Computational Methods in Nonlinear Structural and Solid Mechanics (eBook)

Papers Presented at the Symposium on Computational Methods in Nonlinear Structural and Solid Mechanics

Harvey G. McComb, Ahmed K. Noor (Herausgeber)

eBook Download: PDF

2014 | 1. Auflage
470 Seiten
Elsevier Science (Verlag)
9781483145648 (ISBN)

Infos

Computational Methods in Nonlinear Structural and Solid Mechanics covers the proceedings of the Symposium on Computational Methods in Nonlinear Structural and Solid Mechanics. The book covers the development of efficient discretization approaches; advanced numerical methods; improved programming techniques; and applications of these developments to nonlinear analysis of structures and solids. The chapters of the text are organized into 10 parts according to the issue they tackle. The first part deals with nonlinear mathematical theories and formulation aspects, while the second part covers computational strategies for nonlinear programs. Part 3 deals with time integration and numerical solution of nonlinear algebraic equations, while Part 4 discusses material characterization and nonlinear fracture mechanics, and Part 5 tackles nonlinear interaction problems. The sixth part discusses seismic response and nonlinear analysis of concrete structure, and the seventh part tackles nonlinear problems for nuclear reactors. Part 8 covers crash dynamics and impact problems, while Part 9 deals with nonlinear problems of fibrous composites and advanced nonlinear applications. The last part discusses computerized symbolic manipulation and nonlinear analysis software systems. The book will be of great interest to numerical analysts, computer scientists, structural engineers, and other professionals concerned with nonlinear structural and solid mechanics.

Inhalt

Front Cover 1
Computational Methods in Nonlinear Structural and Solid Mechanics 2
Copyright Page 3
Table of Contents 4
PREFACE 6
Part 1: Nonlinear Mathematical Theories and Formulation Aspects 8
CHAPTER 1. 
10 
Abstract 10
1. INTRODUCTION 10
2. THEORETICAL DEVELOPMENT 11
3. FINITE-DIFFERENCE FORMULATION 14
4. COMPARISON WITH EXPERIMENT OR INDEPENDENT PREDICTIONS 14
5. SUMMARY OF CURRENT RESULTS 15
6. CONCLUSIONS AND COMMENTS 15
REFERENCES 16
CHAPTER 2. 
18 
Abstract 18
INTRODUCTION 18
1. PRELIMINARIES AND A GENERAL VARIATIONAL PRINCIPLE 18
2. FINITE DEFORMATIONS OF A BEAM 19
CLOSURE 24
REFERENCES 25
CHAPTER 3. 
26 
Abstract 26
INTRODUCTION 26
STRATEGIES OF SHELL ELEMENT DERIVATION 26
FORMULATION OF LARGE DEFORMATION SHELL ELEMENT 27
3D CONTINUUM ELEMENT SHELL ELEMENT 27
NUMERICAL EXAMPLES 31
CONCLUSIONS 33
REFERENCES 33
APPENDIX 33
Part 2: Computational Strategies for Nonlinear Programs 36
CHAPTER 4. 
38 
Abstract 38
NOMENCLATURE 38
1. INTRODUCTION 38
2. REDUCTION METHODS FOR NONLINEAR STATIC PROBLEMS 39
3. COMPUTATIONAL PROCEDURE USED WITH REDUCTION METHODS 40
4. CASE OF PRESCRIBED EDGE DISPLACEMENTS 41
5. USE OF REDUCED-BASIS TECHNIQUE IN CONJUNCTION WITH MIXED FINITE ELEMENT MODELS 42
6. REDUCTION METHODS FOR NONLINEAR DYNAMIC PROBLEMS 42
7. TWO-STAGE RAYLEIGH-RITZ AND BUBNOV-GALERKIN TECHNIQUES 43
8. NUMERICAL STUDIES 44
9. FUTURE DIRECTIONS FOR RESEARCH ON REDUCTION METHODS 49
10. CONCLUDING REMARKS 49
REFERENCES 50
CHAPTER 5. 
