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

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Structural Plasticity: Limit, Shakedown and Dynamic Plastic Analyses of StructuresSuurem pilt
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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".
1 Introduction
1
1.1 Background
1
1.2 Unification of Yield and Strength Criteria
3
1.3 Plastic Limit Analysis
4
1.4 Plastic Limit Analysis of Rotating Solids
6
1.5 Shakedown Analysis of Structures
7
1.6 Plastic Limit Analysis Based on the Unified Strength Theory
8
1.7 Summary
9
References
9
2 Fundamental Concepts of Stress and Strain
16
2.1 Stress Components and Invariants
16
2.2 Deviatoric Stress Tensor and the Tensor Invariants
18
2.3 Principal Shear Stresses
19
2.4 Octahedral Shear Stress
21
2.5 Strain Components
22
2.6 Equations of Equilibrium
24
2.7 Generalized Hooke's Law
24
2.8 Compatibility Equations
25
2.9 Governing Equations for Plane Stress Problems
26
2.10 Governing Equations in Polar Coordinates
27
2.11 Bending of Circular Plate
29
2.12 Summary
31
References
31
3 Yield Condition
32
3.1 Introduction
32
3.2 Conventional Yield Criteria
33
3.2.1 Maximum Normal Stress Criterion
33
3.2.2 Maximum Shear Stress-based Criteria Single-shear Theory
33
3.2.3 Octahedral Shear Stress-based Criteria Three-shear Theory
36
3.2.4 Twin-shear Stress-based Criterion-Twin-shear Theory
40
3.3 Unified Yield Criterion for Metallic Materials (Non-SD Materials)
44
3.4 Unified Strength Theory for SD Materials
45
3.4.1 Mechanical Model of the Unified Strength Theory
46
3.4.2 Mathematical Modelling of the Unified Strength Theory
47
3.4.3 Mathematical Expression of the Unified Strength Theory
48
3.4.4 Yield Surfaces and Yield Loci of the Unified Strength Theory
48
3.5 Significance of the Unified Strength Theory
49
3.6 Unified Strength Theory in the Plane Stress State
52
3.6.1 σ1 less than or=toσ2 greater than 0,σ3=0
53
3.6.2 σ1 greater than or=to0,σ2=0,σ3 less than 0
53
3.7 Summary
55
3.8 Problems
56
References
61
4 Theorems of Limit Analysis
64
4.1 Introduction
64
4.2 Perfectly Plastic Solid
66
4.3 Power of Dissipation
66
4.4 Lower-bound Theorem
67
4.5 Upper-bound Theorem
68
4.6 Fundamental Limit Theorems
68
4.7 Important Remarks
69
4.7.1 Exact Value of the Limit Load (Complete Solution)
69
4.7.2 Elastic-plastic and Rigid-plastic Bodies
69
4.7.3 Load-bearing Capacity
70
4.7.4 Uniqueness
70
References
71
5 Plastic Limit Analysis for Simply Supported Circular Plates
74
5.1 Introduction
74
5.2 Basic Equations of Circular Plate
75
5.3 Unified Solutions of Simply Supported Circular Plate for Non-SD Materials
76
5.3.1 Uniformly Distributed Load
78
5.3.2 Arbitrary Axisymmetrical Load
80
5.4 Unified Solutions of Simply Supported Circular Plate for SD Materials
95
5.4.1 Partial-uniform Load
97
5.4.2 Linearly Distributed Load
102
5.5 Summary
107
5.6 Problems
108
References
110
6 Plastic Limit Analysis of Clamped Circular Plates
112
6.1 Introduction
112
6.2 Unified Solutions of Clamped Circular Plate for Non-SD Materials
112
6.2.1 Uniformly Distributed Load
112
6.2.2 Arbitrary Loading Radius
117
6.2.3 Arbitrary Loading Distribution
122
6.3 Unified Solutions of Clamped Circular Plate for SD Materials
127
6.4 Summary
133
6.5 Problems
134
References
134
7 Plastic Limit Analysis of Annular Plate
136
7.1 Introduction
136
7.2 Basic Equations for Annular Plate Based on UYC
137
7.2.1 Case (1)
140
7.2.2 Case (2)
141
7.2.3 Special Case
142
7.3 Unified Solutions of Annular Plate for Non-SD Materials
142
7.4 Unified Solutions of Limit Load of Annular Plate for SD Materials
