Structural design using optimization method

Structural design using optimization method ÄÚÈݼò½é

¡¡¡¡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.