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Crisfield M.A. — Non-Linear Finite Element Analysis of Solids and Structures. Vol. 1: Essentials
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Название: Non-Linear Finite Element Analysis of Solids and Structures. Vol. 1: EssentialsАвтор: Crisfield M.A. Аннотация: 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.
Язык: Рубрика: Математика /Численные методы /Конечные элементы /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Год издания: 1996Количество страниц: 362Добавлена в каталог: 20.02.2005Операции: Положить на полку |
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Iterative correction procedure 153 Iterative displacement direction 256 Iterative solution 8—10 Iterative solution, computer program 39—41 Iterative solution, flowchart 41 Iterative solution, subroutine ITER 41—44 Iterative strains 154 Jacobian 137 234 272 Jang, J.& Pinsky, P.M. 234[J1] Jennings, A. 325[J1] Jetteur, P. 154[J1] 178[J1] 182[J1] 183[J1] 184[J1] 192[J1] 234[J3] [J3] 242[J3] 243[J3] Jetteur, P.& Frey, F. 234[J2] 235[J2] 2431521 Jeusette, J.-P., Laschet, G.& Idelsohn, S. 324[J2] Johnson, C. 193[J3] Johnson, W.& Mellor, P.B. 152[J2] K-value 288 Kapur, W.W.& Hartz, B.J. 2[K1] Karamanlidis, D., Honecker, A.& Knothe, K. 201[Kl] Kearfott, R.B. 266[K1] 326[Kl] Keller, H.B. 266[K2] 325[K3] 326[K3] Kershaw, E. 325[K4] Key, S.W., Stone, C.M.& Krieg, R.D. 155[K1] Kinematic hardening 161—162 Kirchhoff assumption 203 Kirchhoff bending theory 206 Kirchhoff element 21 1 Kirchhoff formulation 236 Kirchhoff hypothesis 208 Kirchhoff stress 123 125 Kirchhoff theory, corotational element using 211—219 Kondoh, K.& Atluri, S. 286[K5] Kouhia, R.& Mikkola, M. 326[K6] Krieg, R.D.& Key, S.M. 167[K3] 171[K3] 177[K3] Krieg, R.D.& Krieg, D.B. 167[K2] 171[K2] 177[K2] Kroplin, B.H. 325[K8] Kuhn-Tucker conditions 193 195 Lagrangian formulation 73—75 Lagrangian function 193 Lagrangian multiplier 128 193 Lagrangian triad 128 130 Lame constants 109—110 Lanczos, K.C. 253[L1] 325[L1] Large-deflection elasto-plastic analysis 269 Layered approach 2 Limit point 2 266 269 270 274 Limit point with two variables 96—98 319—322 Limit-point, small-strain, with one variable 314—316 Line-search technique 254—258 Line-search tolerance 256 Linear Almansi strain increment 122 Linear convergence 13 Linear Euler strain increment 122 Linear stiffness matrix 16 Linear strain increment 83 Linear tangent stiffness matrix 73 Linearised arc-length methods 274—275 Little, G.H. 155[L1] Liu, W.K., Law, E.S., Lam, D.& Belytschko, T. 234[L1] 235[L2] Load increment factor 286—287 Load-controlled continuation method 271 Load/deflection curves 266 Load/deflection relationships 5 17 Load/deflection response 269 Lobatto rule 206 Lobatto rule for numerical integration 334 Local limit point 4 Local tangent stiffness matrix 78 Log-strain relationship 83 Love, A.E.H. 104[L1] Luenberger, D.G. 193[L2] 194[L2] 252[L2] Maeir, G.