Structural optimization method

Chapter 1 Introduction 1.1 Brief History of Structural Optimization 1.2 The Basic Idea 1.3 The Design Process 1.4 Definition of Terms in Structural Optimization 1.5 General Structural Optimization Problem and Its Formulations 1.6 Three Types of Structural Optimization Problems 1.7 Discrete and Distributed Parameter Systems 1.8 Exercise Chapter 2 Basic Mathematical Concepts 2.1 Introduction 2.2 Sets 2.3 n - dimensional Space 2.4 Functions in n - dimensional Space 2.5 Open and Closed Sets 2.6 Sequence 2.7 Convexity 2.8 Conditions for Minima 2.9 Conditions for Constrained Minima 2.10 Duality Chapter 3 Elementary Concepts in Structural Optimization 3.1 Introduction 3.2 Statistically Determinate Structures 3.2.1 Analysis 3.2.2 Optimum Design of Strength - critical Problem 3.2.3 Optimum Design of Stiffness - critical Problem 3.2.4 Displacement - stress - constrained problem 3.2.5 Multiple displacement - constrained problem 3.3 Statically Indeterminate Structure 3.3.1 Analysis 3.3.2 Optimum Design of Strength - critical Problem 3.3.3 Displacement - constrained Statistically Indeterminate Structure 3.4 Analysis of General Structure 3.5 Exercise Chapter 4 Basics of Convex Programming 4.1 Local and Global Optima 4.2 Convexity 4.3 KKT Conditions 4.4 Lagrangian Duality Method 4.5 Exercise Chapter 5 Sequential Explicit, Convex Approximation 5.1 General Solution 5.2 Sequential Linear Programming 5.3 Sequential Quadratic Programming 5.4 Convex Linearization 5.5 Exercise Chapter 6 Stiffness Optimization of a Truss And Its Properties 6.1 The Simultaneous Formulation of the Problem 6.2 Nested Formulation and Some of Its Properties 6.2.1 Convexity of the Nested Problem 6.2.2 Fully Stressed Design 6.3 Minimization of the Volume Under a Compliance Constraint Chapter 7 Optimality Criterion Methods in Structural Optimization 7.1 Introduction 7.2 Basic Equations of Analysis 7.2.1 Displacement Method 7.2.2 Scaling of the Design 7.3 Displacement Constraints 7.3.1 Single Displacement Constraint 7.3.2 Multiple Displacement Constraints 7.4 Stress Constraints 7.5 Algorithm with the Reciprocal Design Variable 7.5.1 Optimality Criterion 7.5.2 Recurrence Relations 7.5.3 Evaluation of the Lagrange Multipliers 7.6 The Variable Thickness Sheet Problem 7.6.1 Problem Statement and FE - discretization 7.6.2 The Optimality Criteria Method 7.7 Exercise Chapter 8 Sensitivity Analysis of Structural Optimization 8.1 Numerical methods 8.2 Analytical Methods 8.2.1 Direct Analytical Method 8.2.2 Adjoint Analytical method 8.3 Sensitivity Calculation of Load and Stiffness Matrix 8.3.1 Bars 8.3.2 Plane Sheets 8.4 Exercise References