基于水平集方法的连续体结构拓扑优化

提出了一种用水平集函数作为设计变量求解连续体结构拓扑优化的方法。优化方法以结构的整体柔度最小为目标函数,以实体材料所占的体积为约束条件,综合采用有限元方法和优化准则法对问题进行求解。该方法与密度惩罚法相比,克服了锯齿形边界,得到了光滑的结构边界;与传统水平集方法相比,不用求解复杂的Hamilton-Jacobi方程,提高了计算效率。在对Heaviside函数正则化处理中,考虑了形状导数和拓扑导数信息,加快了收敛速度。用该方法对梁的拓扑优化设计进行了试算,得到了满意的优化结果。

Topology Optimization of Continuum Structure Based on Level Set Method

A topology optimization approach of continuum structure based on level set method was proposed.The objective function of the problem is the minimum compliance of the structure,and the constraint condition is the material volume.A finite element method and optimization criteria method were incorporated to solve the problem.Compared with solid isotropic material with penalization(SIMP),smooth structural boundaries could be obtained by the approach without zigzag boundaries.The computational efficiency could be saved without solving the complicated Hamilton-Jacobi equation,which was used in traditional level set method.On the process of regularizing the Heaviside function,the information of the shape derivative and the topological derivative of the optimal design were considered.Convergence velocity was accelerated.By using the method,topology optimization design for the beam was tried to calculate,and the satisfactory optimization results were obtained.