结构拓扑优化研究方法综述

结构拓扑优化研究方法目前有解析方法和数值方法两大类.首先介绍了解析方法中的 Michell理论,它在结构拓扑优化领域研究较早,影响最为深远.随后着重讨论了杆系和连 续体结构拓扑优化的数值方法.杆系结构常采用基结构方法,通过删除部分杆件达到结构 拓扑优化的目的.连续体结构一般要划分为有限单元,通过删除单元形成带孔的连续体, 以实现拓扑优化.介绍了连续体结构拓扑优化常采用的材料模型:各向同性、各向异性和 带微结构材料.并对连续体结构(0-1)拓扑优化中的数值计算不稳定问题的机理进行了分 析,给出了解决方法.此外,对应力约束问题存在解的奇异性现象也作了简要介绍.最后, 对数值方法中的主要数学求解方法进行了简单介绍.

A REVIEW ON TOPOLOGY OPTIMIZATION OF STRUCTURES

The methods of optimizing structure's topology include two classes, analytical method and numerical method. The Michell theory is an analytical method, developed early and having a great influence on structural topology optimization study. This paper mainly focuses on the numerical methods of optimizing truss, frame and continuum structures. The ground structure approach is usually used to optimize trusses and frames. The optimum topology is achieved by deleting parts of members in trusses or frames. To optimize continuum structures, the design region is divided into finite elements. The optimum topology is achieved by deleting parts of elements to form continuum structures with holes. Three kinds of material models are generally used, isotropic, anisotropic and that with microstructures. The numerical instabilities in (0-1) topology optimization of continuum structures are analyzed. The methods in common use to overcome this difficulty include perimeter control, local gradient constraint, mesh-independence filter methods and topology analysis. The singular optimum in topology optimization of structures with stress constraints is introduced briefly. The main mathematical methods to solve topology optimization are discussed.