Cover -- Title -- Copyright -- Preface -- Table of Contents -- Chapter 1. Introduction: Historical Perspective and Future Directions -- Introduction -- History and Motivation -- Issues in Multidisciplinary Design Optimization -- Statement and Solution of the Optimization Problem -- Future Directions -- References -- Chapter 2. Fundamental Concepts of Optimum Design -- Nomenclature -- Introduction -- Optimum Design Model -- Basic Definitions and Existence of Solution -- Optimality Conditions -- Unconstrained Problem -- Constrained Problem -- Global Optimality -- Postoptimality Analysis -- Changes in Constraint Limit -- Scaling of Cost Function -- Scaling of Constraint -- Duality in Nonlinear Programming -- Problem with Equality Constraints -- Problem with Inequality Constraints -- Summary -- References -- Chapter 3. Mathematical Programming Methods for Constrained Optimization: Primal Methods -- Introduction -- Basic Concepts -- Optimization Process -- Optimization Algorithms -- Steepest Descent Method -- Conjugate Gradient Method -- Sequential Unconstrained Minimization Techniques -- Method of Feasible Directions -- Modified Method of Feasible Directions -- Sequential Linear Programming Method -- Sequential Quadratic Programming -- Approximate Structural Optimization Problem -- Examples -- Portal Frame -- 18-Bar Truss -- Summary -- References -- Chapter 4. Function Approximations -- Introduction -- Local Approximations -- Approximations Based on Zeroth- and First-Order Function Information -- Differential Equation-Based Approximation -- Approximations Based on Higher-Order Function Information -- Global Approximations -- Response Surface Approach -- Neural Networks -- Intermediate Variables and Response Quantities -- Midrange Approximations -- Multipoint Approximations -- Scaling or Local-Global Approximations -- Concluding Remarks -- References.

Chapter 5. Sequential Linearization and Quadratic Programming Techniques -- Nomenclature -- Introduction -- Design Optimization Model -- Basic Concepts and Definitions -- Constraint Status at a Design Point -- Constraint Normalization -- Potential Constraint Strategy -- Descent Function -- Convergence of an Algorithm -- Good Algorithm: A Definition -- Linearization of the Problem -- Sequential Linear Programming -- Sequential Quadratic Programming: Linearization Method -- Descent Function -- Step Size Determination -- CSD Algorithm -- Observations on the CSD Algorithm -- Use of Potential Set Strategy -- Sequential Quadratic Programming: Quasi-Newton Methods -- Derivation of Quadratic Programming Subproblem -- Quasi-Newton Hessian Approximation -- SQP Algorithm -- Descent Functions -- Numerical Implementation Aspects -- Applications of SQP -- Simultaneous Control and Design of a Structure: A Global Solution Using SQP -- Concluding Remarks -- References -- Chapter 6. Approximate Reanalysis Methods -- Introduction -- Local and Global Approximations -- Combined Approximations -- Model Types -- Approximate Displacement Models -- Approximate Force Models -- Problem Formulation -- Local Approximations: Series Expansion -- Global Approximations: The Reduced Basis Method -- Combined Series Expansion and Scaling -- Combined First-Order Approximations -- Combined Series Expansion and Reduced Basis -- Computational Considerations -- Examples -- Conclusions -- References -- Chapter 7. Mathematical Programming Methods for Constrained Optimization: Dual Methods -- Introduction -- Primal and Dual Problems -- Lagrangian Multiplier Technique (Equality Constraints) -- Duality for Convex Problems (Inequality Constraints) -- Example: Quadratic Problem -- Sequential Convex Programming -- Convex Linearization (CONLIN) Method -- Higher-Order Separable Approximation.

Second-Order Dual Optimizer -- Dual Method Approach for Separable, Quadratic Problems -- Update Formulas for the Inverse Hessian -- General Separable Problems -- References -- Chapter 8. Generalized Optimality Criteria Method -- Introduction -- Statement of the Problem and Optimality Conditions -- Iterative Algorithm-Resizing Algorithm -- Simple and Compound Scaling Algorithm -- Algorithm Implementation-Outline and Details -- Selection of an Initial Variable Vector, x[sup(0)] -- Computation of the Objective Function, F(x) -- Computation of the Constraints: Z[sub(1)], Z[sub(2)], …, z[sub(s)] -- Classification of Constraints -- Computation of the Constraint Gradients -- Computation of the Objective Function Gradients -- Determination of Matrices e and A -- Computation of Matrix Products e[sup(T)]Āe and e[sup(T)]Āl -- Solution for the Lagrangian Multipliers -- Check for Constraint Dependency -- Decision on the Constraint Surface -- Compound Scaling -- Exit Criteria -- Optimization Complete -- Determination of the μ and α Parameters -- Resizing Algorithm -- Results of Applications -- Test Problem 1 -- Test Problem 2 -- Test Problem 3 -- Test Problem 4 -- Test Problem 5 -- Test Problem 6 -- Comparison of Algorithm Performance -- Summary and Conclusions -- References -- Chapter 9. Recent Developments in Structural Optimization Methods -- Introduction -- First-Order Convex Approximation Methods -- Key Role of Reciprocal Variables -- Convex Linearization Method (CONLIN) -- Method of Moving Asymptotes -- Other Convex Approximations (Power Expansions) -- Second-Order Convex Approximation Methods -- Pure Sequential Quadratic Programming -- Diagonal Sequential Quadratic Programming Method -- Zero Curvature Approximation -- Second-Order Method of Moving Asymptotes -- CONLIN Optimizer -- Type of Explicit Approximations -- Optimization Strategies and Algorithms.

