Topology Optimization Benchmarks in 2D: Results for Minimum Compliance and Minimum Volume in Planar Stress Problems

This article proposes a benchmark set of problems for fixed mesh topology optimization in 2 dimensions. We have established the problems based on an analysis of more than 100 articles from the topology optimization specialized literature, gathering the most common dimensions, loads and fixed regions used by researchers. Most of the problems reported in specialized literature present differences in specifications such as lengths, units, materials among others. For instance, some articles propose the same proportions and geometrical shapes but different dimensions. Hence, the purpose of this benchmark is to unify geometrical and mechanical characteristics and load conditions, considering that the proposed problems must be realistic, in the sense that the units are in the International System and a real-world material and load conditions are used. The final benchmark integrates 13 problems for plane stress using ASTM A-36 steel. Additionally, we report approximations to the optimum solutions for both: compliance and volume minimization problems using the Solid Isotropic Material with Penalization (SIMP) and a novel version of SIMP proposed in this article.