Investigation and improvement of sensitivity computation using the area-fraction weighted fixed grid FEM and structural optimization

Boundary based structural optimization methods often employ a fixed grid FEM to compute sensitivities for efficiency and simplicity. A simple and popular fixed grid approach is to modify the stiffness of elements intersected by the boundary by an area-fraction weighting. However, poor sensitivities and numerical instabilities can occur when using this method. Sensitivity computation for a compliance objective is investigated and the results are used to develop a weighted least squares scheme to improve sensitivities computed by the area-fraction approach. This is implemented together with a numerically stable structural topology optimization using the level set method with no additional filtering or regularization. The performance of the proposed scheme is demonstrated by classic benchmark examples of topology optimization.