# Crushing Analysis and Optimization of Adjacent Variable Thickness Hexagonal Tubes
## 1 Introduction  
To improve the safety of trains or automobiles in collision accidents, energy absorption structures (EASs) are usually installed at the front of vehicles to dissipate the impact energy, and EASs are attracting increased attention recently [1; 2; 3].  
Thin-walled (TW) structures, as the most widely used EASs, include tubular structures [4] and foam structures [5; 6]. Many researchers have studied the crushing performance of TW tubular structures through experiments, simulations, and theories [7]. In [8], energy absorption tubes of various cross-section shapes were investigated, and it was found that varying the thickness and taper angle can improve crashworthiness.  
The crushing performance of hexagonal tubes has frequently been reported. In [9], the method of angle elements was applied for studying the crush resistance of polygonal tubes, including hexagonal tubes, and some discussion about the deformation mechanism of energy absorption is presented. In [10], a hexagonal TW tube with partition plates subjected to axial compression was studied, and it raised its average compression load by introducing corner parts. [PERSON] et al. proposed a hierarchical hexagonal multi-cell tube and indicated that the tube is a more weight-efficient energy absorber [11]. In [12], researchersemployed finite element analysis (FEA) with surrogate models to optimize the sectional dimensions of hexagonal tubes. [PERSON] et al. investigated the crushing performance of bitubular hexagonal columns with ribs and selected the best configuration of ribs [13]. These studies focused on hierarchical structures, multi-cells, ribs, and graded thickness for hexagonal tubs, and there is no report on the method of changing the adjacent wall thickness of hexagonal tubes to improve crashworthiness under multiple loadings. However, the crushing performance of square and rectangular tubes with various adjacent wall thicknesses has been investigated [14; 15; 16], and it was found that changing wall thickness affected the force characteristics and deformation mode of square columns and rectangular tubes. Therefore, it is worth studying how changing the wall plate thickness affects the crashworthiness of adjacent variable-thickness hexagonal tubes.  
In addition to axial loading, the TW EASs could be subjected to multiple loadings during collision. The crushing performance of EASs under oblique loadings has been the focus of researchers [17; 18; 19; 20], and it is more complex than that of EASs under axial loading, and more research methods are applied to it. The weight factor technique has been widely applied [21]. Moreover, in [22], the results showed that the method with dimensionless and weighted processing showed a more obvious effect in improving the crashworthiness of the tubes, which has an enlightening effect on the research of this paper.  
In this paper, we proposed a new adjacent variable thickness hexagonal tube (AVTHT), studied its crushing performance under multiple loadings, and performed multi-objective optimization for thickness configuration with a dimensionless and weighted method. Section 2 introduces AVTHTs and defines the methods for simulations, experiments, and optimization. In Section 3, we compared the results between simulations and experiments and validated the FE models; we performed crushing analysis for the AVTHTs under axial and oblique loadings, and discussed the effects of thickness configuration, loading angles, and patterns. Finally, a multi-objective optimization design (MOD) was performed to minimize the maximal crushing force (F\({}_{\text{maxw}}\)) and maximize the specific energy absorption (SEA\({}_{\text{w}}\)) under multiple loadings. The conclusions are summarized in Section 4.