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Crisfield M.A. — Non-Linear Finite Element Analysis of Solids and Structures. Vol. 1: Essentials
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Íàçâàíèå: Non-Linear Finite Element Analysis of Solids and Structures. Vol. 1: EssentialsÀâòîð: Crisfield M.A. Àííîòàöèÿ: Non-linear Finite Element Analysis of Solids and Structures Volume 1 : Essentials M.A. Crisfield Imperial College of Science, Technology and Medicine, London, UK Taking an engineering rather than a mathematical bias, this comprehensive book details the fundamentals of non-linear finite element analysis. The author explains how non-linear techniques can be used to solve practical problems. The main ideas of geometric non-linearity, continuum mechanics, plasticity, element technology and stability theory are explored in detail. The reader is also introduced to the recent research in this developing field. The computer programs in the text are available on the Internet via anonymous ftp, using the URL ftp://cc.ic.ac.uk, directory /pub/depts/aero/nonlin. These useful finite element computer programs illustrate many of the ideas considered in the book. The logic can also be followed without these finer details since these computer programs and subroutines are also represented by examples and flowcharts. The second volume will address advanced topics such as large strains and large rotations, plasticity with a range of yield criteria and hardening rules, stability theory and advanced solution procedures including branch-switching techniques, contact and friction, and non-linear dynamics. It will also include examples from an up-dated non-linear finite element computer program incorporating the advanced solution procedures.
ßçûê: Ðóáðèêà: Ìàòåìàòèêà /×èñëåííûå ìåòîäû /Êîíå÷íûå ýëåìåíòû /Ñòàòóñ ïðåäìåòíîãî óêàçàòåëÿ: Ãîòîâ óêàçàòåëü ñ íîìåðàìè ñòðàíèö ed2k: ed2k stats Ãîä èçäàíèÿ: 1996Êîëè÷åñòâî ñòðàíèö: 362Äîáàâëåíà â êàòàëîã: 20.02.2005Îïåðàöèè: Ïîëîæèòü íà ïîëêó |
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12 ABAQUS 154[A1] 178[A1] Acceleration techniques, secant-related 310—314 Ahmad, S., Irons, B .M.& Zienkiewicz, O.C. 234[A1] Allgower, E.L. 325[A1] Allman, D.J. 235[A3] 242[A2] 255[A2] 326[A4] Almansi strain 63—65 74 120 123 130 148 149 Almroth, B.O. 326[A5] Ang, A.H.S.& Lopez, L.A. 2[A1] Arc-length method 253 266—276 Arc-length method, automatic switching to 288 Arc-length method, cylindrical 276—286 Arc-length method, linearised 274—275 Arc-length method, spherical 273—274 285 Argyris, J. 235[A4] Argyris, J.H. 2[A2] 2[A3] Argyris, J.H., Balmer, H., Doltsinis, J.St., Dunne, P.C., Haase, M., Klieber, M., Malejannakis, G.A., Mlejenek, J.P., Muller, M.& Scharpf, D.W. 211[A1] Argyris, J.H., Vaz, L.E.& Willam, K.J. 154[A2] Armen, H. 152[A3] Armen, H., Pifko, A.B., Levine, H.S.& Isakson, G. 2[A4] Augmented stiffness matrix 273 Automatic increment cutting 288 Automatic increments 286—288 Axial strain 217 Axial symmetry 107—108 181 Axisymmetric membrane 142—144 Backlund, J. 234[B1] Backward-Euler algorithm 174 180 Backward-Euler procedure 167 171 177 195—196 Backward-Euler return 176 181 189—191 Bar under uniaxial load 90 Bar under uniaxial tension or compression 62—65 Bar-spring problems 7 17 26 Bar-spring problems, imperfect buckling with two variables 51—55 Bar-spring problems, perfect buckling with two variables 50—51 Bar-spring problems, single variable with no spring 49—50 Bar-spring problems, single variable with spring 48—49 Bartholomew, P. 255[B1] Bathe, K.J. 136[B2] 146[B2] 148[B2] Bathe, K.J.