中文摘要：

敏度过滤是变密度拓扑优化方法中消除数值不稳定性问题最普遍的方法之一,但易引起模糊边界的优化结果.为了抑制灰度单元,提出一种简易的考虑密度梯度的敏度过滤方法.在原有敏度过滤中增加密度梯度权函数项,使得当密度梯度大于设定阈值时权函数取值较小,修正了敏度过滤中的距离权函数值,可自动判别并弱化了优化边界的过滤平均效果;将该方法与固体各向同性惩罚微结构模型结合,根据不同拓扑优化问题类型,基于优化准则或移动近似算法优化求解.采用经典算例对文中方法的优化效果进行考察,结果表明,该方法的拓扑优化结果无棋盘格现象和网格依赖性,具有清晰的优化边界,优化效率高且易于实施.

英文摘要：

Sensitivity filtering methods have been one of the most popular approaches in the variable density method for topology optimization to eliminate numerical instabilities. However, they usually generate final designs with blurry boundaries. To suppress gray-scale elements, a sensitivity filtering technique considering density gradient is proposed as an efficient approach. The density gradient weighting function is supplemented in the original sensitivity filter expression. When the density gradient is greater than the given threshold, the value of the density gradient weighting function is made smaller to modify the distance weighting function in the original sensitivity. The averaging effect of the topological boundary is recognized automatically and weakened. The proposed method is implemented in the framework of solid isotropic microstructures with penalization model. According to different types of topology optimization problems, the model is solved by optimality criteria or method of moving asymptotes. The optimization effect of the proposed method is illustrated with classical examples. Numerical results show that the application of the method brings more desirable effects of checkerboard-free, mesh independence, crisp boundary, computational efficiency and conceptual simplicity.