Mariusz Bujny, Muhammad Yousaf, Fabian Duddeck,
"Similarity-based Topology Optimization for Crash and Statics",
ECCOMAS Congress 2020, 2021.
Topology Optimization (TO)  is an important technique that redistributes the material within a design domain to optimize certain objective functions under specified constraints. In industry, efficient gradient-based techniques using SIMP (Solid Isotropic Material with Penalization) interpolation with Optimality Criteria (OC)  or heuristic approaches such as Hybrid Cellular Automata (HCA)  are used to optimize structures without taking into account the designer’s preferences about the final material layout. On the other hand, an improved design with a certain similarity to an already present reference design is usually required due to the economic reasons or limitations of the manufacturing and assembly process. To control similarity, one approach can be to directly incorporate similarity constraint in OC using analytical sensitivities of the considered similarity metric. In contrast, we propose a heuristic Energy Scaling Method (ESM)  to obtain designs of different similarity w.r.t. a given reference design. ESM is compared with OC-based SIMP with similarity constraint as well as alternative heuristic approaches such as the weak passive material method and the approach of modified design domain . The main advantage of the heuristic approaches is that they can be used both in gradient-based and non-gradient TO methods such as HCA or Scaled Energy Weighting (SEW)-HCA  to address static and crash problems. In ESM, the design domain is divided into preferred and non-preferred regions based on material distribution in the reference design. Designs varying in similarity w.r.t. the reference design are obtained by applying different scaling factors to the elemental energies in the preferred and non-preferred regions. Initially, the proposed method is coupled with HCA as well as with OC-based SIMP, for TO of a cantilever beam under static point load. Secondly, a 2-D beam fixed at both ends and impacted on the top edge is considered to test the method for a dynamic crash load case using HCA. The obtained results show that ESM is the most promising approach, which can be used to effectively control similarity in TO.
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