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Cover image for Structural plasticity : limit, shakedown and dynamic plastic analyses of structures
Title:
Structural plasticity : limit, shakedown and dynamic plastic analyses of structures
Personal Author:
Series:
Advanced topics in science and technology in China
Publication Information:
Germany : Springer, 2009
Physical Description:
xvii, 384 p. : ill. ; 25 cm.
ISBN:
9783540881513
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30000010197079 TA652 Y8 2009 Open Access Book Book
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Summary

Summary

Limit and shakedown analysis for structures can provide a very useful tool for design and analysis of engineering structures. "Structural Plasticity - Limit, Shakedown and Dynamic Plastic Analyses of Structure" provides more general solutions of limit and shakedown analysis for structures by using a unified strength theory. A series of solutions of plates from circular, annular plates to rhombus plates and square plates, rotating discs and cylinders, pressure vessels are presented. These results encompass the Tresca-Mohr-Coulomb solution of structure as special cases. The unified solution, which cannot be obtained by using a single criterion, is suitable to more materials and structures.

Maohong Yu is professor of Department of Civil Engineering at Xi'an Jiaotong University, China. He has authored 12 books including "Unified Strength Theory and Its Applications" and "Generalized Plasticity".


Author Notes

Maohong Yu is professor of Department of Civil Engineering at Xi'an Jiaotong University, China. He has authored 12 books including Unified Strength Theory and Its Applications and Generalized Plasticity.


Table of Contents

1 Introductionp. 1
1.1 Backgroundp. 1
1.2 Unification of Yield and Strength Criteriap. 3
1.3 Plastic Limit Analysisp. 4
1.4 Plastic Limit Analysis of Rotating Solidsp. 6
1.5 Shakedown Analysis of Structuresp. 7
1.6 Plastic Limit Analysis Based on the Unified Strength Theoryp. 8
1.7 Summaryp. 9
Referencesp. 9
2 Fundamental Concepts of Stress and Srainp. 16
2.1 Stress Components and Invariantsp. 16
2.2 Deviatoric Stress Tensor and the Tensor Invariantsp. 18
2.3 Principal Shear Stressesp. 21
2.4 Octahedral Shear Stressp. 21
2.5 Strain Componentsp. 22
2.6 Equations of Equilibriump. 24
2.7 Generalizes Hooke's Lawp. 24
2.8 Compatibility Equationsp. 25
2.9 Governing Equations for Plane Stress Problemsp. 26
2.10 Governing Equations in Polar Coordinatedp. 27
2.11 Bending of Circular Platep. 29
2.12 Summaryp. 31
Referencesp. 31
3 Yield Conditionp. 32
3.1 Introductionp. 32
3.2 Conventional Yield Criteriap. 33
3.2.1 Maximum Normal Stress Criterionp. 33
3.2.2 Maximum Shear Stress-based Criteria-Single-Shear Theoryp. 33
3.2.3 Octahedral Shear Stress-based Criteria-Three Shear Theoryp. 36
3.2.4 Twin- shear Stress-based Criterion-Twin-shear Theoryp. 40
3.3 Unified Yield Criterion for Metallic Materials (Non-SD Materials)p. 44
3.4 Unified Strength Theory for SD Materialsp. 45
3.4.1 Mechanical Model of the Unified Strength Theoryp. 46
3.4.2 Mathematical Modeling of the Unified Strength Theoryp. 47
3.4.3 Mathematical Expression of the Unified Strength Theoryp. 48
3.4.4 Yield Surfaces and Yield Loci of the Unified Strength Theoryp. 48
3.5 Significance of the Unified Strength Theoryp. 52
3.6 Unified Strength Theory in the Plane Stress Statep. 52
3.6.1 ?1 ? ?2 > 0, ?3 = 0p. 53
3.6.2 ?1 ? 0,?2 = 0, ?3p. 53
3.7 Summaryp. 56
3.8 Problemsp. 56
Referencesp. 61
4 Theorems of Limit Analysisp. 64
4.1 Introductionp. 64
4.2 Perfectly Plastic Solidp. 66
4.3 Power of Dissipationp. 66
4.4 Lower-Bound Thepremp. 67
4.5 Upper-Bound Theoremp. 68
4.6 Fundamental Limit Theoremsp. 68
4.7 Important Remarksp. 69
4.7.1 Exact Value of the Limit Load (Complete Solution)p. 69
4.7.2 Elastic-Plastic and Rigid plastic Bodiesp. 69
4.7.3 Load-bearing Capacityp. 70
4.7.4 Uniquenessp. 71
References