& Bolourchi, S . 201 [B1] 225[B1] 234[R2] 236[B2] 243[B2] Bathe, K.J.& Cimento, A.P. 310[B3] Bathe, K.J.& Dvorkin, E.N. 324[B2] Bathe, K.J., Ramm, E., & Wilson, E. 136[B1] Batoz, J.L.& Dhatt, G. 273[B4] 275[B4] Bauschinger effect 161—162 Beam-theory relationships 213 Beams, two-dimensional formulations 201—233 Belleni, P.X.& Chulya, A. 266[B5] 324[B5] Belytschko, T. 122[B1] Belytschko, T.& Glaum, L.W. 201[B3] 211[B3] 218[B3] Belytschko, T.& Hseih, B.J. 201[B2] 211[B2] 225[B2] Belytschko, T.& Hseih, J. 126[B2] 131[B2] Belytschko, T.& Lin, J.I. 234[B4] Belytschko, T.& Velebit, M. 2[B1] Belytschko, T., Lin, J.& Tsay, C.-S. 234[B6] Belytschko, T., Stolarski, H., Liu, W.K., Carpenter, N.& Ong, J.S.-J. 234[B7] Belytschko, T., Wong, B.L.& Chiang, H.-Y. 234[B3] 235[B3] Belytschko, T., Wong, B.L.& Stolarski, H. 234[B5] Bending stresses and strains 213—214 Bergan, P.G. 287[B6] 288[B6] Bergan, P.G.& Felippa, C.A. 235[B8] Bergan, P.G.& Mollestad, E. 276[B10] Bergan, P.G.& Soreide, T. 252[B7] 266[B7] 287[B7] 287[B9] 288[B7] Bergan, P.G., Horrigmoe, G., Krakeland, B. & Soreide, T.H. 266[B8] 287[B8] 288 Besseling, J.F. 162[B1] Bicanic, N.P. 168[B2] Bifurcation problem 94—96 317—319 Bisplinghoff, R.L., Mar, J.M.& Pian, T.H.H. 104[B3] Boolean matrix 82 Bordered equations 272—273 Braudel, H.J., Abouaf, M.& Chenot, J.L. 154[B3] 167[B3] 178[B3] Brebbia, C.& Connor, J. 2[B2] Brink, K.& Kratzig, W.B. 201[B4] Brittle collapse 266 Brodlie, K.W., Gourlay, A.R.& Greenstadt, J. 307[B11] 308[B11] 309[B11] Broyden, C.G. 307[B12] 307[B13] 308[B12] 309[B13] Buckley, A.& Lenir, A. 311[B15] Buckley, A.G. 308[B14] 311[B14] Buckling criterion 16 Burgoynne, C.& Crisfield, M.A. 206[B5] Bushnell, D. 155[B4] 167[B4] 172[B4] 173[B4] Calladine, C.R. 234[C1] Carey, G.F.& Bo-Nan, J. 253[C1] 314[C1] 325[C1] Carnoy, E. 326[C2] Carpenter, N., Stolarski, H.& Belytschko, T. 234[C2] 235[C2] 236[C2] 238[C2] 239[C2] 240[C2] 242[C2] 244[C2] 247[C2] Cartesian coordinate system 78 Cartesian displacements 78 Cassel, A.C. 325[C3] Cauchy stresses 121—125 132 146—148 Centroidal approach 2 Chen, W.F. 152[C2] Clarke, M.J.& Hancock, G.J. 324[C4] Closest point algorithm 174 Clough, R.W.& Tocher, J.L. 234[C3] 236[C3] Cole, G. 219[C1] Combined incremental/iterative solution, computer program 45—48 Combined incremental/iterative solution, flowchart 44 Combined incremental/iterative solution, using full or modified Newton — Raphson iterations 10—13 Complementarity condition 193 Computer program, NONLTA 37 48 51 Computer program, NONLTB 3 9 4 1 Computer program, NONLTC 45—49 Computer program, NONLTD 298—303 Computer program, updating 291—307 see Consis tent tangents 191—192 Consistent tangent modular matrix 167 178—181 Consistent tangent modular matrix for plane stress 184 Constitutive laws 132—133 Constrained Mindlin — Reissner formulation 239 Continuation method 2 Continuum mechanics 104—136 Convergence criteria 289—290 Corotational element, using Kirchhoff theory 21 1—19 Corotational element, using Timoshenko beam theory 219—220 Corotational formulation 219 Corotational formulation, using engineering-strain 77—80 Corotational stresses and strains 131—132 Cowper, G.R. 203[C2] 207[C2] 208[C2] 109[C2] 210[C2] 225 Crisfield, M.A. 34[C2] 154[C3] 154[C4] 155[C3] 171[C3] 178[C4] 201[C5] 207[C7] 211[C6] 211[C7] 213[C6] 214[C6] 235[C9] 235[C12] 236[C5] 236[C6] 236[C7] 236[C10] 236[C11] 239[C5] 239[C6] 240[C5] 240[C6] 242[C4] 242[C7] 242[C11] 252[C17] 252[C20] 254[C16] 256[C9] 256[C16] 266[C11] 266[C14] 266[C19] 269[C11] 269[C20] 270[C14] 270[C15] 274[C11] 278[C16] 280[C19] 286[C11] 286[C15] 286[C22] 287[C11] 288[C11] 290[C15] 310[C7] 310[C9] 310[C10] 310[C13] 310[C17] 311[C5] 311[C7] 311[C8] 311[C13] 312[C8] 324[8] 324[C11] 324[C16] 324[C17] 324[C19] 325[C5] Crisfield, M.A.