52 
Abstract 52
INTRODUCTION 52
INCREMENTAL SECANT STIFFNESS FORMULATION 53
CONTROLLING LOAD PATH DISCRETIZATION ERROR 55
ADAPTIVE SOLUTION ALGORTIHM 56
EXAMPLE ANALYSES USING ADAPTIVE INCREMENTATION 57
CONCLUSIONS AND FUTURE RESEARCH DIRECTIONS 59
REFERENCES 59
CHAPTER 6. 
62 
Abstract 62
INTRODUCTION 62
RIKS METHOD 63
A MODIFIED RIKS METHOD 63
AN ACCELERATED MODIFIED NEWTON-RAPHSON METHOD WITH FIXED LENGTH INCREMENTS 64
APPLICATIONS 65
CONCLUSIONS 68
REFERENCES 68
CHAPTER 7. AN EFFICIENT AND ACCURATE ITERATIVE METHOD, ALLOWING LARGE INCREMENTAL STEPS, TO SOLVE ELASTO-PLASTIC PROBLEMS 70
Abstract 70
1. INTRODUCTION 70
2. SYSTEM OF EQUATIONS TO SOLVE 70
3. REQUIRED PROPERTIES OF AN EFFICIENT SOLUTION METHOD 71
4. STATE DETERMINATION ALGORITHM 72
5. IMPROVEMENTS OF THE NEWTON-RAPHSON METHOD FOR ELASTO-PLASTIC CASES 74
6. EXAMPLES 74
7. CONCLUSIONS 77
REFERENCES 77
CHAPTER 8. 
80 
Abstract 80
2. NEWTON METHODS 80
3. QUASI-NEWTON METHODS 81
4. COMPUTATIONAL IMPLEMENTATION OF QUASI-NEWTON UPDATES 83
5. NUMERICAL APPLICATIONS 83
CONCLUSIONS 87
REFERENCES 87
CHAPTER 9. 
90 
Abstract 90
INTRODUCTION 90
STUDY OF OPTIMAL GRIDS IN NONLINEAR ANALYSIS 90
MATHEMATICAL FORMULATION 91
SOLUTION SEARCHING TECHNIQUE 91
SAMPLE PROBLEMS 92
DISCUSSION 93
FUTURE WORK 94
REFERENCES 94
APPENDIX A 94
Part 3: Time Integration Techniques and Numerical Solution of Nonlinear Algebraic Equations 96
CHAPTER 10. 
98 
Abstract 98
1. INTRODUCTION 98
2. ONE-STEP METHODS AND STEPLENGTH CONTROL 99
3. THE METHODS TESTED 100
4. STABILITY PROPERTIES. 100
5. EVALUATIONS OF THE JACOBIANS FOR THE TRAPEZOIDAL RULE 101
6. TEST-EQUATIONS 101
7. RESULTS 101
8. COMMENTS 101
9. REFERENCES 103
CHAPTER 11. 
104 
Abstract 104
1. INTRODUCTION 104
2. EQUATIONS OF MOTION 104
3. NUMERICAL FORMULATION 105
4. MATHEMATICAL APPROACH 105
5. STABILITY ANALYSIS 105
6. APPLICATIONS 107
7. FURTHER STUDIES 108
REFERENCES 108
CHAPTER 12. 
110 
Abstract 110
1. INTRODUCTION 110
2. THE SOLUTION MANIFOLD FOR ONE-PARAMETER PROBLEMS 112
3. NUMERICAL DETAILS OF A CONTINUATION PROCESS 112
4. 
117 
REFERENCES 119
CHAPTER 13. 
122 
Abstract 122
1. INTRODUCTION 122
2. FORMULATION 122
3. HÖMOTOPY ALGORIIHM 123
4. QUASH-NEWTON ALGORTfflM 124
5. NUMERICAL RESULTS 125
REFERENCES 126
Part 4: Material Characterization and Nonlinear Fracture Mechanics 128
CHAPTER 14. 