p. 71

5 Plastic Limit Analysis for Simply Supported Circular Platesp. 74
5.1 Introductionp. 74
5.2 Basic Equations of Circular Platep. 75
5.3 Unified Solutions of Simply Supported Circular Plate for Non-SD Materialsp. 76
5.3.1 Uniformly Distributed Loadp. 78
5.3.2 Arbitrary Axisymmetrical Loadp. 80
5.4 Unified Solutions of Simply Supported Circular Plate for SD Materialsp. 95
5.4.1 Partial-uniform Loadp. 97
5.4.2 Linearly Distributed Loadp. 102
5.5 Summaryp. 107
5.6 Problemsp. 108
References

p. 110

6 Plastic Limit Analysis of Clamped Circular Platesp. 112
6.1 Introductionp. 112
6.2 Unified Solutions of Clamped Circular Plate for Non-SD Materialsp. 112
6.2.1 Uniformly Distributed Loadp. 112
6.2.2 Arbitrary Loading Radiusp. 117
6.2.3 Arbitrary Loading Distributionp. 122
6.3 Unified Solutions of Clamped Circular Plate for SD Materialsp. 127
6.4 Summaryp. 133
6.5 Problemsp. 134
References

p. 134

7 Plastic Limit Analysis of Annular Platep. 136
7.1 Introductionp. 136
7.2 Basic Equations for Annular Plate Based on UYCp. 137
7.2.1 Case (1)p. 140
7.2.2 Case (2)p. 141
7.2.3 Special Casep. 142
7.3 Unified Solutions of Annular Plate for Non-SD Meterialsp. 142
7.4 Unified Solutions of Limit Load of Annular Plate for SD Materialsp. 145
7.4.1 Unified Strength Theoryp. 145
7.4.2 Basic Equations for Annular Plate Based on the USTp. 146
7.4.3 Limit Analysisp. 147
7.4.4 Results and Discussionsp. 149
7.5 Summaryp. 150
7.6 Problemsp. 152
Referencesp. 152
8 Plastic Limit Analyses of Oblique, Rhombic, and Rectangular Platesp. 154
8.1 Introductionp. 154
8.2 Equations for Oblique Platesp. 156
8.2.1 The Equilibrium Equation in Ordinary Coordinate Systemp. 156
8.2.2 Field of Internal Motionp. 158
8.2.3 Moment Equation Based on the USTp. 158
8.3 Unified Solution of Limit Analysis of Simply Supported Oblique Platesp. 159
8.4 Limit Load of Rhombic Platesp. 162
8.5 Limit Load of Rectangular Platesp. 163
8.6 Unified Limit Load of Square Platesp. 168
8.7 Tabulation of the Limit Load for Oblique, Rhombic and Square Platesp. 169
8.8 Summaryp. 170
8.9 Problemsp. 172
Referencesp. 173
9 Plastic Limit Analysis of Pressure Vesselsp. 175
9.1 Introductionp. 175
9.2 Unified Solution of Limit Pressure of Thin-walled Pressure Vesselp. 176
9.3 Limit Pressure of Thick-walled Hollow Spherep. 180
9.3.1 Elastic Limit Pressure of Thick-walled Sphere Shellp. 181
9.3.2 Plastic Limit Pressure of Thick-walled Sphere Shellp. 182
9.4 Unified Solution of Elastic Limit Pressure of Thick-walled Cylinderp. 184
9.5 Unified Solution of Plastic Limit Pressure of Thick-walled Cylinderp. 190
9.5.1 Stress Distributionp. 190
9.5.2 Plastic Zone in the Elasto-plastic Rangep. 192
9.5.3 Plastic Zone Radius in the Elasto-plastic Rangep. 193
9.5.4 Plastic Limit Pressurep. 193
9.6 Summaryp. 198
9.7 Problemsp. 200
Referencesp. 202