& Cole, G . 201[C3] 211[C3] Crisfield, M.A.& Puthli, R.S. 201[C4] [C4] Crisfield, M.A.& Wills, J. 236[C8] 238[C8] 242[C8] 269[C18] 270[C12] 278[C6] 286[C12] 288[C6] 289[C18] 290[C6] 291[C6] Crisfield, M.A., Duxbury, P.G.& Hunt, G.W. 26[C1] Current iterative direction 290 Current stiffness parameter 288 Cut-outs 311—312 Cylindrical arc-length method 276—286 Davidenko, D.F. 253[D1] 314[D1] Davidon, W.C. 307[D2] 307[D3] 309[D3] Dawe, D.J. 207[D1] Day, A.S. 325[D4] de Borst, R. 164[D1] 270[D5] 274[D5] Decker, D.W.& Keller, H.B. 326[D6] Decomposition theorem 131 Degenerate-continuum approach 235 Degenerate-continuum element using total Lagrangian formulation 243—247 Den Heijer, C.& Rheinboldt, W.C. 286[D7] 287[D7] Dennis, J.E.& More, J. 252[D8] 287[D8] 307[D8] 308[D8] Desai, C.S.& Siriwardane, H.J. 132[D1] 133[D1] 152[D2] Deviatoric components 108—109 164 Deviatoric space 171 Deviatoric stresses 163 Discrete Kirchhoff formulation 239 Discrete Kirchhoff hypothesis 236 Displacement control 4 Displacement derivative matrix 116 Displacement derivative tensor 137 Dodds, R.H. 152[D3] 156[D3] Drilling rotation 235 Drucker, D .C . 15 2[ D4] Dupius, G.A., Hibbit, H.D., McNamara, S.F. & Marcal, P.V. 2[D1] 26[D1] Duxbury, P.G., Crisfield, M.A.& Hunt, G.W. 26[D1] Dvorkin, E.N.& Bathe, K.J. 234[D1] E-values 74 76 205 Eccentricity 205—206 Eigenvalue problem 128 Elastic response 148—149 Elastic stiffness matrix 2 Elastic/perfectly plastic von Mises material under plane stress 156—159 Elasto-plastic material 144—146 Elasto-plastic modular matrix 156—159 Elasto-plastic tangent stiffness matrix 152 Elasto-plasticity 152 Engineering-strain, corotational formulation using 77—80 Epstein, M.& Murray, D.W. 201[E1] Equilibrium path 9 Eriksson, A. 270[E2] Eriksson, E. 289[E3] 324[E1] Euclidean norm 289 Eulerian strain 120 Eulerian triad 129 Felippa, C.A. 253[F1] 274[F1] 274[F2] 324[F1] 325[F2] 325[F4] Finite differences 152 Finite element computer program 261—264 Finite element formulation 137—139 Finite element method 152 Fink, J.P.& Rheinboldt, W.C. 270[F5] Fletcher, R. 193[F1] 252[F7] 254[F7] 255[F7] 256[F7] 274[F7] 307[F6] 307[F7] 308[F6] 308[F7] Fletcher, R.& Reeves, C.M. 325[F8] Flow rule 193 194 Forde, B.W.R.& Sttemer, S.F. 266[F9] 275[F9] Fortran computer program 23—56 Fortran subroutines 26—36 Fortran subroutines for general truss elements 85 Fortran subroutines for main structural iterative loop 280—285 Fortran subroutines to find new step length 258—261 Fortran subroutines, ACCEL 312—314 Fortran subroutines, application of arc-length constraint 276—280 Fortran subroutines, ARCL 278—280 Fortran subroutines, BCON 32—34 Fortran subroutines, CROUT 34—35 Fortran subroutines, ELEMENT 27—28 Fortran subroutines, ELSTRUC 31—32 Fortran subroutines, FORCE 30—31 Fortran subroutines, INPUT 29—30 87—88 Fortran subroutines, INPUT2 296—298 Fortran subroutines, ITER 280—285 Fortran subroutines, LSLOOP 292—294 Fortran subroutines, NEXINC 305—307 Fortran subroutines, QSOLV 278—280 Fortran subroutines, SCALUP 303—305 Fortran subroutines, SEARCH 259—261 Fortran subroutines, SOLVCR 35—36 Forward — Euler integration 185—188 Forward — Euler predictor 28 6 Forward — Euler procedure 166 167 170 Forward — Euler relationships 182 Forward — Euler tangential algorithm 174 Fox, L.& Stanton, E. 307[F10] Frankel, S.P. 325[F11] Frey, F.