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LUO Zhen CHEN Liping HUANG Yuying ZHANG YunqingNational Engineering Research Center for CAD, Huazhong University of Science and Technology, Wuhan, 430074, China Academy of Civil Engineering and Mechanics, Huazhong University of Science and Technology, Wuhan, 430074, China  
Structural topology optimization techniques are briefly discussed based on finite element approach. The mathematical model, with the objective to minimize compliance, as well as the explicit updating scheme for design variables are both worked out based on density-stiffness interpolation schemes and Optimality Criteria method. The computational model to maximize the fundamental eigenvalue, and the implicit retrieving pattern of design variables for vibrating structures, are also worked out using density method and a convex approach the method of moving asymptotes. Compliant mechanism designs employing topology optimization method, Multi-objective topology optimization problems considering static and vibrating structures, and multi-physics topology optimization problems are all discussed. Numerical instabilities, such as checkerboards and mesh dependencies, are introduced and investigated. The flowchart for topology optimization design is given. The efficiency and validity of methodologies in this paper are demonstrated by several typical examples. The future perspectives of topology optimization designs are outlined.
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