In this paper, we propose a topology optimization (TO) framework where the design is parameterized by a set of convex polygons. Extending feature mapping methods in TO, the representation allows for direct extraction of the geometry. In addition, the method allows one to impose geometric constraints such as feature size control directly on the polygons that are otherwise difficult to impose in density or level set based approaches. The use of polygons provides for more more varied shapes than simpler primitives like bars, plates, or circles. The polygons are defined as the feasible set of a collection of halfspaces. Varying the halfspace's parameters allows for us to obtain diverse configurations of the polygons. Furthermore, the halfspaces are differentiably mapped onto a background mesh to allow for analysis and gradient driven optimization. The proposed framework is illustrated through numerous examples of 2D structural compliance minimization TO. Some of the key limitations and future research are also summarized.

翻译：本文提出一种拓扑优化框架，其中设计变量由一组凸多边形参数化表示。该方法扩展了拓扑优化中的特征映射技术，使几何形状可直接提取。此外，该方法允许在密度法或水平集方法难以施加几何约束的情况下，直接在多边形上施加特征尺寸控制等几何约束。相较于杆件、板件或圆等简单基元，多边形可生成更丰富的形状。多边形定义为半空间集合的可行域，通过改变半空间参数可获取多边形的多样化构型。研究进一步实现半空间到背景网格的可微映射，以支持力学分析与梯度驱动优化。通过二维结构柔度最小化拓扑优化的多个算例验证了所提框架的有效性，并总结了关键局限性与未来研究方向。