Similarity-Driven Topology Optimization for Statics and Crash via Energy Scaling Method

Topology optimization (TO) is used in the initial design phase to optimize certain objective functions under given boundary conditions by finding suitable material distributions in a specified design domain. Currently available methods in the industry work very efficiently to get topologically optimized design concepts under static and dynamic load cases. However, conventional methods do not address the designer’s preferences about the final material layout in the optimized design. In practice, the final design might be required to have a certain degree of local or global structural similarity with an already present good reference design because of economic, manufacturing, and assembly limitations or the desire to re-use parts in different systems. In this article, a heuristic energy scaling method (ESM) for similarity-driven TO under static as well as dynamic loading conditions is presented and thoroughly evaluated. A 2D cantilever beam under static point load is used to show that the proposed method can be coupled with gradient-based and also heuristic, nongradient methods to get designs of varying similarity with respect to a reference design. Further testing of the proposed method for similarity-driven TO on a 2D crash test case and a large-scale 3D hood model of a car body indicates the effectiveness of the method for a wide range of problems in the industry. Finally, the application of similarity-driven TO is further extended to show that ESM also has the potential for sensitivity analysis of performance with respect to the extension of design domain.