Structural Plasticity : Limit, Shakedown and Dynamic Plastic Analyses of Structures

by Yu, Mao-Hong; Ma, Guo-Wei; Li, Jian-chun

• ISBN13: 9783540881513
• ISBN10: 3540881514
• Format: Hardcover
• Copyright: 2009-05-01
• Publisher: Springer Verlag

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 Biography

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

Introduction	p. 1
Background	p. 1
Unification of Yield and Strength Criteria	p. 3
Plastic Limit Analysis	p. 4
Plastic Limit Analysis of Rotating Solids	p. 6
Shakedown Analysis of Structures	p. 7
Plastic Limit Analysis Based on the Unified Strength Theory	p. 8
Summary	p. 9
References	p. 9
Fundamental Concepts of Stress and Srain	p. 16
Stress Components and Invariants	p. 16
Deviatoric Stress Tensor and the Tensor Invariants	p. 18
Principal Shear Stresses	p. 21
Octahedral Shear Stress	p. 21
Strain Components	p. 22
Equations of Equilibrium	p. 24
Generalizes Hooke's Law	p. 24
Compatibility Equations	p. 25
Governing Equations for Plane Stress Problems	p. 26
Governing Equations in Polar Coordinated	p. 27
Bending of Circular Plate	p. 29
Summary	p. 31
References	p. 31
Yield Condition	p. 32
Introduction	p. 32
Conventional Yield Criteria	p. 33
Maximum Normal Stress Criterion	p. 33
Maximum Shear Stress-based Criteria-Single-Shear Theory	p. 33
Octahedral Shear Stress-based Criteria-Three Shear Theory	p. 36
Twin- shear Stress-based Criterion-Twin-shear Theory	p. 40
Unified Yield Criterion for Metallic Materials (Non-SD Materials)	p. 44
Unified Strength Theory for SD Materials	p. 45
Mechanical Model of the Unified Strength Theory	p. 46
Mathematical Modeling of the Unified Strength Theory	p. 47
Mathematical Expression of the Unified Strength Theory	p. 48
Yield Surfaces and Yield Loci of the Unified Strength Theory	p. 48
Significance of the Unified Strength Theory	p. 52
Unified Strength Theory in the Plane Stress State	p. 52
?1 ? ?2 > 0, ?3 = 0	p. 53
?1 ? 0,?2 = 0, ?3 < 0	p. 53
Summary	p. 56
Problems	p. 56
References	p. 61
Theorems of Limit Analysis	p. 64
Introduction	p. 64
Perfectly Plastic Solid	p. 66
Power of Dissipation	p. 66
Lower-Bound Theprem	p. 67
Upper-Bound Theorem	p. 68
Fundamental Limit Theorems	p. 68
Important Remarks	p. 69
Exact Value of the Limit Load (Complete Solution)	p. 69
Elastic-Plastic and Rigid plastic Bodies	p. 69
Load-bearing Capacity	p. 70
Uniqueness	p. 71
	p. 71
Plastic Limit Analysis for Simply Supported Circular Plates	p. 74
Introduction	p. 74
Basic Equations of Circular Plate	p. 75
Unified Solutions of Simply Supported Circular Plate for Non-SD Materials	p. 76
Uniformly Distributed Load	p. 78
Arbitrary Axisymmetrical Load	p. 80
Unified Solutions of Simply Supported Circular Plate for SD Materials	p. 95
Partial-uniform Load	p. 97
Linearly Distributed Load	p. 102
Summary	p. 107
Problems	p. 108
	p. 110
Plastic Limit Analysis of Clamped Circular Plates	p. 112
Introduction	p. 112
Unified Solutions of Clamped Circular Plate for Non-SD Materials	p. 112
Uniformly Distributed Load	p. 112
Arbitrary Loading Radius	p. 117
Arbitrary Loading Distribution	p. 122
Unified Solutions of Clamped Circular Plate for SD Materials	p. 127
Summary	p. 133
Problems	p. 134
	p. 134
Plastic Limit Analysis of Annular Plate	p. 136
Introduction	p. 136
Basic Equations for Annular Plate Based on UYC	p. 137
Case (1)	p. 140
Case (2)	p. 141
Special Case	p. 142
