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Thin-walled structures are inevitably subjected to oblique loads which could result in poor crashworthiness. To improve comprehensive crashworthiness, multilayered hexagonal tubes with 2 to 9 layers denoted as L2 to L9 were proposed, and their crash performances were investigated under axial and oblique quasi-static loads. Based on four crashworthiness criteria, complex proportional assessment (COPRAS) and TOPSIS methods were adopted to select out two optimal structures, L2 and L3. Further multiobjective optimizations of L2 were conducted. When selecting the best configuration using the COPRAS method, structures with lower peak crushing force (PCF), higher PCF, specific energy absorption (SEA) and crushing force efficiency (CFE) are preferred. The results are opposite using the TOPSIS method. [ABSTRACT FROM AUTHOR]

Based on the hypothesis that multi-corner and multi-cell structures can effectively improve energy absorption behavior, this paper designed a multi-cell circumferentially corrugated tube (MCCT) for energy absorption. The MCCT was designed as a variable thickness form to study the influence of the materials distribution on the cross section on energy absorption. The energy absorption performance of the MCCT was investigated under impact condition with finite element simulation validated by a drop hammer test. Support vector machine, a machine learning technique, was used to predict the energy absorption performance and was further used for optimization of the MCCT. The results show that under the same mass, the MCCT with variable decreasing wall thickness (corners thicker than other regions) shows 4.81%, 30.67% and 37.70% improvement, respectively, in PCF, SEA and CFE, compared to the MCCT with variable increasing wall thickness (corners thinner than other regions). Moreover, the optimization results show that most samples in Pareto front lie in the region of tc > tm. These results all indicate that the MCCT with variable decreasing wall thickness performs better than with increasing wall thickness with regards energy absorption. In conclusion, arranging more materials in the corner element area can effectively improve the energy absorption characteristics of the thin-walled tube. This paper highlights the importance of designing thin-walled tubes as multi-corner and variable thickness configurations for energy absorption. [ABSTRACT FROM AUTHOR]

This article optimizes a multicellular thin-walled tube with N-equilateral triangles (MTTN), which was inspired from the microstructure of the cross-section of bamboo. The crashworthiness of MTTN under axial impact was analyzed, and the sensitivity analysis was conducted for the geometric parameters of MTT24, which exhibited the best crashing performance among MTTNs with N ≤ 30. It was found that the order in radial direction has a weak influence on the crashworthiness of MTT24, while the cell-wall thickness and the inner-tube diameter could significantly affect the crashworthiness of MTT24. Then, a multi-objective optimization was carried out for the MTT24 to further improve its crushing performance. The wall thickness and inner diameter of the thin-walled tube were selected as design variables, while the minimum peak crushing force (PCF) and the maximum specific energy absorption (SEA) were set as objectives. The obtained Pareto front enables the thin-walled tube to achieve the best possible crush resistance under the conditions of maximum SEA and minimum PCF. With a constraint of PCF ≤ 200 kN, the SEA and MCF of MTT24 were improved by 11.40% and 68.20%, respectively, compared with the benchmark. [ABSTRACT FROM AUTHOR]

An energy absorbing tube combining multi-corner and multi-cell configurations was designed in this study. Machine learning was adopted to predict and optimize the crashworthiness of the proposed tube because it can handle both numerical and categorical responses. The results showed the increases in the considered geometric parameters caused the increases in the specific energy absorption and peak crushing force, while also made the unstable deformation mode prone to appear. Besides, with the help of machine learning, the accurate optimization results were obtained, in which the unstable deformation was removed. This work highlights the prospect of machine learning in structural optimizations. [ABSTRACT FROM AUTHOR]

Inspired by the micro-structure of horse-hoof-wall, we proposed a series of thin-walled corrugated tubes and investigated their crushing behaviors under multiple loading angles. After the complex proportion assessment, the tube with circle vertex was selected as the optimal structure because its relative significance of the alternatives is 0.1306, up to 10.26% higher than that of other tubes at most. The best geometric parameters t = 0.54 mm, D 2 = 3.10 mm, A = 1.10 mm, and N = 8 were obtained by multi-objective optimization. In conclusion, this study provides some design inspirations for improving the crashworthiness of structures. [ABSTRACT FROM AUTHOR]

