Since 1970s， structural optimization has passed through a period of rapid development during which it has moved from an assorted collection of interesting techniques to a mature discipline routinely used in engineering design. A variety of approaches have emerged which are used in a wide range of industries and have found a permanent place in several of the computer-aided design systems which are becoming commercially available.The text is written for students with a background in solid and structural mechanics with a basic knowledge of the finite element method， although in our experience such knowledge could be replaced by a certain mathematical maturity. Previous exposure to basic optimization theory and convex programming is helpful but not strictly necessary.In Chapter 1 we introduce the basic idea of mathematical design optimization and indicate its place in the broader frame of product realization， as well as define basic concepts and terminology. Chapter 2 is devoted to typical field of optimization， especially the Lagrange Multiplier and stiffness optimization.Chapter 3 gives some widely attractive tools in structural optimization， such as KKT conditions and sequential explicit， convex approximation for large problems. In Chapter 4， convex programming is introduced to approximately make the nonconvex problem become convex， moreover， the Lagrangian duality method is provided to solve the separable variable design. As for Chapter 5，based on the statistically determinate structure， statistically indeterminate structure and general structure， we introduced some important structural optimization in stiffness， stress and the combined optimization problem. Chapter 6 derives optimality criteria for displacement constraint， stress constraint and the variable thickness sheet design. Chapter 7 presents some sensitivity analysis methods， more than that， the stiffness sensitivity and force sensitivity are provided for finite element discretize structure. In Chapter 8， we provide some mechanical design optimization examples， such as gear train， multiple disc clutch brake and four stage gear train. In the last Chapter， multicriteria optimization is discussed including Pareto optimal sets and methods for converting multicriteria problems to conventional optimization problems. Appendix A and B give the Excel Solver and 99 lines plane stress topology optimization code for the readers to practice.
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