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## A REVIEW ON TOPOLOGY OPTIMIZATION OF STRUCTURES

ZHOU Kemin LI Junfeng LI Xia School of Civil Engineering, Huaqiao University, Fujian 362021, China Department of Engineering Mechanics, Tsinghua University, Beijing 100084, China
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.
【Fund】： 高等学校优秀青年教师教学科研奖励基金 华侨大学科研基金资助项目
【CateGory Index】： TB11
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