Numerical Examples -- Cantilever Beam -- Two-Bar Truss -- Eight-Bar Truss -- References -- Chapter 10. Multicriteria Optimization in Engineering: A Tutorial and Survey -- Introduction -- What is Multicriteria Optimization? -- Historical Development of Multicriteria Optimization -- Mathematical Concepts -- Multicriteria Optimization Problem -- Multicriteria Problem Statement -- Survey of Numerical Methods -- Sampling the Feasible Set -- Multiple-Objective Linear Programs -- Numerically Analyzing Nonlinear Problems -- Related Methods -- Survey of Engineering Problems -- Some Rudimentary Examples in Optimal Structural Design -- Survey -- References -- Chapter 11. Compromise Decision Support Problem and the Adaptive Linear Programming Algorithm -- Our Frame of Reference -- Introduction to Goal Programming -- Difference Between Objectives and Goals -- Development of the Baseline Model for Multiobjective Optimization -- Conversion of the Baseline Model to a Goal Programming Model -- Deviation Variables and Goals -- Lexicographic Minimum and the Achievement Function -- Compromise Decision Support Problem -- Characteristics of Engineering Design Problems -- Compromise Decision Support Problem -- System Descriptors of the Compromise Decision Support Problem -- Relationship Between the Compromise DSP, Goal Programming, and Mathematical Programming -- Adaptive Linear Programming for Solving Compromise Decision Support Problems -- Background of the Algorithm -- Approximation of a Nonlinear Compromise Decision Support Problem -- Solving the Approximate Problem: Solution of the Linearized DSP -- Adaptation of the Approximate Problem -- Special Features of the ALP Algorithm -- Computer Implementation and Applications -- Conclusion -- References -- Chapter 12. Sensitivity Analysis of Discrete Systems -- Introduction -- Finite Difference Sensitivities.

Truncation and Condition Errors -- Iteratively Solved Problems -- Sensitivity of Static Response -- First Derivatives of Linear Response -- Calculation of Second Derivatives -- Stress Derivatives -- Derivatives of Nonlinear Response -- Sensitivity of Eigenvalues and Eigenvectors -- Distinct Eigenvalues -- Repeated Eigenvalues -- Sensitivity Derivatives for Nonlinear Eigenvalue Problems -- Sensitivity of Transient Response -- General -- Direct Method -- Green's Function Method -- Adjoint Variable Method -- Finite Difference Method -- Linear Structural Dynamics -- Concluding Remarks -- References -- Chapter 13. Sensitivity Analysis: Distributed Systems -- Introduction -- Sensitivity Analysis: Variation of Material or Dimensional Variables -- Structural Shape Variation -- Shape Transformation Problem -- Sensitivity Analysis with Shape Transformation -- Sensitivity Analysis for Beam Structures -- References -- Chapter 14. Occurrence of Multiple Eigenvalues in Design Optimization of Slender Structures -- Elementary Examples -- Some Engineering Examples -- Arnol'd's Theorem, Multiple Eigenvalues, and Effects of the "Small and Neglected" Terms -- Is the Postbuckling Equilibrium Corresponding to a Double Eigenvalue a Stable Equilibrium? -- Appearance of Multiple Eigenvalues in Designs of Very Slender Structures Subjected to Rapid Accelerations and Gyroscopic Forces -- Additional Remarks -- Appendix -- References -- Chapter 15. Design Sensitivity Analysis of Nonlinear Structures I: Large-Deformation Hyperelasticity and History-Dependent Material Response -- Nomenclature -- Introduction -- Goals of Design Sensitivity Analysis in a Numerical Setting -- General Performance Functional -- Domain Parameterization Method for Shape Design -- Parametric Representation of the Design and the Sensitivity Problem -- Alternative Approaches to Design Sensitivity Analysis.

Large-Deformation, Hyperelastic Response: The Adjoint Variable Method.