机械结构优化设计是实现材料最优利用的关键，既可提升结构的承载性能，又可减少材料的应用，还可实现复合材料结构设计、人工材料、增材设计等，也是数字化设计和制造—体化的关键。本书从结构设计出发，介绍了典型的优化领域和一些优化工具方法，对于重要的凸规划问题，重点介绍了拉格朗日对偶法，分别以离散结构和连续结构为研究对象，介绍了静定结构和静不定结构的几种典型优化问题，对重要的优化方法——优化准则法进行了系统的分析，提供了优化求解中关键的灵敏度分析方法，最后对典型结构进行了优化建模和简要介绍了多目标优化的建模方法。本书可作为大专院校工科相关专业师生的教材或参考书，也可供机械工程技术人员参考。

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