145
7.4.1 Unified Strength Theory
145
7.4.2 Basic Equations for Annular Plate Based on the UST
146
7.4.3 Limit Analysis
147
7.4.4 Results and Discussions
149
7.5 Summary
150
7.6 Problems
152
References
152
8 Plastic Limit Analyses of Oblique, Rhombic, and Rectangular Plates
154
8.1 Introduction
154
8.2 Equations for Oblique Plates
156
8.2.1 The Equilibrium Equation in Ordinary Coordinate System
156
8.2.2 Field of Internal Motion
158
8.2.3 Moment Equation Based on the UST
158
8.3 Unified Solution of Limit Analysis of Simply Supported Oblique Plates
159
8.4 Limit Load of Rhombic Plates
162
8.5 Limit Load of Rectangular Plates
163
8.6 Unified Limit Load of Square Plates
168
8.7 Tabulation of the Limit Load for Oblique, Rhombic and Square Plates
169
8.8 Summary
170
8.9 Problems
172
References
173
9 Plastic Limit Analysis of Pressure Vessels
175
9.1 Introduction
175
9.2 Unified Solution of Limit Pressure of Thin-walled Pressure Vessel
176
9.3 Limit Pressure of Thick-walled Hollow Sphere
180
9.3.1 Elastic Limit Pressure of Thick-walled Sphere Shell
181
9.3.2 Plastic Limit Pressure of Thick-walled Sphere Shell
182
9.4 Unified Solution of Elastic Limit Pressure of Thick-walled Cylinder
184
9.5 Unified Solution of Plastic Limit Pressure of Thick-walled Cylinder
190
9.5.1 Stress Distribution
190
9.5.2 Plastic Zone in the Elasto-plastic Range
192
9.5.3 Plastic Zone Radius in the Elasto-plastic Range
193
9.5.4 Plastic Limit Pressure
193
9.6 Summary
198
9.7 Problems
200
References
202
10 Dynamic Plastic Response of Circular Plate 205
10.1 Introduction
205
10.2 Dynamic Equations and Boundary Conditions of Circular Plate
206
10.2.1 First Phase of Motion (0 less than or = to T less than or=toτ)
209
10.2.2 Second Phase of Motion (τ less than or=tot less than or=toT)
212
10.3 Static and Kinetic Admissibility
214
10.4 Unified Solution of Dynamic Plastic Response of Circular Plate
216
10.5 Special Cases of the Unified Solutions
221
10.6 Summary
229
References
229
11 Limit Angular Speed of Rotating Disc and Cylinder 231
11.1 Introduction
231
11.2 Elastic Limit of Discs
232
11.3 Elasto-plastic Analysis of Discs
233
11.4 Elasto-plastic Stress Field of Rotating Disc
236
11.5 Solution Procedure and Results
238
11.6 Unified Solution of Plastic Limit Analysis of Rotating Cylinder
239
11.7 Limit Analysis of a Solid Disc with Variable Thickness
242
11.8 Limit Analysis of an Annular Disc with Variable Thickness
246
11.8.1 Case (1) (1β greater than or=toβ0)
247
11.8.2 Case (2) (0 less than β less than or=toβ0)
248
11.9 Special Case of b= 0
251
11.10 Results and Discussion
252
11.11 Summary
258
11.12 Problems
258
References
259
12 Projectile Penetration into Semi-infinite Target 261
12.1 Introduction
261
12.2 Spatial Axisymmetric Form of Unified Strength Theory
262
12.3 Fundamental Equations for Concrete Targets
263
12.3.1 Conservation Equations
263
12.3.2 Relation between Pressure and Bulk Strain
264
12.3.3 Failure Criterion Expressed by σr and σo
264
12.3.4 Interface Conditions
265
12.4 Cylindrical Cavity Expansion Analysis
265
12.4.1 Elastic Zone (cqt less than or=tor less than or=tocdt, β1/β less than or=toξ less than or=to1/α)
266
12.4.2 Interface of Elastic-cracked Zones (r=c1t, ξ=β1/β)
270
12.4.3 Radial Cracked Zone (ct less than or=tor less than or=toc1t, 1 less than or=toξ less than or=toβ1/β)
271
12.4.4 Interface of the Plastic and Cracked Zones (r = ct, ξ = 1)
273
12.4.5 Plastic Zone (upsilonrt less than or=tor less than or=toct, δ less than or=toξ less than or=to1)
275
12.5 Cavity Expansion Pressure and Velocity
276
12.5.1 Incompressible Material
