ABSTRACT

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.

摘要

涂层结构是具有封闭基材的实心薄壁涂层的结构。增材制造中通常采用具有多孔基材（填充物）的涂层结构，以降低材料成本和打印时间，同时提高对局部屈曲、未知载荷和材料缺陷的鲁棒性。本文提出了一种新的密度滤波方法，用于涂层结构的拓扑优化。与之前的工作相比，新方法仅使用密度滤波器及其投影，而不依赖密度场的梯度，这在大规模问题中可能会带来数值挑战。由于所提出的密度滤波器的输出恰好在 0 和 1 之间，它也将消除近似密度梯度最大幅度的需要，其不准确会导致涂层厚度不均匀。所提出的过滤器还实现了基材和涂层材料之间更平滑的变化，并在优化过程中促进了涂层的合并和分裂。提出了关于合规性最小化的几个数值例子，以证明所提出的密度滤波器的有效性和有效性。