Level Set-based Structural Topology Optimization using Particle Method
Recently, topology optimization for structures is applied to nonlinear problems1,2,3. But, in topology optimization for structures with geometrical nonlinearity, there are problems on nonlinear analysis using FEM (Finite Element Method). Those problems are caused by the mesh used in FEM. In this study, we propose a new method of topology optimization considering geometrical nonlinearity based on the level set method. The proposed method is developed for optimizing elastic structures with finite deformation. In the proposed method, MPS (Moving Particle Semi-implicit) method, one of particle methods, is used for stress and displacement response analysis. MPS method doesnt use the mesh on geometrically nonlinear analysis. The optimization problem is solved by the level set method, which can control the geometrical complexity of optimal configurations. First, a topology optimization problem is formulated based on the level set method and the method of regularizing the optimization problem by introducing fictitious interface energy is explained. Next, the reaction-diffusion equation that updates the level set function is derived and an optimization algorithm is then constructed, which uses the Finite Element Method to solve the equilibrium equations and the reaction-diffusion equation when updating the level set function. Finally, several numerical examples show the effectiveness of the proposed method in topology optimization with geometrically nonlinear problems.
topology optimization, level set method, particle method, moving particle semi-implicit method
M. Manabe T. Yamada S. Nishiwaki K. Izui
Graduate School of Engineering, Kyoto University, Japan
国际会议
南京
英文
132
2009-10-12（万方平台首次上网日期，不代表论文的发表时间）