Table of Contents
Preface vii
Introduction xi
Chapter 1. Truss Layout Optimization 1
1.1. Standard theory of mathematical programming 1
1.2. Governing equations of truss structures 3
1.3. Layout and topology optimization 7
1.3.1. Basic problem statement 7
1.3.2. Problem equivalence and numerical solution 11
1.4. Generalization 15
1.4.1. Self-weight and multiple loading 15
1.4.2. Compliance optimization 16
1.4.3. Volume optimization 17
1.4.4. Stress singularity 21
1.4.5. Local buckling singularity 25
1.5. Truss geometry and topology optimization 27
1.5.1. Optimization of nodal positions 27
1.5.2. Melting node effect 30
1.6. Concluding remarks 32
Chapter 2. Unified Formulation 33
2.1. Literature review 33
2.2. Disaggregation of equilibrium equations 36
2.3. Minimum volume problem 38
2.4. Minimum compliance problem 41
2.5. Reduced formulation for single loading 44
2.6. Nonlinear programming 46
2.6.1. Barrier problem 47
2.6.2. Sequential quadratic programming with trust regions 49
2.6.3. Verification test 51
2.7. Design settings 56
2.8. Concluding remarks 62
Chapter 3. Stability Considerations 65
3.1. Literature review 65
3.2. Lower bound plastic design formulation 69
3.3. Nominal force method for local stability 71
3.4. Local buckling criterion 75
3.5. Formulation including stability constraints 76
3.6. Numerical examples 78
3.6.1. Three-hinged arch 78
3.6.2. L-shaped frame 80
3.7. Concluding remarks 82
Chapter 4. Structural Design Applications 83
4.1. Reticulated dome 83
4.2. Lateral bracing of Winter’s type column 86
4.3. Arch bridge 88
4.4. Suspension bridge 90
4.5. Dutch Maritime Museum 92
Conclusions and Future Prospects 99
Appendix 105
Bibliography 113
Index 135