Topology optimization of periodic structures for crash and static load cases using the evolutionary level set method

Assembly complexity and manufacturing costs of engineering structures can be significantly reduced by using periodic mechanical components, which are defined by combining multiple identical unit cells into a global topology. Additionally, the superior energy-absorbing properties of lattice-based periodic structures can potentially enhance the overall performance in crash-related applications. Recent research developments in periodic topology optimization (PTO) have shown its efficacy for tackling new design problems and finding advanced novel structures. However, most of these methods rely on gradient information in the optimization process, which poses difficulties for crash problems where analytical sensitivities are usually not directly applicable. In this paper, we present an effective periodic evolutionary level set method (P-EA-LSM) for the optimization of periodic structures. P-EA-LSM uses a low-dimensional level-set representation based on moving morphable components to parametrize a single unit cell, which is replicated in the design domain according to a predefined pattern. The unit cell is optimized using an evolutionary algorithm and the structural responses are calculated for the entire system. We initially assess the performance of P-EA-LSM using three 2D minimum compliance test cases with varying periodicities. Our results demonstrate that our approach produces solutions comparable to other state-of-the-art methods for PTO while keeping a low dimensionality of the optimization problem. Subsequently, we effectively evaluate the capabilities of P-EA-LSM in a crashworthiness scenario. This particular application highlights the significant potential of the method, which does not rely on analytical sensitivities.