中文摘要：

固定过滤半径的敏度过滤方法可以有效解决棋盘格现象和网格依赖性,但处理后拓扑优化结果普遍存在边界扩散现象,图形边缘存在大量的灰度单元。提出了一种考虑密度补偿的变过滤半径敏度过滤方法,即正向补偿相对密度为0.5~1的单元,反向补偿相对密度为0~0.5的单元,同时在拓扑优化计算的后期逐步缩小过滤半径至1。结合固体各向同性惩罚微结构模型,利用经典结构柔度最小化算例验证可行性。研究结果表明,考虑密度补偿的变过滤半径敏度过滤方法能够消除棋盘格现象,体现了网格无关性,拓扑优化结果具有清晰的边界,且优化效率和优化效果明显提升。

英文摘要：

Constant filter radius sensitivity filtering method could effectively eliminate checkerboard patter and mesh dependence,the optimized results had boundary diffusion,the edges of the graph existed many gray-scale elements.A considering density compensation variable filter radius sensitivity filtering method was proposed as an efficient approach,compensated the elements of relative density in 0.5-1,and reduced element density value in 0-0.5,and gradually reduced the filter radius to 1.Combining the solid isotropic microstructure with penalization model（SIMP）,the classical topology optimization problems were used to prove the superiority of the new method.The experimental results show that the new sensitivity filtering method may eliminate checkerboard patter and mesh independence,then the optimized results have clear boundary,and the optimization efficiency and optimization performance are improved significantly.