277
12.5.2 Compressible Material
279
12.6 Penetration Resistance Analysis
284
12.7 Analysis and Verification of Penetration Depth
288
12.8 Summary
290
References
291
13 Plastic Analysis of Orthogonal Circular Plate 293
13.1 Introduction
293
13.2 Orthotropic Yield Criteria
293
13.3 General Solutions
296
13.4 Simply Supported Orthotropic Circular Plate
301
13.4.1 Case I: Point A' Falls on Segment KL
301
13.4.2 Case II: Point A' Falls on Segment LA
302
13.4.3 Case III: Point A' Falls on Segment AB
302
13.4.4 Case IV: Point A' Falls on Segment BC
302
13.4.5 Moment, Velocity Fields and Plastic Limit Load
303
13.5 Fixed Supported Circular Plate
307
13.5.1 Case I: Point A' Falls on Segment KL
307
13.5.2 Case II: Point A' Falls on Segment LA
307
13.5.3 Case III: Point A' Locates on Segment AB
307
13.5.4 Case IV: Point A' Falls on Segment BC
308
13.5.5 Moment Fields, Velocity Fields, and Plastic Limit Load
308
13.6 Summary
312
References
313
14 Unified Limit Analysis of a Wellbore 314
14.1 Introduction
314
14.2 Unified Strength Theory
315
14.3 Equations and Boundary Conditions for the Wellbore
316
14.3.1 Strength Analysis for Wellbore
316
14.3.2 Pore Pressure Analysis
318
14.4 Elastic and Plastic Analysis
318
14.4.1 Elastic Phase
318
14.4.2 Plastic Limit Pressure
319
14.4.3 Elastic-plastic Boundary
320
14.4.4 Example
321
14.4.5 Limit Depth for Stability of a Shaft
322
14.5 Summary
324
14.6 Problems
324
References
325
15 Unified Solution of Shakedown Limit for Thick-walled Cylinder 327
15.1 Introduction
327
15.2 Shakedown Theorem
329
15.2.1 Static Shakedown Theorem (Melan's Theorem)
329
15.2.2 Kinematic Shakedown Theorem (Koiter Theorem)
329
15.3 Shakedown Analysis for Thick-walled Cylinders
330
15.4 Unified Solution of Shakedown Pressure of Thick-walled Cylinders
334
15.5 Connection between Shakedown Theorem and Limit Load Theorem
336
15.6 Shakedown Pressure of a Thick-walled Spherical Shell
339
15.7 Summary
340
15.8 Problems
340
References
341
16 Unified Solution of Shakedown Limit for Circular Plate 344
16.1 Introduction
344
16.2 Unified Solution of Shakedown Limit for Simply Supported Circular Plate
345
16.2.1 Elastic State
345
16.2.2 Elastic-plastic State
346
16.2.3 Completely Plastic State
348
16.2.4 Shakedown Analysis
348
16.2.5 Discussion
349
16.3 Unified Solution of Shakedown Limit for Clamped Circular Plate
350
16.3.1 Elastic State
350
16.3.2 Elastic-plastic State
350
16.3.3 Completely Plastic State
351
16.3.4 Shakedown Analysis
351
16.3.5 Discussion
352
16.4 Comparison between Shakedown Solution and Limit Results
353
16.5 Summary
354
16.6 Problems
354
References
355
17 Shakedown Analysis of Rotating Cylinder and Disc 357
17.1 Introduction
357
17.2 Elasto-plastic and Shakedown Analyses of Rotating Cylinder and Disc
358
17.2.1 Elastic Analyses of Hollow Rotating Circular Bars
358
17.2.2 Elasto-plastic Analyses of Hollow Rotating Circular Bars
360
17.2.3 Shakedown Analyses of Hollow Rotating Circular Bars
362
17.2.4 Elasto-plasticity and Shakedown of Solid Rotating Circular Bars
364
17.3 Summary of Elasto-plasticity and Shakedown Analyses of Rotating Circular Bars
366
17.4 Elasto-plastic and Shakedown Analyses of Rotating Disc
367
17.4.1 Elastic Analyses of Hollow Rotating Discs
368
17.4.2 Plastic Limit Analyses of Hollow Rotating Discs
371
17.4.3 Shakedown of Hollow Rotating Discs
373
17.5 Elasto-plastic and Shakedown Analyses of Solid Rotating Discs
376
17.6 Summary of Elastic and Plastic Analyses of Rotating Discs
377
17.7 Summary
378
References
379
Index 381
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