Thin-walled tubes are widely used as energy absorption devices because of their excellent crashworthiness. In this paper, a novel tubular configuration with a double-layer sinusoidal corrugated section, namely, a double-layer sinusoidal tube (D-LSCT), is proposed to improve the energy absorption capacities. Quasi-static compression experiments and finite element simulations were used to analyse the axial crushing behaviour and energy absorption performance of the D-LSCTs. The results revealed that the geometric parameters had a significant effect on the crashworthiness of the D-LSCTs and that the D-LSCTs had four deformation modes: ordered progression extensional mode (OPEM), ordered progression inextensional mode (OPIM), inextensional mode (IM) and mushroom mode (MM). OPEM and OPIM were more ideal modes, while the IM and MM were unideal modes. To further improve the deformation stability, D-LSCTs were transformed into a three-layer structure by superimposing a regular polygon tube. Experiments and simulations showed that the improved structural design can indeed stabilise deformation and improve the crashworthiness performance. [ABSTRACT FROM AUTHOR]

• A tapered-straight shrink (STS) tube is proposed for energy absorption. • A theoretical model is developed for the STS tube to predict its plateau force. • The deformation modes of the tapered-straight shrink tube are classified and the effects of geometric parameters on crashworthiness are discussed. This paper proposes a new straight-tapered shrink (STS) circular tube, which is planned to be applied on railway coupler for energy absorbing and overload protection. Quasi-static experiment and finite element (FE) simulation were adopted to investigate the crashworthiness performance of the STS tube. In the FE analysis we found that the compressive material properties were more suitable for accurately modeling the STS tube. The results showed that the STS tube can develop two deformation modes, i.e., shrink mode (S-mode) and buckling mode (B-mode), and the B-mode cannot meet the application requirement. Moreover, the distribution of deformation modes under different geometric parameters, namely, wall thickness (t), slope angle (α) and straight zone length (L 1), were obtained. It was found that the B-mode mainly occurs when t, α and L 1 are all large. The force-displacement characteristics showed that a plateau force occurred in some STS tubes. A theoretical model for predicting the plateau force was then proposed. Finally, the effects of geometric parameters on the peak crush force (F max) and specific energy absorption (SEA) were performed. It was found that the increases in the three parameters all result the increases in SEA and F max , and α has the most significant effect on the crashworthiness performance of the STS tube. Image, graphical abstract [ABSTRACT FROM AUTHOR]

Abstract This paper proposes a new circumferentially corrugated square tube (CCST) with a cosine profile. The cross section of the CCST is controlled by a cosine expression with parameters that include the number (N) of cosine wave crests, the amplitude (A) and the nominal side length (2 L 0). Finite element (FE) models validated by experimental results were constructed in Ls_dyna to analyse the crashworthiness performance of the CCSTs. The numerical results show that the collapse modes of CCSTs are classified into five types, i.e., non-ordered progressive mode (NPM), ordered progressive mode (OPM), inversion mode (IM), global buckling mode (GBM) and extensional mode (EM). After analysing the collapse characteristics, force-displacement characteristics and crashworthiness indexes, we found that the OPM has better crashworthiness performance than the other modes. Moreover, a more comprehensive parametric study was conducted to understand the effects of the geometric parameters N , A and wall thickness (t) on the crashworthiness performance of CCSTs. The results show that the collapse modes of CCSTs are fairly sensitive to the cross-sectional configuration and wall thickness. Increases in N , A and t all cause increases in the initial peak crushing force (IPCF), and the wall thickness t has the most significant effect on IPCF. However, the effects of the three geometric parameters on specific energy absorption (SEA) are much more complicated and are largely dependent on whether the collapse modes change or not with increases in the three parameters. The numerical results also show that the SEA of CCSTs is improved by 51.62% compared with that of a square tube (ST) when they have the same mass (55.3 g) and by 69.24% when they have the same wall thickness (t = 1.25 mm). These results reveal that CCSTs with OPM have good energy absorption ability. Highlights • A corrugated square tube (CCST) with a cosine profile is designed. • The collapse modes of CCSTs are classified with numerical method. • The effects of geometry parameters of CCST on crashworthiness performance are discussed. [ABSTRACT FROM AUTHOR]