& Nappi, A. 154[M1] 193[M1] Mallet, R.H.& Marcal, P.V. 1[M1] 2[M1] Mallet, R.H.& Schmidt, L.A. 2[M2] Malvern, L.E. 104[M1] 105[M1] 124[M1] Marcal, P.V. 2[M3] 2[M5] 6[M6] Marcal, P.V.& King, I.P. 2[M4] Marcal, P.V.& Pilgrim, W.R.A. 2[M7] Marguerre's equations 119 Marguerre, K. 119[M2] Marques, J.M.M.C. 153[M4] 154[M4] 167[M4] 172[M4] 173[M4] Martin, J.B. 152[M10] 154[M10] 160[M3] 193[M10] Martin, J.B.& Bird, W.W. 154[M2] Mase, G.E. 104[M3] Material axes 128 Material non-linearity 205—206 Material triad 130 Mathematical programming and plasticity 193—196 Matthies, H. 154[M6] 160[M6] Matthies, H.& Strang, G. 308[M1] 309[M1] Matthies, H.G. 193[M5] 194[M5] Mattiason, K. 211[M1] Mattiasson, K. 104[M4] Maximum norm 289 Mean-normal procedure 175 Meek, J.L.& Loganthan, S . 286[M2] 286[M3] Meek, J.L.& Tan, H.S. 286[M4] Melhem, R.G.& Rheinboldt, W.C. 286[M3] Membrane locking 207 242 Membrane strains 235 Mendelson, A. 152[M7] 154[M7] Mid-point algorithms, generalised trapezoidal 173—176 Mid-point geometric vector 83 Mid-point incremental strain updates 82—85 Milford, R.V.& Schnobrich, W.C. 234[M2] 235[M2] 236[M2] 242[M2] Mindlin — Reissner analysis 236 237 239 Minimisation procedure 195 Mitchell, G.P.& Owen, D.R.J. 154[M8] Moan, T.& Soreide, T. 201[M2] 207[M2] Mohr's circle 131 Moore, G . 270[M5] 326[M5] Morley, L.S.D. 234[M4] 242[M4] 242[M5] Mroz, 2, 162[M9] Munay, D.W.& Wilson, E.L. 2[M8] 2[M9] 2[M10] NAFEMS (National Agency of Finite Elements) 1 90 Nagtegal, J.C. 167[N1] 173[N1] Nanson's formula 125 Nayak, G.C.& Zienkiewicz, O.C. 2[N1] 2[N2] Nazareth, L. 308[N1] 311[N1] Nemat-Nasser, S. 152[N3] Newton — Raphson algorithm 154 Newton — Raphson method 1 2 8—13 98 167 178 180 183 252 254 271—273 282 Newton — Raphson method, computer program 39—41 Newton — Raphson method, flowchart 41 Newton — Raphson method, subroutine ITER 41—44 Nocedal, J. 308[N2] 311[N2] Nodal displacement 138 Nominal stress 123 125 Non-associative plasticity 158—159 Non-linear finite elements history 1—2 Non-linear finite elements, general introduction 1 Non-linear materials 205—206 Non-linear shell analysis 234 Non-proportional loading 289 Noor, A.E.& Peters, J.M. 326[N3] Nour-Omid, B. 325[N5] Nour-Omid, B.& Rankin, C.C. 211[N1] 213[N1] Nour-Omid, B., Parlett, B.N.& Taylor, R.L. 325[N4] Numerical integration 206—207 Numerical integration, Lobatto rule for 334 Nygard, M.K. 235[N1] 242[N1] Nyssen, C. 156[N4] 167[N4] 172[N4] 173[N4] Oden, J.T. 2[O1] 2[O2] 12[O2] Operator splitting 171 Oran, C. 211[O2] 212[O2] 213[O2] Oran, C.& Kassimali, A. 201[O1] 212[O1] 213[O1] Ortiz, M.& Popov, E.P. 167[O2] 171[O2] 175[O2] Ortiz, M.& Simo, J.C. 171[O1] Otter, J.R.H.& Day, A.S. 325[O1] Out-of-balance forces 10—12 14 18 19 44 137 148 255—257 Owen, D.R.J.& Hinton, E. 152[O4] 170[O4] Owen, D.R.J., Prakahs, A.& Zienkiewicz, O.C. 162[O5] Padovan, J.P.