10 Dynamic Plastic Response of Circular Platep. 205
10.1 Introductionp. 205
10.2 Dynamic Equations and Boundary Conditions of Circular Platep. 206
10.2.1 First Phase of Motion (0 ? T ? ?)p. 209
10.2.2 Second Phase of Motion (? ? t ? T)p. 212
10.3 Static and Kinetic Admissibilityp. 214
10.4 Unified Solution of Dynamic Plastic Response of Circular Platep. 216
10.5 Special Cases of the Unified Solutionsp. 221
10.6 Summaryp. 229
Referencesp. 229
11 Limit Angular Speed of Rotating Disc and Cylinderp. 231
11.1 Introductionp. 231
11.2 Elastic Limit of Discsp. 232
11.3 Elasto-plastic Analysis of Discsp. 233
11.4 Elasto-plastic Stress Field of Rotating Discp. 236
11.5 Solution Procedure and Resultsp. 238
11.6 Unified Solution of Plastic Limit Analysis of Rotating Cylinderp. 239
11.7 Limit Analysis of a Solid Disc with Variable Thicknessp. 242
11.8 Limit Analysis of an Annular Disc with Variable Thicknessp. 246
11.8.1 Case (1) (1 > ? ? ?0)p. 247
11.8.2 Case (2) (0 ? ? ? ?0)p. 248
11.9 Special Case of b = 0p. 251
11.10 Results and Discussionp. 252
11.11 Summaryp. 258
11.12 Problemsp. 258
Referencesp. 259
12 Projectile Penetration into Semi-infinite Targetp. 261
12.1 Introductionp. 261
12.2 Spatial Axisymmetric Form of Unified Strength Theoryp. 262
12.3 Fundamental Equations for Concrete Targetsp. 263
12.3.1 Conservation Equationsp. 263
12.3.2 Relation between Pressure and Bulk Strainp. 264
12.3.3 Failure Criterion Expressed by ?r and ??p. 264
12.3.4 Interface Conditionsp. 265
12.4 Cylindrical Cavity Expansion Analysisp. 265
12.4.1 Elastic Zone (c1t ? r ? cdt, ?1/? ? ? ? 1/?)p. 266
12.4.2 Interface of Elastic-cracked Zones (r = C1t, ? = ?1/?p. 270
12.4.3 Radial Cracked Zone (ct ? r ? C1t, 1 ? ? ? ?1/?)p. 271
12.4.4 Interface of the Plastic and Cracked Zones (r = ct, ? = 1)p. 273
12.4.5 Plastic Zone (vrt ? r ? ct, ? ? ? ? 1)p. 275
12.5 Cavity Expansion Pressure and Velocityp. 276
12.5.1 Incompressible Materialp. 277
12.5.2 Compressible Materialp. 279
12.6 Penetration Resistance Analysisp. 284
12.7 Analysis and Verification of Penetration Depthp. 288
12.8 Summaryp. 290
Referencesp. 291
13 Plastic Analysis of Orthogonal Circular Platep. 293
13.1 Introductionp. 293
13.2 Orthotropic Yield Criteriap. 293
13.3 General Solutionsp. 296
13.4 Simply Supported Orthotropic Circular Platep. 301
13.4.1 Case I: Point A' Falls on Segment KLp. 301
13.4.2 Case II: Point A' Falls on Segment LAp. 302
13.4.3 Case III: Point A! Falls on Segment ABp. 302
13.4.4 Case IV: Point A' Falls on Segment BCp. 302
13.4.5 Moment, Velocity Fields and Plastic Limit Loadp. 303
13.5 Fixed Supported Circular Platep. 307
13.5.1 Case I: Point A' Falls on Segment KLp. 307
13.5.2 Case II: Point A' Falls on Segment LAp. 307
13.5.3 Case III: Point A' Locates on Segment ABp. 307
13.5.4 Case IV: Point A1 Falls on Segment BCp. 308
