A hybrid sensitivity filtering method for topology optimization

In topology optimization, filtering techniques have become quite popular in practice. In this paper, an accurate and efficient hybrid sensitivity filtering approach based on the traditional and bilateral sensitivity filtering approaches is proposed. In the present hybrid approach, the traditional sensitivity filter is applied to a subdomain where numerical instabilities are likely to occur to overcome the numerical instabilites robustly. Filtering on mesh-independent holes identified by an image-processing-based technique is prohibited to reduce the computational cost. The bilateral approach is employed for the corresponding nearest neighboring elements of the mesh-independent holes to drive the 0-1 convergence of their boundaries. As a result, the optimal designs can be checkerboard-free, mesh-independent and mostly black-and-white. The possible side effects of the traditional and bilateral sensitivity filtering approaches can be alleviated. Existence of solutions can be ensured in a more accurate manner. The high accuracy and efficiency of the present approach are illustrated with classical examples in minimum compliance design. It is suggested that the present hybrid approach for topology optimization be highly appealing.