抑制拓扑优化中灰度单元的双重SIMP方法

Double-SIMP Method for Gray-scale Elements Suppression in Topology Optimization

为了抑制连续体结构拓扑优化结果中的灰度单元,在实体各向同性材料惩罚密度法(Solid isotropic microstructures with penalization,SIMP)的基础上提出一种双重SIMP方法。首先利用含有灵敏度过滤的SIMP方法对设计变量进行迭代和优化,将优化结果作为中间变量,然后用不含有灵敏度过滤的SIMP方法对中间变量进行优化迭代,得到最终优化结果。以简支梁的结构柔顺度最小为例,将双重SIMP方法用于柔性结构的优化设计中并与标准SIMP算法相比;结果表明,双重SIMP方法得到清晰的拓扑分布结构,有效抑制了灰度单元,并且双重SIMP方法可以得到更小的结构柔顺度,证明了该方法的有效性;双重SIMP算法的灰度单元对惩罚因子的依赖性很小,可以选用较小的惩罚因子;针对不同的网格划分模型,双重SIMP算法得到的优化目标和灰度单元数更稳定,体现出了很好的网格依赖性。说明该方法具有很好的适用性和稳定性。

To suppress gray-scale elements in topology optimization for continuum structures, a new double-SIMP （Solid isotropic mierostructures with penalization） method was presented based on standard SIMP approaches. It is found that the SIMP method without sensitivity filter could suppress gray-scale elements in the topological structures. Therefore, a two-pass method was presented. Firstly, the standard SIMP method with sensitivity filter was employed to generate intermediate design variables; secondly, the SIMP method without sensitivity filter was adopted to update the intermediate design variables again and produce the final solution. Taking simple supported beam as an example, it is successful to apply double- SIMP method in the topological design of flexible body. According to the results, gray-scale elements were suppressed successfully. What is more, the results showed that smaller structural compliance could be obtained through double-SIMP method. The mesh-dependence problem of double-SIMP method was also better. Besides, to suppress the gray-scale elements, the standard SIMP method would need to increase the penalty factor. However, the bigger the penalty factor was, the more the iterations were. The double-SIMP method didn＇t rely on the penalty factor. Compared with standard SIMP method, there were not extra parameters and constraints in the double-SIMP method. As a consequence, the applicability is similar between the two kinds of methods.