130 
Abstract 130
1. INTRODUCTION 130
2. THEORETICAL BACKGROUND 131
3. EXAMPLES FOR TWO SPECIAL LOAD HISTORIES 132
4. COMPARISON WTTH EXPERHVOENTAL DATA 133
CONCLUSIONS 134
REFERENCES 134
CHAPTER 15. 
136 
Abstract 136
INTRODUCTION 136
PRESENTATION OF THE CONSTITUTIVE THEORY 136
THE VARIATIONAL PRINCIPLE 138
COMPUTER CODE IMPLEMENTATION 139
EXAMPLE PROBLEMS 139
CONCLUSION 141
REFERENCES 142
CHAPTER 16. 
144 
Abstract 144
INTRODUCTION 144
PLASTIC FRACTURE CRITERIA 144
J-RESISTANCE CURVES 145
PREDICTION OF CRACK GROWTH 149
CONCLUSIONS 151
REFERENCES 151
CHAPTER 17. 
152 
Abstract 152
1. INTRODUCTION 152
2. REVIEW OR PREVIOUS APPROACHES 153
3. THE FICTITIOUS CRACK MODEL 156
4. NUMERICAL RESULTS 157
5. DISCUSSION, FUTURE RESEARCH 159
REFERENCES 160
Part 5: 
162 
CHAPTER 18. COMPUTATIONAL METHOD FOR SOIL/STRUCTURE INTERACTION PROBLEMS 164
Abstract 164
INTRODUCTION 164
GENERALIZED DRUCKER-PRAGER MATERIAL MODEL 165
REINFORCED CONCRETE MATERIAL MODEL 165
STRUCTURE/MEDIA INTERFACE MATERIAL MODEL 166
NUMERICAL SOLUTION PROCEDURE 167
NUMERICAL APPLICATION 168
DISCUSSION 168
REFERENCES 169
CHAPTER 19. 
170 
Abstract 170
INTRODUCTION 170
GENERAL DESCRIPTION OF THE SOLUTION ALGORITHMS 170
SUMMARY 173
REFERENCES 173
CHAPTER 20. 
174 
Abstract 174
1. INTRODUCTION 174
2. GOVERNING EQUATIONS 174
3. FINITE ELEMENT DISCRETIZATION 175
4. SOLUTION OF COUPLED NONLINEAR FLUID-STRUCTURE SYSTEMS 175
5. EXAMPLE PROBLEM 176
6. DISCUSSION OF RESULTS 176
7. FUTURE INVESTIGATIONS 176
8. CONCLUSIONS 176
REFERENCES 176
CHAPTER 21. 
178 
Abstract 178
1. INTRODUCTION 178
2. DESCRIPTION OF THE PHYSICAL MODEL 178
3. A BEAM COLUMN ELEMENT FOR MODERATELY LARGE ELASTIC DEFORMATION 179
4. FLUID ELEMENT FORMULATION 182
5. FLUID/THERMAL/STRUCTURAL INTERACTION EXAMPLE 184
6. FUTURE PROJECTIONS AND RESEARCH 184
REFERENCES 184
Part 6: Seismic Response and Nonlinear Analysis of Concrete Structures 186
CHAPTER 22. 
188 
Abstract 188
1. INTRODUCTION 188
2. A MODEL FOR HYSTERETIC BEHAVIOR OF NONLINEAR ELEMENTS 188
3. EQUATIONS OF MOTION FOR THE SYSTEM 189
4. NUMERICAL SOLUTION OF THE DIFFERENTIAL EQUATIONS OF MOTION 190
5. NUMERICAL EXAMPLE 192
6. CONCLUSIONS 195
REFERENCES 195
CHAPTER 23. 
196 
Abstract 196
INTRODUCTION 196
METHOD OF ANALYSIS 196
NUMERICAL EXAMPLE, OBSERVATIONS AND FUTURE 201
REFERENCES 202
CHAPTER 24. 
204 
Abstract 204
NOMENCLATURE 204
1. INTRODUCTION 204
DERIVATION OF EQUATIONS OF MOTION 205
STABILITY OF COUPLED RESPONSE 206
TYPICAL RESULTS AND DISCUSSION 208
SUMMARY AND CONCLUSIONS 210
FUTURE RESEARCH 211
REFERENCES 211
CHAPTER 25. 
