Elements of Structural Optimization

Methods.- Applications to Analysis.- 4.3 Specialized Quasi-Newton Methods.- Exploiting Sparsity.- Coercion of Hessians for Suitability with Quasi-Newton Methods.- Making Quasi-Newton Methods Globally Convergent.- 4.4 Probabilistic Search Algorithms.- Simulated Annealing.- Genetic Algorithms.- 4.5 Exercises.- 4.6 References.- 5. Constrained Optimization.- 5.1 The Kuhn-Tucker Conditions.- General Case.- Convex Problems.- 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.- Exterior Penalty Function.- Interior and Extended Interior Penalty Functions.- Unconstrained Minimization with Penalty Functions.- Integer Programming with Penalty Functions.- 5.8 Multiplier Methods.- 5.9 Projected Lagrangian Methods (Sequential Quadratic Prog.).- 5.10 Exercises.- 5.11 References.- 6. Aspects of the Optimization Process in Practice.- 6.1 Generic Approximations.- Local Approximations.- Global and Midrange Approximations.- 6.2 Fast Reanalysis Techniques.- Linear Static Response.- Eigenvalue Problems.- 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.- Ten-Bar Truss.- Twenty-Five-Bar Truss.- Seventy-Two-Bar Truss.- 6.8 Exercises.- 6.9 References.- 7. Sensitivity of Discrete Systems.- 7.1 Finite Difference Approximations.- Accuracy and Step Size Selection.- Iterative Methods.- Effect of Derivative Magnitude on Accuracy.- 7.2 Sensitivity Derivatives of Static Displacement and Stress Constraints.- Analytical First Derivatives.- Second Derivatives.- The Semi-Analytical Method.- Nonlinear Analysis.- Sensitivity of Limit Loads.- 7.3 Sensitivity Calculations for Eigenvalue Problems.- Sensitivity Derivatives of Vibration and Buckling Constraints.- Sensitivity Derivatives for Non-Hermitian Eigenvalue Problems.- Sensitivity Derivatives for Nonlinear Eigenvalue Problems.- 7.4 Sensitivity of Constraints on Transient Response.- Equivalent Constraints.- Derivatives of Constraints.- Linear Structural Dynamics.- 7.5 Exercises.- 7.6 References.- 8. Introduction to Variational Sensitivity Analysis.- 8.1 Linear Static Analysis.- The Direct Method.- The Adjoint Method.- Implementation Notes.- 8.2 Nonlinear Static Analysis and Limit Loads.- Static Analysis.- Limit Loads.- Implementation Notes.- 8.3 Vibration and Buckling.- The Direct Method.- The Adjoint Method.- 8.4 Static Shape Sensitivity.- The Material Derivative.- Domain Parametrization.- The Direct Method.- The Adjoint Method.- 8.5 Exercise.- 8.6 References.- 9. Dual and Optimality Criteria Methods.- 9.1 Intuitive Optimality Criteria Methods.- Fully Stressed Design.- Other Intuitive Methods.- 9.2 Dual Methods.- General Formulation.- Application to Separable Problems.- Discrete Design Variables.- Application with First Order Approximations.- 9.3 Optimality Criteria Methods for a Single Constraint.- The Reciprocal Approximation for a Displacement Constraint.- A Single Displacement Constraint.- Generalization for Other Constraints.- Scaling-based Resizing.- 9.4 Several Constraints.- Reciprocal-Approximation Based Approach.- Scaling-based Approach.- Other Formulations.- 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.- Simultaneous Analysis and Design.- Other Applications.- 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.- Orthotropic Lamina.- Classical Laminated Plate Theory.- Bending, Extension, and Shear Coupling.- 11.2 Laminate Design.- Design of Laminates for In-plane Response.- Design of Laminates for Flexural Response.- 11.3 Stacking Sequence Design.- Graphical Stacking Sequence Design.- Penalty Function Formulation.- Integer Linear Programming Formulation.- Probabilistic Search Methods.- 11.4 Design Applications.- Stiffened Plate Design.- Aeroelastic Tailoring.- 11.5 Design Uncertainties.- 11.6 Exercises.- 11.7 References.- Name Index.