Topology Optimization of Thin-Walled Structures Under Static/Crash Loading Case in the Hybrid Cellular Automaton Framework

Crashworthiness design and optimization is of great importance in the automotive industry. However, due to the high computational cost and numerical noise, crashworthiness topology optimization is not studied so intensively. In this paper, a relatively new method, the Hybrid Cellular Automata for Thin-walled Structures (HCATWS) is used in its improved version. In particular, its applicability is extended from structures with an initially regular grid to structures with different size of cells (sets of a higher number of finite elements). The corresponding modifications of the algorithm are discussed here. This also affects the updating rules used in the improved version; hence, the theory is revised and modified where necessary. In the outer loop of the HCATWS, bi-section search within limited length is used to define the target mass. In the inner loop, HCATWS utilizes proportional updating to redistribute the mass for each cell. Then mass correction is conducted to make sure the real mass converges to the target mass. Here the different sizes of the cells need to be considered. As applications, one linear static case is studied to demonstrate efficiency of the approach. Then, additional crash cases using nonlinear dynamic FEM are considered. Finally, the potential of using this approach for identification of optimal cross-sections of structures originating from Additive Manufacturing (AM) is explored. Here, it is important that optimized topology results from HCATWS are more easily manufactured compared to those obtained by traditional element-based, i.e. voxel-based, topology optimization.