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