Computational Design of Lightweight Structures: Form Finding and Optimization

The author of this book presents a general, robust, and easy-to-use method that can handle many design parameters efficiently. Following an introduction, Chapter 1 presents the general concepts of truss layout optimization, starting from topology optimization where structural component sizes and system connectivity are simultaneously optimized. To fully realize the potential of truss layout optimization for the design of lightweight structures, the consideration of geometrical variables is then introduced. Chapter 2 addresses truss geometry and topology optimization by combining mathematical programming and structural mechanics: the structural properties of the optimal solution are used for devising the novel formulation. To avoid singularities arising in optimal configurations, this approach disaggregates the equilibrium equations and fully integrates their basic elements within the optimization formulation. The resulting tool incorporates elastic and plastic design, stress and displacement constraints, as well as self-weight and multiple loading. The inherent slenderness of lightweight structures requires the study of stability issues. As a remedy, Chapter 3 proposes a conceptually simple but efficient method to include local and nodal stability constraints in the formulation. Several numerical examples illustrate the impact of stability considerations on the optimal design. Finally, the investigation on realistic design problems in Chapter 4 confirms the practical applicability of the proposed method. It is shown how we can generate a range of optimal designs by varying design settings.

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