& Arechaga, T. 274[P1] Papadrakakis, M. 325[P2] 325[P4] Papadrakakis, M.& Gantes, C.J. 325[P3] Papadrakakis, M.& Nomikos, N. 325[P5] 26 Parisch, H. 234[P2] 235[P1] Park, K.C. 274[P7] Park, K.C.& Rankin, C.C. 325[P6] Parlett, B .N. 325 [PSI Path-measuring parameters 289 Pawsey, S.E.& Clough, R.W. 234[P3] Pecknold, D.A., Ghaboussi, J.& Healey, T.J. 90[P1 Pica, A.& Hinton, E. 310[P9] Piola-Kirchhoff stresses 68 73 118—119 131 143 146—147 238 Planar truss element 80 Plane strain 107—108 181 Plane stress 107—108 181—184 190—192 Plane stress, consistent tangent modular matrix for 184 Plastic strain-rate multiplier 157 158 Plasticity 152—200 Plasticity algorithms 153 Plasticity and mathematical programming 193—196 Plasticity, numerical solution 152 Polak, E.& Ribiere 325[P10] Polar-decomposition theorem 126—130 Pope, G.A. 2[P1] Popov, E.P., Khojasteh Baht, M.& Yaghmai, S. 2[P2] potential energy 19 see Powell, G .& Simons, J. 276[P11] Prager, W. 152[P1] 153[P1] 154[P1] 162[P2] Prandtl — Reuss flow rules 157 Prathap, G . 201[P1] Predictor solution 285—286 Predictors 170—171 Principal strain 130 Principle of virtual work 68 125 214 Providos, E. 235[P4] 242[P4] Pythagoras' theorem 3 66 96 Quadratic convergence 9 12 Quasi-Newton formula 3 11 Quasi-Newton methods 252 307—310 Radial-return algorithm 177—178 Radial-return method 164 Ramm, E. 234[R1] 236[R1] 243[R1] 266[R1] 266[R2] 274[R1] 274[R2] 287[R1] 287[R2] Ramm, E.& Matzenmiller, A. 178[R1] 184[R1] 234[R2] 235[R2] 236[R2] 243[R2] Rankin, C.C.& Brogan, F.A. 213[R1] Rate equations, integrating 166—178 Reissner's beam theory 221—225 Reissner, E. 221 [R2] Restart facilities 290—291 Rheinboldt, W.C. 252[R3] 252[R4] 252[R6] 266[R6] 274[R6] Rheinboldt, W.C.& Riks, E. 252[R7] 270[R7] 324[R7] Rib, E. 253[R8] 253[R9] 266[R8] 266[R9] 271[R8] 271[R9] 275[R8] R9] 275[R11] 286[R13] 324[R11] 324[R12] 326[R10] 326[R11] 326[R12] Rice, J.R.& Tracey, D.M. 175[R2] Rigid-body rotation 113—115 Riks, E.& Rankin, C.C. 272[R14] 274[R14] Rods, two-dimensional formulations 201—233 Rotated engineering strain 58—59 213 Rotated log-strain 59—60 76—77 Rotated log-strain, formulation allowing for volume change 60—61 Rotating bar, deep truss (large strains) 90—91 Rotating bar, shallow truss (small strains) 91—93 Rotation variables 235 Runesson, K.& Samuelsson, A. 154[R3] 193[R3] 194[R3] Sabir, A.B.& Lock, A.C. 2[S1] Samuelsson, A.& Froier, M. 152[S1] 154[S1] 193[S1] 194[S1] Scalar loading parameter 271 Scaling parameter 271 Schmidt, F.K., Bognor, F.K.& Fox, R.L. 2[S2] Schmidt, W.F. 266[S1] 269[S1] 287[S1] Schreyer, H.L., Kulak, R.F.& Kramer, J.M. 167[S3] 172[S3] 173[S3] 177[S3] Schweizerhof, K.& Wriggers, P. 266[S2] 275[S2] Secant-related acceleration techniques 310—314 Shallow arch equations 218 219 Shallow arch formulation 201—201 1 Shallow shells 236—243 Shallow shells, formulation extensions 242—243 Shallow truss element 23—56 Shallow truss strain relationships 57 Shallow truss theory 23 Shallowness assumption 1 Shanno, D.F. 266[S3] 274[S3] 308[S4] 311[S3] Shape functions 70—72 137 204 217 223—225 Sharifi, P.