Chapter 1 Introduction 1.1 Brief History of Structural Optimization 1.2 The Basic Idea 1.3 The Design Process 1.3.1 Structural Optimization Design 1.3.2 Design Steps 1.4 General Mathematical Form of a Structural Optimization Problem 1.4.1 Multicriteria Optimization 1.4.2 Simultaneous Formulation and Nested formulation 1.5 Three Types of Structural Optimization Problems 1.6 Exercise Chapter 2 Typical Field of Optimization 2.1 Problem Statement 2.2 An Optimization Problem 2.3 Elementary Calculus 2.4 Optimal Slope for Truss Bars 2.5 An Arch Problem 2.6 The Gradient of a Function 2.7 The Lagrange Multiplier Rule 2.8 Newton's Method 2.9 Solving Linear Equations 2.10 Linear Systems Versus Optimization 2.11 Equations of Structures 2.12 A Beam Problem 2.13 General P'rocess of Deriving the Stiffness Matrix of Truss 2.14 Compliance Optimization Problem 2.14.1 Convexity of the Nested Problem 2.14.2 Fully Stressed Design of Nested Problem 2.15 Quadratic Programming Chapter 3 Some Tools of Optimization 3.1 The Lagrange Multiplier Rule 3.2 The Kuhn - Tucker Conditions 3.3 Newton's Method 3.4 Linear Programming 3.5 Sequential Explicit, Convex Approximations 3.5.1 Sequential Linear Programming (SLP) 3.5.2 Sequential Quadratic Programming (SQP) 3.5.3 Convex Linearization (CONLIN) 3.6 Duality Chapter 4 Basics of Convex Programming 4.1 Local and Global Optima 4.2 Convexity 4.3 KKT Conditions 4.4 Lagrangian Duality 4.5 Exercise Chapter 5 Discrete and Distributed Parameter System 5.1 Statistically Determinate Structures 5.1.1 Optimum Design of Strength Constraint Problem 5.1.2 Optimum Design of Stiffness Constraint Problem 5.1.3 Optimum Design of Displacement - stress - constrained Problem
5.1.4 Optimum Design of Strength and Instability Problem 5.2 Statically Indeterminate Structure 5.2.1 Optimum Design of Strength Constraint Problem 5.2.2 Optimum Design of Displacement - constrained Problem 5.3 General Structure Analysis 5.4 Exercise Chapter 6 Optimality Criterion Methods in Structural Optimization 6.1 Basic Equations of Analysis 6.1.1 Displacement Method 6.1.2 Scaling of the Design 6.2 Displacement Constraints 6.2.1 Single Displacement Constraint 6.2.2 Multiple Displacement Constraints 6.3 Fully Stressed Design (FSD) Method 6.4 Algorithm With the Reciprocal Design Variable 6.4.1 Optimality Criterion 6.4.2 Recurrence Relations 6.4.3 Evaluation of the Lagrange Multipliers 6.5 The Variable Thickness Sheet Problem 6.5.1 Problem Statement and FE - discretization 6.5.2 The Optimality Criteria Method 6.6 Exercise Chapter 7 Sensitivity Analysis Methods 7.1 Numerical methods 7.2 Analytical Methods 7.2.1 The Direct Analytical Method 7.2.2 The Adjoint Analytical Method 7.3 Calculation of Sensitivities for Loads and Stiffness 7.3.1 Load and Stiffness Matrix Sensitivity of Bars 7.3.2 Load and Stiffness Matrix Sensitivity of Plane Sheets 7.4 Exercise Chapter 8 Examples of Mechanical Design Optimization 8.1 Optimization of a Gear Train 8.2 Optimization of a Multiple Disc Clutch Brake 8.3 Discrete Optimization of a Four Stage Gear Train Chapter 9 Multicriteria Optimization 9.1 Introduction 9.2 Solving Multicriteria Optimization Problems Appendix 1 Microsoft ExcelThe Solver Routine Appendix 2 99 lines topology optimization References
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