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
