基于步长因子改进的导重法求解拓扑优化问题

Based step factor improved Guide-weight method for solving topology optimization problems

结合固体各向同性惩罚微结构模型SIMP(Solid Isotropic Microstructures with Penalization),将导重法用于求解拓扑优化问题。针对导重法迭代公式中步长因子的取值问题,提出两种变步长因子的控制策略,以结构最优性指标为参考,自动确定每步迭代的步长因子。同时引入密度补偿方法,以结构最优性指标为依据自动判断加入密度补偿的时机。利用经典拓扑优化算例,验证两种步长因子控制策略的优越性;通过细长梁算例,比较优化准则法OC(Optimality Criteria)和导重法的差异,分析对比两种步长因子控制策略施加密度补偿方法前后的计算结果。研究结果表明,两种步长因子控制策略能够取得更优解,有效提升求解效率;对于细长梁的拓扑优化问题,导重法求得的解较OC算法更具有全局性,优化效果更佳;密度补偿方法可进一步提升导重法的求解效率。

The Guide-weight method combined with SIMP theory was used to solve topology optimization problems. In order to define the step factor of iterative formula,two variable step factor control method was proposed,automatically determining the step factors of each iteration referring to structural optimization index.Density compensation method was also introduced,automatically determining the timing of density compensation based on the structural optimization index. The classical topology optimization case was presented to prove the superiority of the two step factor control method. The difference between OC algorithm and Guide-weight method was found by analyzing the elongate beam problems and the experiment result of the two step factor control method with and without density compensation were compared. The experimental results show that the two step control method can bring a better solution and improve solving efficiency. The Guide-weight method can get a more closed global optimal solution compared with the OC algorithm,and the density compensation method can further improve the efficiency of Guide-weight method.