A simple density filter for the topology optimization of coated structures

Coated structures are structures with a solid thin-walled coating enclosing substrates. Coated structures with porous substrates (infills) are often adopted in additive manufacturing to reduce the material cost and printing time, while improving robustness against local bucking, unknown loads and material deficiencies. This article presents a new density filter method for the topology optimization of coated structures. Compared to previous work, the new method uses only the density filter and its projection, and does not rely on the gradient of the density field, which can pose a numerical challenge in large-scale problems. Since the output of the proposed density filter is bounded exactly between zero and one, it will also eliminate the need to approximate the maximum magnitude of the density gradient, the inaccuracy of which can cause non-uniform thickness of the coating. The proposed filter also realizes a smoother change between substrate material and coating material, and encourages the merging and splitting of coatings during optimization. Several numerical examples on compliance minimization are presented to demonstrate the validity and effectiveness of the proposed density filter.