Unified Solutions of Annular Plate for Non-SD Meterials	p. 142
Unified Solutions of Limit Load of Annular Plate for SD Materials	p. 145
Unified Strength Theory	p. 145
Basic Equations for Annular Plate Based on the UST	p. 146
Limit Analysis	p. 147
Results and Discussions	p. 149
Summary	p. 150
Problems	p. 152
References	p. 152
Plastic Limit Analyses of Oblique, Rhombic, and Rectangular Plates	p. 154
Introduction	p. 154
Equations for Oblique Plates	p. 156
The Equilibrium Equation in Ordinary Coordinate System	p. 156
Field of Internal Motion	p. 158
Moment Equation Based on the UST	p. 158
Unified Solution of Limit Analysis of Simply Supported Oblique Plates	p. 159
Limit Load of Rhombic Plates	p. 162
Limit Load of Rectangular Plates	p. 163
Unified Limit Load of Square Plates	p. 168
Tabulation of the Limit Load for Oblique, Rhombic and Square Plates	p. 169
Summary	p. 170
Problems	p. 172
References	p. 173
Plastic Limit Analysis of Pressure Vessels	p. 175
Introduction	p. 175
Unified Solution of Limit Pressure of Thin-walled Pressure Vessel	p. 176
Limit Pressure of Thick-walled Hollow Sphere	p. 180
Elastic Limit Pressure of Thick-walled Sphere Shell	p. 181
Plastic Limit Pressure of Thick-walled Sphere Shell	p. 182
Unified Solution of Elastic Limit Pressure of Thick-walled Cylinder	p. 184
Unified Solution of Plastic Limit Pressure of Thick-walled Cylinder	p. 190
Stress Distribution	p. 190
Plastic Zone in the Elasto-plastic Range	p. 192
Plastic Zone Radius in the Elasto-plastic Range	p. 193
Plastic Limit Pressure	p. 193
Summary	p. 198
Problems	p. 200
References	p. 202
Dynamic Plastic Response of Circular Plate	p. 205
Introduction	p. 205
Dynamic Equations and Boundary Conditions of Circular Plate	p. 206
First Phase of Motion (0 ? T ? ?)	p. 209
Second Phase of Motion (? ? t ? T)	p. 212
Static and Kinetic Admissibility	p. 214
Unified Solution of Dynamic Plastic Response of Circular Plate	p. 216
Special Cases of the Unified Solutions	p. 221
Summary	p. 229
References	p. 229
Limit Angular Speed of Rotating Disc and Cylinder	p. 231
Introduction	p. 231
Elastic Limit of Discs	p. 232
Elasto-plastic Analysis of Discs	p. 233
Elasto-plastic Stress Field of Rotating Disc	p. 236
Solution Procedure and Results	p. 238
Unified Solution of Plastic Limit Analysis of Rotating Cylinder	p. 239
Limit Analysis of a Solid Disc with Variable Thickness	p. 242
Limit Analysis of an Annular Disc with Variable Thickness	p. 246
Case (1) (1 > ? ? ?0)	p. 247
Case (2) (0 ? ? ? ?0)	p. 248
Special Case of b = 0	p. 251
Results and Discussion	p. 252
Summary	p. 258
Problems	p. 258
References	p. 259
Projectile Penetration into Semi-infinite Target	p. 261
Introduction	p. 261
Spatial Axisymmetric Form of Unified Strength Theory	p. 262
Fundamental Equations for Concrete Targets	p. 263
Conservation Equations	p. 263
Relation between Pressure and Bulk Strain	p. 264
Failure Criterion Expressed by ?r and ??	p. 264
Interface Conditions	p. 265
Cylindrical Cavity Expansion Analysis	p. 265
Elastic Zone (c1t ? r ? cdt, ?1/? ? ? ? 1/?)	p. 266
Interface of Elastic-cracked Zones (r = C1t, ? = ?1/?	p. 270
Radial Cracked Zone (ct ? r ? C1t, 1 ? ? ? ?1/?)	p. 271
Interface of the Plastic and Cracked Zones (r = ct, ? = 1)	p. 273
Plastic Zone (vrt ? r ? ct, ? ? ? ? 1)	p. 275
Cavity Expansion Pressure and Velocity	p. 276
Incompressible Material	p. 277
Compressible Material	p. 279
