi-analytical finite element 289456 Subject index
Rigid footing, failure of 98
Rigid motions 398
Rods, definition of 1
Rotating disc, numerical example 409
Rotation, nodal 255
Rotation-free elements 162
Rotational constraints, on joints/couplings 406,
407
Rotational parameters 208
Rotational stiffness, 6 DOF 225
Rotational treatment 227
Rotations 202
and displacement fields 270
Runge-Kutta method/process/procedure 36. 57
flat element approximation for 217
general theories 218
hemispherical 251
in-plane force resultants 216
inelastic behaviour 279
non-linear response and stability 386
problem treatment methods 216
and rigid bodies 404
shallow, co-rotational forms 388
shallow shell theory 217
spherical shell problem 227
stability of 390
stress representation 274
thick, axisymmetric, curved 275
and thick plates 277
three-dimensional analysis 266
toroidal, under pressure 258
Sherman—Morrison—Woodbury formula 69
Single rotational constraint joints 407
Single translational constraint joints 407
Skew curved bridge 137
Skew-symmetric stress component 229
Slave nodes 348, 351
Slip line (localization) capture 93
Slope-displacement interpolation 261
Slopes, normal 146
Small deformation non-linear solid mechanics
problems 3
Small rotations, large displacement formulation
Saint-Venant-Kirchhoff material model 409
Saint-Venant-Kirchhoff relation 397
Saint-Venant-Kirchhoff stored energy model
320
Secant method 28
Secant procedure 30
Secant update method 29
Second-order system solution using GN22 423
Second-order tensors, invariants of 432
Seepage flow 101
Selective integration 182
Semi-analytical finite strips 305
Semi-analytical finite element processes 289
Serendipity element, eight-node 286
Serendipity functions 201
Serendipity quadratic elements 179, 183
Shallow shells 388
Shape functions 124, 129, 133, 145, 208, 290
and continuity requirements 122
simple triangular element 145
substitute 150
thin plates 112
Shear deformation, plates 114
Shear locking 369
Shear relaxation modulus function 43
Shear rigidity 189
Shearing stresses, and laminar material 87
Shells:
as an assembly of flat elements 216
axisymmetric 217, 244, 387
axisymmetric, curved , thick 275
axisymmetric with non-symmetrical load 303
bending 111
branching 260
classical treatment of 216
curved 249, 267
cylindrical 250, 281
definition 1
with displacement and rotation parameters 266
divided into triangular elements 223
finite element method 217
370
Smoothed elements 150
Softening behaviour 31
Softening of plastic material 48
Softening/hardening rules 52
Soil mechanics/behaviour:
associated and non-associated issue 83
viscoplastic models for 82
Solid mechanics:
general problems 1
small deformation 3
Solution, fine element 377
Solution by analogies 48
Solutions:
elasto-plastic 249
large deflection problems 383
Newton-Raphson 324, 326, 339
Spherical cap 284
Spherical dome 257, 279
Spherical dome under uniform pressure 281
Spherical path controls 31
Spherical points 407
Spherical shell problem 227
Spherical test problem 226
Spinning constrained disc 405
Spline finite strip method 305, 308
Spline functions 306Subject index 457
Spontaneous ignition 15, 102
SPR methods 94
Spring-dashpot model 39
Square plates, clamped edges 136, 139
Stability:
of equilibrium 373
and large plate deflections 385
and neutral equilibrium 374
shells 390
Standard barrel vault problem 230
Static condensation 203, 249, 336
Static equilibrium, Euler equations for 321
Static problems, computer program solutions
415
Steady-state problems:
computer program solutions 415
non-linear formulation 6
Steel pressure vessel, plastic computation with 75
Step-size control, computer programs 416
Stiffness:
geometric 3, 328
initial stress 3
rotational 225
Stiffness matrix 127, 128, 131, 133, 134, 219, 221,
248, 272, 293
isotropic elastic material 300
Stored energy function 340
Saint-Venant —Kirchhoff model 320
Strain:
enhanced strain methods 332
global 276
Green 322
Green-Lagrange 376, 387
mixed form expression 10
recovery procedures 94
Strain components 245
Strain-displacement equations, mixed form 11
Strain-displacement matrices:
evaluation of 182
finite element evaluation 378
Strain-displacement matrix 5
Strain-displacement operator 174
Strain-displacement relations 247
Strain-driven form 42
Strain expressions for curved elements 254
Strain rates:
plastic 51
plastic deviatoric 64
Strain softening 89, 97
Strain tensor, Green-Lagrange 368
Strain tensors 316
Strains and stresses, definitions 271, 303
Stress:
Cauchy 316, 318, 325, 329, 339, 342, 345, 359
Kirchhoff 316, 317, 325, 329, 342, 343, 344,
345, 358
membrane 250
mixed form expression 10
multiaxial 49
Piola Kirchhoff 317. 320, 321, 328, 339, 345,
368
recovery procedures 94
stress function 302
uniaxial 49
Stress deviator 41
Stress divergence 6
Stress field, equilibrating 157
Stress force 6
Stress hardening relations 66
Stress increment computation 56
explicit methods 57
implicit methods 57
Stress measures 316
Stress rate form, Jaumann-Zaremba 346
Stress representation, shells 274
Stress resultants 113, 245
Stress tensor, Piola-Kirchhoff 334
Stress transfer method 26
Stresses and strains, definitions
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