& Popov, E.P. 2[S3] Shear deformation 208 Shear factor 238 Shear-locking 210—211 shells 234—251 Shells, degenerate-continuum element using total Lagrangian formulation 243—247 Shells, non-linear analysis 234—235 Shells, smooth and non-smooth 235 see Simo, J.C. 221[S1] Simo, J.C.& Fox, D.D. 235[S1] Simo, J.C.& Govindjee, S . 154[S7] 178[S7] 182[S7] 183[S7] 192[S7] Simo, J.C.& Hughes, T.J.R. 152[S5] 178[S5] 193[S5] 194[S5] Simo, J.C.& Taylor, R.L. 153[S6] 178[S4] 178[S6] 182[S6] 184[S6] 192[S6] Simo, J.C.& Vu-Quoc, L. 214[S2] 221[S2] Simo, J.C., Fox, D.D.& Rafai, M.S. 235[S2] 235[S3] Simo, J.C., Wriggers, P., Schweizerhof, K.H. & Taylor, R.L. 266[S6] Simons, J.& Bergan, P.G. 276[S5] Simpson's rule 2 Sixth degree of freedom 235 Sloan, S.W. 167[S8] 172[S8] Small-strain limit-point example with one variable 314—316 Snap-backs 26 100—101 270 323—324 Snap-throughs 2 266 270 Space truss elements 80—82 Spencer, A.J.M. 104[S1] Spherical arc-length method 273—274 285 Stabilisation technique 234 Stander, N., Matzenmiller, A.& Ramm, E. 234[S4] 243[S4] Stanley, G.M. 234[S5] 235[S5] Stanley, G.M., Park, K.C.& Hughes, T.J.R. 234[S6] 235[S6] Stiffness matrix 272 Stolarski, H.& Belytschko, T. 207[S3] Stolarski, H., Belytschko, T., Carpenter, N. & Kennedy, J.M. 234[S7] 243[S7] strain See Stress and strain; Stress-strain relationships Strain hardening 159—160 160—161 Strain increment using updated coordinates 72—73 Strain-displacement relationships 65—68 6—7 Strain-displacement vector 68 Strain-inducing ex tension 2 13 Strang, G., Matthies, H.& Temam, R. 154[S9] 193[S9] Stress and strain measures 57—103 122 124—126 Stress and strain, tensor and vector rotations 105—106 Stress rates 166 Stress resultants 235 Stress updating, incremental or iterative strain 154—156 Stress-strain laws 132—133 Stress-strain relationships 107—101 0 144 Stretching stresses and strains 213 Stricklin, J.A., Haisler, W.E.& Von Riesemann, W.A. 2[S4] 252[S7] Sub-increments 172—173 188—189 Surana, K.S. 201[S4] 225[S4] 234[S8] 236[S8] 243[S8] Tang, S.C., Yeung, K.S.& Chon, C.T. 211[T2] Tangent modular matrix 2 153 154 166 Tangent stiffness 11 Tangent stiffness matrix 4 73 78 148 205 209 211 212 216 223 225 236 241 246—247 Tangential incremental solution 10 Taylor expansion 254 Taylor, R.L.& Simo, J.C. 235[T1] Tensor notation 165 Terazawa, K., Ueda, Y.& Matsuishi, M. 2[T1] Thompson, J.M.T.& Hunt, G.W. 326[T1] Three-dimensional formulation 140—141 Through-thickness integration 234 Thurston, G.A. 326[T2] 326[T4] Thurston, G.A., Brogan, EA.& Stehlin, P. 326[T3] Time-independent el asto-plasticity 152 Timoshenko beam formulation 208
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