Bilateral Filtering for Structural Topology Optimization

Filtering has been a major approach used in the homogenization-based methods for structural topology optimization to suppress the checkerboard pattern and relieve the numerical instabilities. In this paper a bilateral filtering technique originally developed in image processing is presented as an efficient approach to regularizing the topology optimization problem. A nonlinear bilateral filtering process leads to a suitable problem regularization to eliminate the checkerboard instability, pronounced edge preserving smoothing characteristics to favor the 0-1 convergence of the mass distribution, and computational efficiency due to its single pass and non-iterative nature. Thus, we show that the application of the bilateral filtering brings more desirable effects of checkerboard-free, mesh independence, crisp boundary, computational efficiency and conceptual simplicity. The proposed bilateral technique has a close relationship with the conventional domain filtering and range filtering. The proposed method is implemented in the framework of a power-law approach based on the optimality criteria and illustrated with 2D examples of minimum compliance design that has been extensively studied in the recent literature of topology optimization and its efficiency and accuracy are highlighted.