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Structural dynamic response topology optimization under basic harmonic excitation

LI Xiang,WANG Hao(Department of Mechanics and Engineering Science,Fudan University,Shanghai 200433,China)  
As to the facts that there are few studies on structural dynamic response topology optimization and it can not be achieved by the topology optimization modules of finite element analysis software,the dynamic response topology optimization of continuum structure under basic harmonic excitation is studied by variable density method.To control the response under basic harmonic excitation,an optimization model is established with an aim for minimization response amplitude of concern points under volume constraint;the response amplitude sensitivity equation of certain points is derived for structure with damp under basic harmonic excitation;then the optimization problem is solved by variable density method.The affiliated effect of SIMP(Solid Isotropic Microstructure with Penalization) model is solved by polynomial penalty model;a gray filtration method is used to solve the low convergence rate of gray elements in the optimization using classical variable density method,and the optimization iteration steps of variable density method are decreased and the optimization result becomes clearer.a plane cantilever plate is optimized,and the result indicates that the method can improve the optimization on the response amplitude of concern points and the gray filtration function can decrease optimization steps.
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