Limit States of Materials and Structures (eBook)

Preface 5
Contents 6
Contributors 8
The Linear Matching Method for Limit Loads, Shakedown Limits and Ratchet Limits 12
1 Introduction 12
2 Definition of the Problem 13
3 Shakedown Theorems 15
4 The Linear Matching Method 17
5 The Ratchet Limit 23
6 Further Applications 29
7 Conclusions 30
References 30
Large Problems in Numerical Limit Analysis: A Decomposition Approach 33
1 Introduction 34
2 Interior Point Method and Convex Optimization 35
3 Succinct Presentation of Limit Analysis 36
4 Kinematic Method of LA: A Mixed Finite Element Formulation 37
5 The Proposed Decomposition Method 40
6 Kinematical Tests 45
7 Extension to the Statical Approach: First Results 50
8 Conclusion 51
References 52
Gurson Model for Porous Pressure Sensitive Materials 54
Nomenclature 54
1 Introduction 55
2 Succinct Presentation of Limit Analysis 55
3 Homogenization Technique—The Gurson’s Model 57
4 Finite Element and Optimization Implementation 58
5 The Statical Approach for a Porous Coulomb Material 59
pa 61
6 The Kinematical Approach for a Porous Coulomb Material 62
pa 63
7 Applications 66
Ad Hoc 68
8 Conclusion 73
References 74
A Direct Method for the Determination of Effective Strength Domains for Periodic Elastic- Plastic Media 75
1 Introduction 76
2 The Static Approach of Shakedown 77
3 Periodic Heterogeneous Media 80
4 Periodic Heterogeneous Plates 82
5 Conclusion 92
References 92
Stochastic Limit Load Analysis of Elasto- Plastic Plane Frames 95
1 Introduction 96
2 State and Cost Functions 98
3 Minimum Expected Quadratic Costs 104
4 Deterministic Substitute Problems 107
5 Limit Load Analysis 109
6 Complete Limit Load Analysis 111
7 Numerical Example 115
References 118
Limit Load Analysis of Plane Frames Under Stochastic Uncertainty 120
1 Formulation of the Problem 120
2 Substitute Problems 131
3 Numerical Results 132
4 Conclusion 140
References 141
Reliability Analysis of Inelastic Shell Structures Under Variable Loads 142
1 Introduction 143
2 Plastic Dissipation Function in Terms of Strain Resultants 144
3 Deterministic Limit and Shakedown Algorithm 146
4 Probabilistic Limit and Shakedown Algorithm 147
5 Numerical Examples 154
6 Conclusions 162
References 162
Static Shakedown Theorem for Solids with Temperature- Dependent Elastic Modulus 164
1 Introduction 164
2 Basic Relations 165
3 New Static Shakedown Theorem 167
4 Static Shakedown Factor 170
5 Numerical Examples 170
A2 179
6 Conclusion 179
References 183
On Shakedown of Structures Under Variable Loads with a Kinematic Non- linear and Non- associated Hardening Rule 185
1 Introduction 185
2 Implicit Standard Materials and Shakedown 186
3 Computation of Shakedown Load for a Homogeneous Constant Tension and Alternating Torsion State 189
.l 193
References 201
Limit Analysis of Orthotropic Laminates by Linear Matching Method 203
1 Introduction 203
2 Limit Analysis for Nonstandard Orthotropic Materials 205
3 Linear Matching for Orthotropic Materials 207
4 Validation: Numerical and Experimental Results 216
5 Concluding Remarks and Future Developments 221
References 224
Mechanical Surface Treatments and Life Improvement 227
1 Introduction 227
2 MASSI Method 228
3 Prediction of Shot Peening Stresses 231
4 MI2 Identification Process 234
5 Conclusion 237
References 238
Force Method – Based Procedures in the Limit Equilibrium Analysis of Framed Structures 239
1 Introduction 239
2 Construction of a Cycle Basis 240
3 Limit Analysis of Plane Frames 243
4 Shakedown Analysis of Plane Frames 248
5 Limit Analysis of Space Frames 253
6 Concluding Remarks 258
References 258
Shakedown Analysis of Composite Materials Based on Non- linear Mathematical Programming 259
1 Introduction 259
2 Kinematic Shakedown Analysis of a Macrostructure 261
3 Kinematic Shakedown Analysis of a Microstructure 265
4 Iterative Solution Algorithm 269
5 Applications 272
6 Conclusions 274
References 274
A Non-linear Programming Approach to Shakedown Analysis for a General Yield Condition 277
1 Introduction 277
2 Shakedown Analysis Based on a General Yield Criterion 279
3 Finite Element Modelling 283
4 Iterative Solution Algorithm 284
5 Applications 288
6 Conclusions 291
References 292
Application of Shakedown Analysis to Large- Scale Problems with Selective Algorithm 294
1 Introduction 294
2 Lower-Bound Shakedown Theorem 295
3 Selective Algorithm 296
4 Industrially Relevant Examples 297
5 Conclusions 309
References 309