212 
Abstract 212
1. INTRODUCTION 212
2. IDEALIZATION OF THE STRUCTURE 213
3. METHOD OF ANALYSIS 213
4. MODEL TEST AND COMPARISON WITH THE THEORY 215
5. APPLICATION TO ACTUAL STRUCTURE 215
6. CONCLUSION 218
REFERENCES 218
CHAPTER 26. 
220 
Abstract 220
Untitled 220
CRACK REPRESENTATION 220
CONCEPT OF RELATIVE STRAIN ACROSS THE CRACK 220
INTERFACE-STRESS-TRANSFER MODEL FOR CRACKSES IN PLAIN CONCRETE 221
POST-CRACKING MODEL FOR PLAIN CONCRETE 222
INTERFACE SHEAR TRANSFER CAPACITY OF CRACKED CONCRETE 223
RESIDUAL INTERFACE SHEAR TRANSFER CAPACITY OF CRACKED CONCRETE 224
CRACK OPENING AND CLOSING, NORMAL STRESS AND NORMAL STIFFNESS OF A CRACK 224
INITIAL SHEAR MODULUS, SHEAR STRESS AND SHEAR STIFFNESS OF A CRACK 225
COUPLED SHEAR STIFFNESS OF A CRACK 226
DILATANT-CONTRACTANT STIFFNESS OF A CRACK 227
CROSS SHEAR 227
CONCLUSION 228
REFERENCES 228
CHAPTER 27. 
230 
Abstract 230
INTRODUCTION 230
PRESENT METHOD 230
CONCLUSIONS 232
REFERENCES 233
APPENDIX 233
Part 7: Nonlinear Problems for Nuclear Reactors 236
CHAPTER 28. FUTURE NEEDS FOR INELASTIC ANALYSIS IN DESIGN OF HIGH-TEMPERATURE NUCLEAR PLANT COMPONENTS 238
Abstract 238
1. INTRODUCTION 238
2. THE HIGH-TEMPERATURE STRUCTURAL DESIGN METHODOLOGY 238
3. MATERIAL DEFORMATION MODELING 240
4. TIME-DEPENDENT FAILURE CRITERIA 242
5. INELASTIC ANALYSES AND THEIR VALIDATION 243
6. SUMMARY 247
REFERENCES 247
CHAPTER 29. 
248 
Abstract 248
INTRODUCTION 248
AXISYMMETRIC MODEL OF PIPE OR ELBOW BENDING PROBLEM 249
NUMERICAL RESULTS 251
CONCLUSIONS 254
REFERENCES 254
CHAPTER 30. 
256 
Abstract 256
INTRODUCTION 256
PROGRAM DESCRIPTION 256
ANALYSIS OF HIGH-TEMPERATURE REACTOR PIPING COMPONENT 260
FUTURE RESEARCH DIRECTIONS 262
REFERENCES 263
CHAPTER 31. 
264 
Abstract 264
BACKGROUND 264
SOLUTION METHOD 265
EXAMPLES 266
DISCUSSION 267
CONCLUSIONS 267
FUTURE TRENDS IN NON-LINEAR STRUCTURAL ANALYSIS 268
REFERENCES 268
APPENDIX A 268
APPENDIX B 269
APPENDIX C 269
CHAPTER 32. 
270 
Abstract 270
1. INTRODUCTION 270
2. PROBLEM STATEMENT 270
3. FINITE ELEMENT MODEL 270
4. NUMERICAL RESULTS 274
5. CONCLUSIONS 276
REFERENCES 281
Part 8: Crash Dynamics and Impact Problems 282
CHAPTER 33. 
284 
Abstract 284
INTRODUCTION 284
DYCAST FORMULATION 286
AUTOMOBILE CRASH SIMULATION 288
AIRCRAFT CRASH SIMULATION 290
CONCLUDING REMARKS 291
REFERENCES 291
CHAPTER 34. 
