Crushing analysis and multiobjective optimization for functionally graded foam-filled tubes under multiple load cases

Functionally graded foam (FGF)-filled tubes have been recently gaining comprehensive attention due to its excellent energy absorption capacity under axial impact. However, energy absorption devices generally rarely experience pure axial loading in real working condition, but rather oblique loads, especially during a vehicle crash event. This paper aims at investigating the crashworthiness of the FGF-filled square tubes under multiple load cases. The foam density of the FGF-filled tubes varies along the axial direction and is controlled by the gradient exponent. Numerical comparative analysis results reveal that impact angle and the gradient exponent have a significant effect on crashworthiness of the FGF-filled tubes, and the FGF-filled tubes surpass the uniform foam (UF)-filled tubes in crashworthiness for various impact angles. To optimize the crashworthiness of FGF-filled tubes, the non-dominated sorting genetic algorithm (NSGA-II) is used to seek for an optimal gradient exponent, where the specific energy absorption is maximized and peak crashing force is minimized simultaneously. The multiple impact angles are considered to improve the robustness of the optimal results. The optimal designs of the FGF-filled tube demonstrate better crashworthiness characteristics than the UF-filled tubes.