Crashworthiness Efficiency Optimisation For Two-Directional Functionally Graded Foam-Filled Tubes Under Axial Crushing Impacts

Recent advancements in crashworthiness analysis of functionally graded foam-filled tubes are achieved by studying the energy absorption characteristics in lateral or axial directions, separately. In this paper, for the first time, two-directional (lateral and axial directions together) functionally graded foams (TDFGFs) under axial crushing loads are considered. The effect of variations of foam density on the specific energy absorption (SEA) and peak crushing force (PCF) is studied by controlling the gradient exponential parameters which give rise to significant effects on the crashworthiness of TDFGFs. Also, it is further analysed that how the mass of the TDFGF tube changes values of SEA in crushing process. In addition, as the result of performing multi-objective particle swarm optimisations, it is seen that the energy absorption characteristics of TDFGFs for higher values of gradient exponential parameters are improved significantly. The crashworthiness properties of optimum configurations for TDFGF are compared with the extreme cases of minimum, maximum densities and uniform foam-filled tubes with the same weight as the corresponding TDFGF tubes. Finally, a global sensitivity analysis is carried out. The results of this analysis reveal that the SEA and PCF functions are generally sensitive to the variations of the gradient exponential parameters.