294 
Abstract 294
INTRODUCTION 294
DESCRIPTION OF EXPERIMENTS 294
EXPERIMENTAL RESULTS 295
COMPARISON OF EXPERIMENTAL RESULTS WITH ANALYSIS 297
CONCLUSIONS 299
REFERENCES 301
CHAPTER 35. 
302 
Abstract 302
INTRODUCTION 302
TWO-DIMENSIONAL ANALYSIS 303
THREE-DIMENSIONAL ANALYSIS 305
CONCLUDING REMARKS 307
REFERENCES 307
APPENDIX 308
CHAPTER 36. 
310 
Abstract 310
INTRODUCTION 310
OBJECTIVE 310
APPROACH 310
COMPUTER MODEL DEVELOPMENT 310
CODE CALIBRATION AND EXPERIMENTAL RESULTS 312
VELOCITY AUGMENTOR OPTIMIZATION 313
H.E. TAMPING OPTIMIZATION 313
SHOCK ATTENUATOR OPTIMIZATION 314
MOMENTUM TRAP DESIGN 315
CONCLUSIONS 315
FUTURE EFFORT 315
REFERENCES 316
CHAPTER 37. 
318 
Abstract 318
INTRODUCTION 318
TARGET STRUCTURE 318
MISSILE IMPACT CONDITIONS 319
MATERIAL MODEL 319
PROBLEM SIMULATION 320
COMPUTATIONAL ALGORITHM 320
DYNAMIC RESPONSE CALCULATIONS 321
CONCLUSION 324
REFERENCES 325
Part 9: Nonlinear Problems of Fibrous Composites and Advanced Nonlinear Applications 326
CHAPTER 38. FINITE ELEMENT ANALYSIS OF ELASTIC-PLASTIC FIBROUS COMPOSITE STRUCTURES 328
Abstract 328
INTRODUCTION 328
A CONTINUUM ELEMENT FOR FIBROUS MATERIALS 329
PAC78 COMPUTER PROGRAM 331
APPLICATION TO LAMINATED PLATES WITH DISCONTINUITIES 334
CONCLUSIONS 336
Acknowledgements 336
REFERENCES 337
APPENDIX 337
CHAPTER 39. 
338 
Abstract 338
INTRODUCTION 338
INCREMENTAL VIRTUAL WORK EQUATION 339
DESCRIPTION OF THE ELEMENT 339
MATERIAL MODELING 342
NUMERICAL CHARACTERISTICS OF THE ELEMENT 343
NUMERICAL EXAMPLES 344
CONCLUSION 346
REFERENCES 346
CHAPTER 40. LARGE-DEFLECTION AND LARGE-AMPLITUDE FREE VIBRATIONS OF LAMINATED COMPOSITE-MATERIAL PLATES 348
Abstract 348
INTRODUCTION 348
2. GOVERNING EQUATIONS OF MODERATELY THICK PLATES ACCOUNTING FOR LARGE DEFLECTIONS 349
3. VARIATIONAL FORMULATION 349
4. FINITE ELEMENT MODEL 350
5. NUMERICAL RESULTS AND DISCUSSION 350
6. SUMMARY, CONCLUSIONS, AND SUGGESTIONS FOR FUTURE RESEARCH 353
REFERENCES 353
CHAPTER 41. 
356 
Abstract 356
2. EXPRESSIONS FOR ENERGY DENSITIES 357
3. TRIAL SOLUTIONS 359
4. FORMAL STATEMENT OF THE RESULTS OF RAYLEIGFHUTZ PROCEDURE 359
5. EXPLICIT EXPRESSIONS FOR THE ORDINARY DIFFERENTIAL EQUATIONS OF MOTION 360
6. EXPRESSIONS FOR NONLINEAR MASS, GYROSCOPIC STIFFENESS AND LOAD MATRICES 361
7. GENIRAL NATURE OF THE DISCRETIZATION AND ITS COST 361
8. CONCLUSIONS 362
REFERENCES 362
CHAPTER 42. 
