Contents -- Preface -- 1. Introduction -- 1.1 Probabilistic Analysis: Bad News -- 1.2 Probabilistic Analysis: Good News -- 1.3 Convergence of Probability and Anti-Optimization -- 2. Optimization or Making the Best in the Presence of Certainty/Uncertainty -- 2.1 Introduction -- 2.2 What Can We Get from Structural Optimization? -- 2.3 Definition of the Structural Optimization Problem -- 2.4 Various Formulations of Optimization Problems -- 2.4.1 Overview of optimization problems -- 2.4.2 Classification of optimization problems -- 2.4.3 Parametric programming -- 2.4.4 Multiobjective programming -- 2.5 Approximation by Metamodels -- 2.6 Heuristics -- 2.6.1 Overview of heuristics -- 2.6.2 Basic approaches of single-point search heuristics -- 2.6.2.1 Neighborhood solutions -- 2.6.2.2 Basic algorithm of single-point search heuristics -- 2.6.2.3 Greedy method -- 2.6.3 Simulated annealing -- 2.7 Classification of Structural Optimization Problems -- 2.8 Probabilistic Optimization -- 2.9 Fuzzy Optimization -- 3. General Formulation of Anti-Optimization -- 3.1 Introduction -- 3.2 Models of Uncertainty -- 3.3 Interval Analysis -- 3.3.1 Introduction -- 3.3.2 A simple example -- 3.3.3 General procedure -- 3.4 Ellipsoidal Model -- 3.4.1 Definition of the ellipsoidal model -- 3.4.2 Properties of the ellipsoidal model -- 3.5 Anti-Optimization Problem -- 3.6 Linearization by Sensitivity Analysis -- 3.6.1 Roles of sensitivity analysis in anti-optimization -- 3.6.2 Sensitivity analysis of static responses -- 3.6.3 Sensitivity analysis of free vibration -- 3.6.4 Shape sensitivity analysis of trusses -- 3.7 Exact Reanalysis of Static Response -- 3.7.1 Overview of exact reanalysis -- 3.7.2 Mathematical formulation based on the inverse of the modi ed matrix -- 3.7.3 Mechanical formulation based on virtual load -- 4. Anti-Optimization in Static Problems.

4.1 A Simple Example -- 4.2 Boley's Pioneering Problem -- 4.3 Anti-Optimization Problem for Static Responses -- 4.4 Matrix Perturbation Methods for Static Problems -- 4.5 Stress Concentration at a Nearly Circular Hole with Uncertain Irregularities -- 4.5.1 Introduction -- 4.5.2 An asymptotic solution -- 4.5.3 A worst-case investigation -- 4.6 Anti-Optimization of Prestresses of Tensegrity Structures -- 4.6.1 Introduction -- 4.6.2 Basic equations -- 4.6.2.1 Equilibrium equations -- 4.6.2.2 Self-equilibrium forces -- 4.6.2.3 Tangent stiffness matrix -- 4.6.2.4 Lowest eigenvalue of tangent stiffness matrix -- 4.6.2.5 Compliance against external load -- 4.6.3 Anti-optimization problem -- 4.6.4 Numerical examples -- 5. Anti-Optimization in Buckling -- 5.1 Introduction -- 5.2 A Simple Example -- 5.3 Buckling Analysis -- 5.4 Anti-Optimization Problem -- 5.5 Worst Imperfection of Braced Frame with Multiple Buckling Loads -- 5.5.1 Definition of frame model -- 5.5.2 Worst imperfection of optimized frame -- 5.5.3 Mode interaction -- 5.5.4 Worst-case design and worst imperfection under stress constraints -- 5.6 Anti-Optimization Based on Convexity of Stability Region -- 5.7 Worst Imperfection of an Arch-type Truss with Multiple Member Buckling at Limit Point -- 5.7.1 Introduction -- 5.7.2 Hilltop branching point of perfect system -- 5.7.3 Imperfection sensitivity of hilltop branching point -- 5.7.4 Worst imperfection -- 5.7.5 Worst imperfection of an arch-type truss -- 5.8 Some Further References -- 6. Anti-Optimization in Vibration -- 6.1 Introduction -- 6.2 A Simple Example of Anti-Optimization for Eigenvalue of Vibration -- 6.2.1 Anti-optimization for forced vibration -- 6.3 Bulgakov's Problem -- 6.4 Non-probabilistic, Convex-Theoretic Modeling of Scatter in Material Properties -- 6.4.1 Introduction -- 6.4.2 Basic equations for vibrating viscoelastic beam.

