Topology Optimization of Multiple Materials Compliant Mechanisms Based on Sequence Interpolation Model and Multigrid Method

Publication Type:
Journal Article
Jixie Gongcheng Xuebao/Journal of Mechanical Engineering, 2018, 54 (13), pp. 47 - 56
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© 2018 Journal of Mechanical Engineering. The topological optimization of multi-material compliant mechanism based on solid isotropic material with penalization (SIMP) interpolation model is to decompose the original problem into a hierarchy of single material sub-optimization, the design variables are doubled, and the number of structural grids is bound to be huge to get clear configuration when the traditional finite element method is used, the inefficiency of the method are caused by these two factors. Therefore, the sequence interpolation model is proposed based on power function polynomial to iterate the layout of multiple materials, so that the ordered density of different material gathered to the predefined numbers of material points in the design domain without any decomposition and increasing of design variables in a single optimization framework to realize multi-material topology optimization. The optimization model of multi-material compliant mechanism is established based on the geometrical advantage of the mechanism. In the process of solving the control equation by using the finite element method, the multigrid method is imposed, the meshing granularity is progressive, and the displacement field under the coarse grid level is taken as the initial field on the finer grid without any unnecessary high computational costs by overall discrete of the design domain. The computational efficiency is greatly improved. The optimal layout pattern of multi-material compliant mechanism is obtained by using the modified optimality criterion method. Widely studied numerical examples are conducted and compared with the corresponding results of SIMP method, which demonstrate the effectiveness of the proposed method.
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