13.5.5 Moment Fields, Velocity Fields, and Plastic Limit Loadp. 308
13.6 Summaryp. 312
Referencesp. 313
14 Unified Limit Analysis of a Wellborep. 314
14.1 Introductionp. 314
14.2 Unified Strength Theoryp. 315
14.3 Equations and Boundary Conditions for the Wellborep. 316
14.3.1 Strength Analysis for Wellborep. 316
14.3.2 Pore Pressure Analysisp. 318
14.4 Elastic and Plastic Analysisp. 318
14.4.1 Elastic Phasep. 328
14.4.2 Plastic Limit Pressurep. 319
14.4.3 Elastic-plastic Boundaryp. 320
14.4.4 Examplep. 321
14.4.5 Limit Depth for Stability of a Shaftp. 322
14.5 Summaryp. 324
14.6 Problemsp. 324
Referencesp. 325
15 Unified Solution of Shakedown Limit for Thick-walled Cylinderp. 327
15.1 Introductionp. 327
15.2 Shakedown Theoremp. 329
15.2.1 Static Shakedown Theorem (Melan's Theorem)p. 329
15.2.2 Kinematic Shakedown Theorem (Koiter Theorem)p. 329
15.3 Shakedown Analysis for Thick-walled Cylindersp. 330
15.4 Unified Solution of Shakedown Pressure of Thick-walled Cylindersp. 334
15.5 Connection between Shakedown Theorem and Limit Load Theoremp. 336
15.6 Shakedown Pressure of a Thick-walled Spherical Shellp. 339
15.7 Summaryp. 340
15.8 Problemsp. 340
Referencesp. 341
16 Unified Solution of Shakedown Limit for Circular Platep. 344
16.1 Introductionp. 344
16.2 Unified Solution of Shakedown Limit for Simply Supported Circular Platep. 345
16.2.1 Elastic Statep. 345
16.2.2 Elastic-plastic Statep. 346
16.2.3 Completely Plastic Statep. 348
16.2.4 Shakedown Analysisp. 348
16.2.5 Discussionp. 349
16.3 Unified Solution of Shakedown Limit for Clamped Circular Platep. 350
16.3.1 Elastic Statep. 350
16.3.2 Elastic-plastic Statep. 350
16.3.3 Completely Plastic Statep. 351
16.3.4 Shakedown Analysisp. 351
16.3.5 Discussionp. 352
16.4 Comparison between Shakedown Solution and Limit Resultsp. 353
16.5 Summaryp. 354
16.6 Problemsp. 354
Referencesp. 355
17 Shakedown Analysis of Rotating Cylinder and Discp. 357
17.1 Introductionp. 357
17.2 Elasto-plastic and Shakedown Analyses of Rotating Cylinder and Discp. 358
17.2.1 Elastic Analyses of Hollow Rotating Circular Barsp. 358
17.2.2 Elasto-plastic Analyses of Hollow Rotating Circular Barsp. 360
17.2.3 Shakedown Analyses of Hollow Rotating Circular Barsp. 362
17.2.3 Elasto-plasticity and Shakedown of Solid Rotating Circular Barsp. 364
17.3 Summary of Elasto-plasticity and Shakedown Analyses of Rotating Circular Barsp. 366
17.4 Elasto-plastic and Shakedown Analyses of Rotating Discp. 367
17.4.1 Elastic Analyses of Hollow Rotating Discsp. 368
17.4.2 Plastic Limit Analyses of Hollow Rotating Discsp. 371
17.4.3 Shakedown of Hollow Rotating Discsp. 373
17.5 Elasto-plastic and Shakedown Analyses of Solid Rotating Discsp. 376
17.6 Summary of Elastic and Plastic Analyses of Rotating Discsp. 377
17.7 Summaryp. 378
Referencesp. 379
Indexp. 381
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