364 
Abstract 364
INTRODUCTION 364
DESCRIPTION AND VERIFICATION 364
APPLICATION TO AUTO FRAME CRUSH 367
REFERENCES 369
CHAPTER 43. 
370 
Abstract 370
INTRODUCTION 370
FORMULATION 371
FINITE ELEMENT AND CONTACT CONDITIONS 372
NUMERICAL EXAMPLES 374
SUMMARY AND DISCUSSION 375
REFERENCES 376
APPENDIX 376
CHAPTER 44. 
378 
Abstract 378
1. INTRODUCTION 378
2. METHODS FOR APPROXIMATE RANDOM VIBRATION ANALYSIS OF M-D-O-F SYSTEMS 379
3. SYSTEM DEFINITION 379
4. SYSTEM RESPONSE SIMULATIONS 379
5. APPLICATION OF EQUIVALENT LINEARIZATION 382
6. SUMMARY 382
REFERENCES 383
Part 10: Computerized Symbolic Manipulation and Nonlinear Analysis Software Systems 384
CHAPTER 45. 
386 
Abstract 386
NOMENCLATURE 386
1. INTRODUCTION 386
2. FINITE ELEMENT FORMULATION 387
3. MACSYMA PROGRAMS 389
4. TASKS WHICH CAN BE EFFICIENTLY PERFORMED USING SYMBOLIC MANIPULATION 390
5. PROBLEM AREAS IN THE APPLICATION OF SYMBOLIC COMPUTING TO NONLINEAR ANALYSIS 390
CONCLUDING REMARKS 391
REFERENCES 391
APPENDIX A 391
CHAPTER 46. 
412 
Abstract 412
1. BACKGROUND 412
2. THE GENESIS OF NICE 413
3. ARCHITECTURE AND PROCESSORS 413
4. PROCESSOR CONTROL 415
5. WHAT THE USER SEES 416
6. CENTRAL DIFFERENCE INTEGRATION 418
7. CONCLUDING REMARKS 419
REFERENCES 419
APPENDIX A 419
APPENDIX B 420
CHAPTER 47.MAGNA: A FINITE ELEMENT SYSTEM FOR THREE-DIMENSIONAL NONLINEAR STATIC AND DYNAMIC STRUCTURAL ANALYSIS 422
Abstract 422
INTRODUCTION 422
THEORETICAL CONSIDERATIONS 422
FINITE ELEMENT LIBRARY 423
ELEMENT LEVEL COMPUTATIONS 424
NUMERICAL EXAMPLES 425
SUMMARY AND CONCLUSIONS 429
FUTURE DEVELOPMENTS 429
REFERENCES 429
CHAPTER 47. 
432 
INTRODUCTION 432
SOURCES OF INFORMATION ABOUT COMPUTER PROGRAMS 432
BACKGROUND MATERIAL NEEDED FOR EFFECTIVE EVALUATION AND USE OF FINITE ELEMENT PROGRAMS 432
GUIDELINES FOR SELECTION OF A COMPUTER PROGRAM 433
SUMMARY OF PROGRAM CAPABILITIES 433
PROGRAM SURVEY AND DESCRIPTION 433
ANSR-I AND ANSR-II 448
ANSYS 449
ASAS-NL 450
ASKA 450
BEAM 451
BOSOR4 452
BOSORS 452
BOVA 453
BOVAC 454
BRICK 454
DIAL 456
DRAIN-2D, DRAIN-TABS 456
PLANS, DYCAST 457
ELAS55 458
HONDO II 459
JAC 459
LARSTRAN 80 460
MARC 460
MSC/NASTRAN 461
NEPSAP 462
PAC78 463
POLO-FINITE 463
SAMCEF 464
SAMSON 465
SESAM-69 465
SMART 466
STAGSC-1 467
STRAW 467
TEPSA 468
ULARC 468
WECAN 469
WHAMS 469
REFERENCES 470

Produkt-Details

• Erscheint lt. Verlag: 20.5.2014
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Analysis
• Themenwelt: Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
• Themenwelt: Technik ► Bauwesen
• ISBN-13: 9781483145648 / 9781483145648