This paper evaluates the crashworthiness performance of concentric structures with different numbers of tubes (i.e. one to five) and cross-sectional shapes (i.e. hexagon, octagon, decagon and circle) under the multiple loadings of θ = 0, 10, 20 and 30°. An experimentally validated finite element model generated in LS-DYNA is employed to calculate the crashworthiness parameters including the specific energy absorption, maximum crush force and crush force efficiency. A total of 20 concentric structures are analyzed to explore the effects of number of tubes and cross-sectional shapes on the crushing performance. A multi-criteria decision-making method known as TOPSIS is also used to compare and rank the concentric structures in terms of crushing performance. Based on the results, the hexagonal structure including two tubes and octagonal, decagonal and circular structures including three tubes demonstrate the best results among their corresponding cross-sectional shapes. These structures show 9, 39, 38 and 39% higher specific energy absorption compared to their corresponding single tubal cases, respectively. However, in comparison to single tubal cases, they generate 4, 57, 57 and 58% higher maximum crush force, respectively. As such, the values for the improvement of the crush force efficiency are 3, 26, 25 and 21%, respectively. Furthermore, the decagonal structure including three tubes provides the highest energy absorbing characteristics as compared with all the other structures studied in this research. Meanwhile, taking into account all the multiple loading conditions, this structure shows 50% higher specific energy absorption than the hexagonal structure including single tube (as the weakest structure).
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