The Use of Convex Uniform Honeycomb Tessellations in Structural Topology Optimization

This paper explores the use of specific tessellations of the design domain in the topology optimization of structures. By the use of particular shapes for the design cells used for design discretization, corner contact between adjacent cells can be avoided. This in turn eliminates the possibility of the formation of topological anomalies such as checkerboard patterns, de facto hinges and diagonal element chains, and the associated numerical problems. A methodology and numerical results are presented for both two- and three-dimensional problems, initially based on convex uniform honeycomb tessellations. After demonstrating the effectiveness of the proposed approach, simplified versions are presented that are equally effective but require less computational and implementation effort. At an increase of the compuational cost comparable to the use of quadratic instead of linear finite elements, the presented cell-based approach rigorously eliminates topological singularities, without introducing new constraints or parameters in the optimization problem. Keywords: honeycomb tessellations, space-fillings, checkerboard patterns, corner contact, de facto hinges.