& Cescotto, S. 201[F1] 234[F1] [F1] Fried, I. 275[F12] Frieze, P.A., Hobbs, R.E.& Dolwing, P.J. 325[F13] Gallagher, R.J.& Padlog, J. 2[G1] Gallagher, R.J., Gellatly, R.A., Padlog, J.& Mallet, R.H. 2[G2] Gauss point 166 167 221 223 224 256 Gaussian integration 206 210—211 General isoparametric element 223—225 Generalised displacement control 27 1—6 Geometric matrix 4 Geometric non-linearity 1 Geometric non-linearity with one degree of freedom 2—1 3 Geometric non-linearity with two variables 13—19 Geometric stiffness matrix 2 73 209 21 1 Georg, K. 325[G1] Geradin, M., Idelsohn, S .& Hogge, M. 325[G1] Gerdeen, J.C., Simonen, F.A.& Hunter, D.T. 2[G3] Gierlinski, J.T.& Graves-Smith, T.R. 310[G2] Gill, P.E.& Murray, W. 254[G4] 256[G4] 266 274[G3] 276[G3] 307[G4] Green elastic materials 132 Green — Lagrange strain tensor 116 Green's strain 59 63 70 73 75 81 130 136 138 146 149 201 Green's strain, truss element based on 65—75 Green's strain, virtual work expressions using 118—119 Green, A.E.& Zerna, W. 104[G1] Gupta, A.K.& Ma, P.S. 207[G1] Haefner, L.& Willam, K.J. 201[H2] Haftka, R.T., Mallet, R.H.& Nachbar, W. 326[H1] Haisler, W.E., Stricklin, J.E.& Stebbins, F.J. 2[H1] 12[H1] Hardening concepts 159—162 Hardening solution with one variable 93—94 16—11 Hardening solution with two variables 98—100 322—323 Harris, H.G.& Pifko, A.B. 2[H2] Haselgrove, C.B. 266[H2] 275[H2] Hestenes, M.& Steifel, E. 325[H3] Hibbitt, H.D. 154[H1] 178[H1] 193[H1] 194[H1] Hierarchical displacement functions 21 0 Hill, R. 152[H2] 160[H2] 161[H2] 193[H2] Hinton, E.& Ezzat, M.H. 185[H4] Hinton, E., Abdal-Rahman, H.H.& Zienkiewicz, O.C. 310[H4] Hinton, E., Hellen, T.K.& Lyons, L.P.R. 185[H3] Hodge, P.G. 152[H5] Holand, I.& Moan, T. 2[H3] Honigmoe, G.& Bergan, P.G. 234[H1] 235[H1] 242[H1] Hsiao, K.M.& Hou, F.Y. 201[H1] 211[H1] Hu — Washizu variational principle 207 Huang, H.C.& Hinton, E. 234[H2] Huffington, N.G. 167[H6] 172[H6] Hughes, T.J.R. 234[H5] Hughes, T.J.R.& Hinton, E. 235[H4] Hughes, T.J.R.& Liu, W.K. 234[H3] Hughes, T.J.R.& Pister, K.S. 153[H7] Hughes, T.J.R., Ferencz, R.M.& Hallquist, J.O. 325[H6] Hughes, T.J.R., Levit, I.& Winget, J. 325[H5] Hunter, S.C. 104[H1] Hyperelastic materials 132 133 Hyperplane control method 276 Hypoelastic materials 133 144—146 Ilyushin, A.A. 152[11] Implicit formulation 195—196 Inconsistent tangents 191—192 Incremental formulation, approximate 149—150 Incremental formulation, involving updating after convergence 147—148 Incremental mid-point algorithm 85 Incremental procedures 2 Incremental solution 6—8 Incremental solution, computer program 37—38 Incremental solution, flowchart 36—37 Incremental solution, using program NONLTA 4 8 5 Incremental strains 144—146 155—156 Incremental/iterative control input 294—296 IncrementaNterative solution, using program NONLTC 49 IncrementaNterative solution, using program NONLTC with displacement control 55 IncrementaNterative solution, using program NONLTC with large increments 54—55 IncrementaNterative solution, using program NONLTC with small increments 52—54 Inextensional bending 207 Initial displacement 4 Initial displacement matrix 2 Initial local slopes 219 Initial slope matrix 4 Initial stress matrix 4 13 15 16 26 73 153 209 219 Initial stress method 2 10—13 Internal force vector 68—70 240—241 Intersection point 185 Irons, B.& Elsawaf, A. 311[11] Irons, B.M.& Ahmad, S. 235[11] Isoparametric degenerate-continuum approach 225—229 Isotropic hardening 152 Isotropic strain hardening 159—160 Isotropic work hardening 160—161
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