Elements of Structural Optimization

1. Introduction.- 1.1 Function Optimization and Parameter Optimization.- 1.2 Elements of Problem Formulation.- 1.3 The Solution Process.- 1.4 Analysis and Design Formulations.- 1.5 Specific Versus General Methods.- 1.6 Exercises.- 1.7 References.- 2. Classical Tools in Structural Optimization.- 2.1 Optimization Using Differential Calculus.- 2.2 Optimization Using Variational Calculus.- 2.3 Classical Methods for Constrained Problems.- 2.4 Local Constraints and the Minmax Approach.- 2.5 Necessary and Sufficient Conditions for Optimality.- 2.6 Use of Series Solutions in Structural Optimization.- 2.7 Exercises.- 2.8 References.- 3. Linear Programming.- 3.1 Limit Analysis and Design of Structures Formulated as LP Problems.- 3.2 Prestressed Concrete Design by Linear Programming.- 3.3 Minimum Weight Design of Statically Determinate Trusses.- 3.4 Graphical Solutions of Simple LP Problems.- 3.5 A Linear Program in a Standard Form.- 3.6 The Simplex Method.- 3.7 Duality in Linear Programming.- 3.8 An Interior Method—Karmarkar’s Algorithm.- 3.9 Integer Linear Programming.- 3.10 Exercises.- 3.11 References.- 4. Unconstrained Optimization.- 4.1 Minimization of Functions of One Variable.- 4.2 Minimization of Functions of Several Variables.- 4.3 Specialized Quasi-Newton Methods.- 4.4 Probabilistic Search Algorithms.- 4.5 Exercises.- 4.6 References.- 5. Constrained Optimization.- 5.1 The Kuhn-Tucker Conditions.- 5.2 Quadratic Programming Problems.- 5.3 Computing the Lagrange Multipliers.- 5.4 Sensitivity of Optimum Solution to Problem Parameters.- 5.5 Gradient Projection and Reduced Gradient Methods.- 5.6 The Feasible Directions Method.- 5.7 Penalty Function Methods.- 5.8 Multiplier Methods.- 5.9 Projected Lagrangian Methods (Sequential Quadratic Prog.).- 5.10 Exercises.- 5.11References.- 6. Aspects of the Optimization Process in Practice.- 6.1 Generic Approximations.- 6.2 Fast Reanalysis Techniques.- 6.3 Sequential Linear Programming.- 6.4 Sequential Nonlinear Approximate Optimization.- 6.5 Special Problems Associated with Shape Optimization.- 6.6 Optimization Packages.- 6.7 Test Problems.- 6.8 Exercises.- 6.9 References.- 7. Sensitivity of Discrete Systems.- 7.1 Finite Difference Approximations.- 7.2 Sensitivity Derivatives of Static Displacement and Stress Constraints.- 7.3 Sensitivity Calculations for Eigenvalue Problems.- 7.4 Sensitivity of Constraints on Transient Response.- 7.5 Exercises.- 7.6 References.- 8. Introduction to Variational Sensitivity Analysis.- 8.1 Linear Static Analysis.- 8.2 Nonlinear Static Analysis and Limit Loads.- 8.3 Vibration and Buckling.- 8.4 Static Shape Sensitivity.- 8.5 Exercise.- 8.6 References.- 9. Dual and Optimality Criteria Methods.- 9.1 Intuitive Optimality Criteria Methods.- 9.2 Dual Methods.- 9.3 Optimality Criteria Methods for a Single Constraint.- 9.4 Several Constraints.- 9.5 Exercises.- 9.6 References.- 10. Decomposition and Multilevel Optimization.- 10.1 The Relation between Decomposition and Multilevel Formulation.- 10.2 Decomposition.- 10.3 Coordination and Multilevel Optimization.- 10.4 Penalty and Envelope Function Approaches.- 10.5 Narrow-Tree Multilevel Problems.- 10.6 Decomposition in Response and Sensitivity Calculations.- 10.7 Exercises.- 10.8 References.- 11.Optimum Design of Laminated Composite Materials.- 11.1 Mechanical Response of a Laminate.- 11.2 Laminate Design.- 11.3 Stacking Sequence Design.- 11.4 Design Applications.- 11.5 Design Uncertainties.- 11.6 Exercises.- 11.7 References.- Name Index.