Penetration Resistance Analysis	p. 284
Analysis and Verification of Penetration Depth	p. 288
Summary	p. 290
References	p. 291
Plastic Analysis of Orthogonal Circular Plate	p. 293
Introduction	p. 293
Orthotropic Yield Criteria	p. 293
General Solutions	p. 296
Simply Supported Orthotropic Circular Plate	p. 301
Case I: Point A' Falls on Segment KL	p. 301
Case II: Point A' Falls on Segment LA	p. 302
Case III: Point A! Falls on Segment AB	p. 302
Case IV: Point A' Falls on Segment BC	p. 302
Moment, Velocity Fields and Plastic Limit Load	p. 303
Fixed Supported Circular Plate	p. 307
Case I: Point A' Falls on Segment KL	p. 307
Case II: Point A' Falls on Segment LA	p. 307
Case III: Point A' Locates on Segment AB	p. 307
Case IV: Point A1 Falls on Segment BC	p. 308
Moment Fields, Velocity Fields, and Plastic Limit Load	p. 308
Summary	p. 312
References	p. 313
Unified Limit Analysis of a Wellbore	p. 314
Introduction	p. 314
Unified Strength Theory	p. 315
Equations and Boundary Conditions for the Wellbore	p. 316
Strength Analysis for Wellbore	p. 316
Pore Pressure Analysis	p. 318
Elastic and Plastic Analysis	p. 318
Elastic Phase	p. 328
Plastic Limit Pressure	p. 319
Elastic-plastic Boundary	p. 320
Example	p. 321
Limit Depth for Stability of a Shaft	p. 322
Summary	p. 324
Problems	p. 324
References	p. 325
Unified Solution of Shakedown Limit for Thick-walled Cylinder	p. 327
Introduction	p. 327
Shakedown Theorem	p. 329
Static Shakedown Theorem (Melan's Theorem)	p. 329
Kinematic Shakedown Theorem (Koiter Theorem)	p. 329
Shakedown Analysis for Thick-walled Cylinders	p. 330
Unified Solution of Shakedown Pressure of Thick-walled Cylinders	p. 334
Connection between Shakedown Theorem and Limit Load Theorem	p. 336
Shakedown Pressure of a Thick-walled Spherical Shell	p. 339
Summary	p. 340
Problems	p. 340
References	p. 341
Unified Solution of Shakedown Limit for Circular Plate	p. 344
Introduction	p. 344
Unified Solution of Shakedown Limit for Simply Supported Circular Plate	p. 345
Elastic State	p. 345
Elastic-plastic State	p. 346
Completely Plastic State	p. 348
Shakedown Analysis	p. 348
Discussion	p. 349
Unified Solution of Shakedown Limit for Clamped Circular Plate	p. 350
Elastic State	p. 350
Elastic-plastic State	p. 350
Completely Plastic State	p. 351
Shakedown Analysis	p. 351
Discussion	p. 352
Comparison between Shakedown Solution and Limit Results	p. 353
Summary	p. 354
Problems	p. 354
References	p. 355
Shakedown Analysis of Rotating Cylinder and Disc	p. 357
Introduction	p. 357
Elasto-plastic and Shakedown Analyses of Rotating Cylinder and Disc	p. 358
Elastic Analyses of Hollow Rotating Circular Bars	p. 358
Elasto-plastic Analyses of Hollow Rotating Circular Bars	p. 360
Shakedown Analyses of Hollow Rotating Circular Bars	p. 362
Elasto-plasticity and Shakedown of Solid Rotating Circular Bars	p. 364
Summary of Elasto-plasticity and Shakedown Analyses of Rotating Circular Bars	p. 366
Elasto-plastic and Shakedown Analyses of Rotating Disc	p. 367
Elastic Analyses of Hollow Rotating Discs	p. 368
Plastic Limit Analyses of Hollow Rotating Discs	p. 371
Shakedown of Hollow Rotating Discs	p. 373
Elasto-plastic and Shakedown Analyses of Solid Rotating Discs	p. 376
Summary of Elastic and Plastic Analyses of Rotating Discs	p. 377
Summary	p. 378
References	p. 379
Index	p. 381
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