Sensitivity Filtering Method Considering Density Gradient

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.