Topology Optimization for Polymeric Foam Shock-Absorbing Structure Using Hybrid Cellular Automata

The foam shock-absorbing structures such as cushioning packages are popularly utilized to protect various products from mechanical shock and vibration during transportation. Although a thick cushion is required to avoid damage of products, it accompanies increasing costs for transportation and material. Therefore, packaging design engineers have tried to find optimal geometry parameters. They want to obtain a cushioning package structure minimizing the volume of the package in despite of better performance through various optimization techniques. In this paper, we propose a new topology optimization method suitable for the polymeric foam shock-absorbing structure such as a cushioning package under drop load conditions of multiple directions. Conventional approaches of topology optimization based on sensitivity information are practically infeasible due to the very high computational cost and difficulties for nonlinear dynamic analysis. In our approach, a heuristic topology optimization method, known as the hybrid cellular automata (HCA), is used. The HCA algorithm distributes uniformly internal energy density and controls the relative density of cellular automata (CAs) making up the design space in order to maintain or increase the performance of shock absorption and to decrease the amount of material. Especially, this paper presents a modified SIMP (Solid Isotropic Material with Penalization) model for foam materials, which parameterizes the design region and interpolates the material properties. We try to optimize a simple bottom-cushioning package of the refrigerator using the proposed foam SIMP model with commercial S/W, LS-DYNA for drop/impact dynamic simulation and LSOPT/TOPOLOGY for the HCA algorithm. The drop simulation and topology optimization are performed considering multiple drop-directions. As a result, our approach removes elements which not related to the shock-absorption performance and induce an optimal cushioning structure using a sfoam material.