6.4.3 Application to a simply supported beam -- 6.4.4 Least and most favorable responses -- 6.4.5 Numerical examples and discussion -- 6.5 Anti-Optimization of Earthquake Excitation and Response -- 6.5.1 Introduction -- 6.5.2 Formulation of the problem -- 6.5.3 Maximum structural response -- 6.5.4 Ellipsoidal modeling of data -- 6.5.4.1 Basic ideas -- 6.5.4.2 Preliminary statements -- 6.5.4.3 Search of the smallest ellipsoid containing all points -- 6.5.4.4 Numerical application -- 6.6 A Generalization of the Drenick-Shinozuka Model for Bounds on the Seismic Response -- 6.6.1 Preliminary comments -- 6.6.2 Credible accelerograms -- 6.6.3 Application -- 6.6.4 Discussion and conclusion -- 6.7 Aeroelastic Optimization and Anti-Optimization -- 6.7.1 Introduction -- 6.7.2 Deterministic theoretical analysis -- 6.7.3 Stability analysis within two-term approximation -- 6.7.4 Convex modeling of uncertain moduli -- 6.7.5 Anti-optimization problem: polygonal region of uncertainty -- 6.7.6 Anti-optimization problem: ellipsoidal region of uncertainty -- 6.7.7 Minimum weight design -- 6.7.8 A numerical example -- 6.7.9 Conclusion -- 6.8 Some Further References -- 7. Anti-Optimization via FEM-based Interval Analysis -- 7.1 Introduction -- 7.2 Interval Analysis of MDOF Systems -- 7.3 Interval Finite Element Analysis for Linear Static Problem -- 7.4 Interval Finite Element Analysis of Shear Frame -- 7.4.1 Basic equations -- 7.4.2 A numerical example -- 7.5 Interval Analysis for Pattern Loading -- 7.6 Some Further References -- 8. Anti-Optimization and Probabilistic Design -- 8.1 Introduction -- 8.2 Contrasting Probabilistic and Anti-Optimization Approaches -- 8.2.1 Problem formulation -- 8.2.2 Probabilistic analysis -- 8.2.3 Uniformly distributed random initial imperfections -- 8.2.4 Random initial imperfections with truncated exponential distribution.

8.2.5 Random initial imperfection with generic truncated distribution -- 8.2.7 Conclusion -- 8.3 Anti-Optimization Versus Probability: Vector Uncertainty -- 8.3.1 Introduction -- 8.3.2 Deterministic analysis -- 8.3.3 Probabilistic analysis -- 8.3.4 Initial imperfections with uniform probability density: Rectangular domain . -- 8.3.5 Initial imperfections with general probability density: Rectangular domain -- 8.3.6 Initial imperfection with uniform probability density function: Circular domain -- 8.3.7 Initial imperfections as interval variables: Interval analysis -- 8.3.8 Initial imperfections as convex variables: Circular domain -- 8.3.9 Concluding remarks -- 9. Hybrid Optimization with Anti-Optimization under Uncertainty or Making the Best out of the Worst -- 9.1 Introduction -- 9.2 A Simple Example -- 9.3 Formulation of the Two-Level Optimization-Anti-Optimization Problem -- 9.4 Algorithms for Two-Level Optimization-Anti-Optimization -- 9.4.1 Cycle-based method -- 9.4.2 Methods based on monotonicity or convexity/concavity -- 9.4.3 Other methods -- 9.4.3.1 Approximation methods -- 9.4.3.2 Parametric programming approach -- 9.5 Optimization against Nonlinear Buckling -- 9.5.1 Introduction -- 9.5.2 Problem formulation -- 9.5.3 Numerical examples -- 9.6 Stress and Displacement Constraints -- 9.7 Compliance Constraints -- 9.7.1 Introduction -- 9.7.2 Optimization problem and optimization algorithm -- 9.7.3 Numerical examples -- 9.8 Homology Design -- 9.8.1 Introduction -- 9.8.2 Deterministic loading -- 9.8.3 A numerical example -- 9.8.4 Convex model of uncertain loading -- 9.8.5 Worst-case estimation -- 9.8.6 A numerical example of worst-case estimation of homology design -- 9.8.7 Concluding remarks -- 9.9 Design of Flexible Structures under Constraints on Asymptotic Stability -- 9.9.1 Introduction -- 9.9.2 Definition of asymptotic stability.

9.9.3 Optimization problem -- 9.9.4 Numerical examples -- 9.9.4.1 A 2-bar truss -- 9.9.4.2 A 24-bar truss -- 9.10 Force identification of prestressed structures -- 9.10.1 Introduction -- 9.10.2 Equations for self-equilibrium state -- 9.10.3 Formulation of identification error -- 9.10.3.1 Force errors -- 9.10.3.2 Identi cation error -- 9.10.4 Sensitivity analysis with respect to nodal coordinates -- 9.10.5 Optimal placement of measurement devices -- 9.10.5.1 Problem formulation -- 9.10.5.2 Solution process -- 9.10.6 Numerical examples -- 9.11 Some Further References -- 10. Concluding Remarks -- 10.1 Why Were Practical Engineers Reluctant to Adopt Structural Optimization? -- 10.2 Why Didn't Practical Engineers Totally Embrace Probabilistic Methods? -- 10.3 Why Don't the Probabilistic Methods Find Appreciation among Theoreticians and Practitioners Alike? -- 10.4 Is the Suggested Methodology a New One? -- 10.5 Finally, Why Did We Write This Book? -- Bibliography -- Index -- Author Index.