Numerical study on a fractal-like multi-cell tubes with the Fibonacci helical section under axial crushing

Abstract

A novel bio-inspired fractal-like multi-cell tube (FMT) was developed based on the Fibonacci spiral structure in creatures. A numerical study on FMTs with different sectional configurations was conducted under axial crushing using the nonlinear finite element method. Three criteria used to evaluate the crashworthiness of the FMTs: initial peak crush force ( Fp), specific energy absorption ( Es), and crush force efficiency ( Cf). The effects of different numbers of helical ribs N and wall thickness t on the crashworthiness and deformation mode of the FMTs were analyzed. Secondly, an analytic hierarchy process (AHP) method and a complex proportional assessment (COPRAS) method were applied to select the best possible sectional configuration. According to this method, three types of FMT with one, three, and five ribs (FMT1, FMT3, and FMT5) were determined to have a superior sectional configuration. Finally, a metamodel-based multi-objective optimization method based on a polynomial regression metamodel and multi-objective particle optimization (MOPSO) algorithm were employed to optimize the structural parameters of the FMT1, FMT3 and FMT5 under six designed cases, including two criteria cases and three criteria cases, where t and basic diameter D1 of the Fibonacci helical were considered the design variables. The multi-objective optimization results indicated that the optimal D1 does not exceeding 15 mm, the optimal t ranges from 0.29 to 0.72 mm under three criteria cases. Further research pertaining to the crashworthiness analysis of FMTs under oblique crushing should be conducted.