Table of Contents
Preface xi Chapter 1. Origins and Topicality of a Concept 1
1.1. Historical milestones 1
1.2. Topicality of the yield design approach 8
1.3. Bibliography 11
Chapter 2. An Introductory Example of the Yield Design Approach 19
2.1. Setting the problem 19
2.2. Potential stability of the structure 22
2.3. To what extent potential stability is a relevant concept? 24
2.4. Bibliography 28
Chapter 3. The Continuum Mechanics Framework 29
3.1. Modeling the continuum 29
3.2. Dynamics 34
3.3. The theory of virtual work 41
3.4. Statically and kinematically admissible fields 46
3.5. Bibliography 48
Chapter 4. Primal Approach of the Theory of Yield Design 51
4.1. Settlement of the problem 51
4.2. Potentially safe loads 57
4.3. Comments 60
4.4. Some usual isotropic strength criteria 66
4.5. Bibliography 70
Chapter 5. Dual Approach of the Theory of Yield Design 73
5.1. A static exterior approach 73
5.2. A kinematic necessary condition 76
5.3. The π functions 78
5.4. π functions for usual isotropic strength criteria 84
5.5. Bibliography 88
Chapter 6. Kinematic Exterior Approach 91
6.1. Equation of the kinematic exterior approach 91
6.2. Relevant virtual velocity fields 94
6.3. One domain, two approaches 100 6.4. Bibliography 107
Chapter 7. Ultimate Limit State Design from the Theory of Yield Design 111
7.1. Basic principles of ultimate limit state design 111
7.2. Revisiting the yield design theory in the context of ULSD 113
7.3. The yield design theory applied to ULSD 114
7.4. Conclusion 117
7.5. Bibliography 118
Chapter 8. Optimality and Probability Approaches of Yield Design 119
8.1. Optimal dimensioning and probabilistic approach 119
8.2. Domain of potential stability 120
8.3. Optimal dimensioning 130
8.4. Probabilistic approach of yield design 133
8.5. Bibliography 141
Chapter 9. Yield Design of Structures 145
9.1. The curvilinear one-dimensional continuum 145
9.2. Implementation of the yield design theory 157
9.3. Typical strength criteria 164
9.4. Final comments 172
9.5. Bibliography 174
Chapter 10. Yield Design of Plates: the Model 177
10.1. Modeling plates as two-dimensional continua 177
10.2. Dynamics 182
10.3. Theorem/principle of virtual work 191
10.4. Plate model derived from the three-dimensional continuum 198
10.5. Bibliography 204
Chapter 11. Yield Design of Plates Subjected to Pure Bending 205
11.1. The yield design problem 205
11.2. Implementation of the yield design theory 208
11.3. Strength criteria and π functions 213
11.4. Final comments 226
11.5. Bibliography 234
Index 237