基于改进灵敏度过滤策略的SIMP方法

发布时间：2018-07-02 10:27

  本文选题：变密度法 + 灰度单元　； 参考：《计算力学学报》2017年01期

【摘要】：在传统变密度法SIMP(Solid Isotropic Microstructures with Penalization)中,Sigmund灵敏度过滤策略是解决拓扑优化结果数值不稳定问题的重要方法之一。但在SIMP方法中采用Sigmund灵敏度过滤策略时,有时优化结果会有较多的灰度单元。为了减少拓扑优化结果中灰度单元的数量,提出了一种基于改进灵敏度过滤策略的SIMP方法。在过滤后单元灵敏度的计算中,增加了一个与中心单元过滤前灵敏度有关的部分,该部分在过滤后灵敏度中所占的比重需要通过过滤权重来调节。通过对灵敏度过滤需要的分析,确定了过滤半径和中心单元密度值是影响过滤权重的因素。根据拓扑优化实例的优化结果给出了过滤半径影响过滤权重的情况,并基于过滤半径对过滤权重的影响情况构建了过滤权重的函数。在改进灵敏度过滤策略的基础上,结合双重SIMP算法给出了本文SIMP方法的流程。最后,以悬臂梁结构和简支梁结构为例,验证了本文方法的有效性。与Sigmund灵敏度过滤策略相比,改进的灵敏度过滤策略能有效地减少灰度单元。与双重SIMP方法相比,本文SIMP方法能有效地减少数值不稳定现象。
[Abstract]:Sigmund sensitivity filtering strategy is one of the most important methods to solve the numerical instability problem of topological optimization results in traditional simp (solid Isotropic structures with Penalization). However, when Sigmund sensitivity filtering strategy is used in SIMP method, sometimes there are more gray units in the optimization results. In order to reduce the number of gray units in topology optimization, a SIMP method based on improved sensitivity filtering strategy is proposed. In the calculation of the sensitivity of the filtered unit, a part related to the sensitivity of the central unit before filtering is added. The proportion of this part in the sensitivity after filtering needs to be adjusted by the filter weight. By analyzing the need of sensitivity filtering, it is determined that the filter radius and the density of the central unit are the factors affecting the filter weight. The influence of filter radius on filter weight is given according to the optimization result of topology optimization example, and the function of filter weight is constructed based on the influence of filter radius on filter weight. Based on the improved sensitivity filtering strategy, the flow chart of the SIMP method is given by combining the dual SIMP algorithm. Finally, the effectiveness of this method is verified by taking cantilever beam structure and simply supported beam structure as examples. Compared with Sigmund's sensitivity filtering strategy, the improved sensitivity filtering strategy can effectively reduce gray level units. Compared with the double SIMP method, the SIMP method in this paper can effectively reduce the numerical instability.
【作者单位】： 桂林电子科技大学机电工程学院;
【基金】：国家自然科学基金(51265006)资助项目
【分类号】：O224
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本文编号：2089823