• A structural design method combing multi-cell and multi-corrugation was proposed to improve crashworthiness of tubes. • Three types of corrugations reinforced multi-cell tubes were tested. • The integrated entropy TOPSIS method was used to select the best configuration among the proposed tubes and the optimization results. Improving the crashworthiness performance of thin-walled tubes is of vital significance for vehicle safety because thin-walled tubes are the most common and economical energy absorption structures. To this end, a new structural design method combining multicorrugation and multicell configurations was proposed in this study. Triangular, circular and square corrugation reinforced multicell tubes (CRMTs) were designed with this method. Finite element simulation validated by quasi-static compression experiments was adopted to investigate the crashworthiness performances of the CRMTs. The integrated entropy TOPSIS method was used to select the best of the proposed tubes. The results showed that the circular CRMT with a 3-order cell number (C-C-3) performed the best of the proposed CRMTs. Then, multiobjective optimization incorporating the integrated entropy TOPSIS method was conducted to search for the optimum geometric parameters of C-C-3. After optimization, the SEA increased by 2.39% and the CFE increased by 7.69%. In conclusion, the design combining the multicorrugation and multicell configurations can dramatically improve the crashworthiness of thin-walled tubes; therefore, the proposed structures can be used for energy absorption in the automobile and train industries. Image, graphical abstract [ABSTRACT FROM AUTHOR]

Multi-cell tubes are widely used as energy-absorption components in transportation field due to its high energy absorption capacity and good weight efficiency. However, with the increase of vehicle speed, people have high requirements for safety, and therefore, the crashworthiness performance of multi-cell tubes should be further improved. To this end, we proposed a new type of multi-cell circumferentially corrugated square tubes (CCSTs) by implementing multi-corrugation on the cross sections of the traditional multi-cell square tubes (STs). Experimental, numerical and theoretical methods were adopted to investigate the crushing mechanics of the multi-cell CCSTs. The results showed that the crashworthiness performance of the multi-cell CCSTs was significantly superior to that of the multi-cell STs. In addition, parametric study was performed to reveal the effects of geometric parameters on the crashworthiness characteristics. In conclusion, this work is of positive significance for improving the level of crashworthiness of thin-walled tubes, and this structural design method can also be used for other traditional structures. • Multi-cell and multi-corrugation configurations were combined to enhance the crashworthiness of thin-walled tube. • A theoretical model was proposed to predict the mean crushing force of the corrugations reinforced multi-cell square tubes. • The crashworthiness performance of the corrugations reinforced multi-cell square tubes was significantly superior to that of traditional multi-cell square tubs. [ABSTRACT FROM AUTHOR]

• New bio-inspired multi-cell corrugated tubes (MCTs) were proposed. • The crashworthiness performance of the MCTs were investigated. • The deformation modes of the MCTs were classified into four modes. • The effects of geometry parameters of MCTs on crashworthiness performance are discussed. • Choosing the right geometrical parameters, the MCTs can reduce IPCF without sacrificing SEA when corrugations are adopted. This paper proposes a bio-inspired multi-cell corrugated tube for use in energy absorption. The proposed structure consists of two parts: an inner rib and a corrugated tube into which the inner rib is inserted. The structure of the corrugated tube is specified using a cosine expression based on two parameters, that is, the number of cosine wave crests and their amplitude. Two inner ribs with different sections (X-shaped and Y-shaped) were designed and the crashworthiness of the resulting tubes was analyzed. The crashworthiness was determined using the finite-element program LS-DYNA. The numerical results show that the modes of collapse of the multi-cell corrugated tubes can be classified into four types: unstable, diamond, ring, and mixed modes. Each mode is strongly affected by the number of cosine wave crests and their amplitude. By analyzing the force–displacement performance and crashworthiness indicators, it was found that tubes with appropriate number of wave crests and amplitudes, and inner rib shape experience lower initial peak forces and increase energy absorption and specific energy absorption (compared with a traditional straight tube with the same inner rib). The undulation in the load-carrying capacity is also decreased. Thus, the multi-cell corrugated tubes have good crashworthiness. [ABSTRACT FROM AUTHOR]

• Multi-cell and multi-corner configurations were combined to enhance the crashworthiness of thin-walled tube. • The crashworthiness under multiple loading angles was analyzed. • The complex proportional assessment (COPRAS) method was used to select the optimal structures. • The optimizations with two different ways were conducted to find the optimal parametric configurations. Multi-cell and multi-corner configurations are the most common methods to improve the crashworthiness performance of thin-walled tubes. However, the crashworthiness of a thin-walled tube combining these two configurations has not yet been evaluated. This paper proposed a series of multi-cell circumferentially corrugated square tubes (CCSTs) in which multi-corner configurations were achieved by introducing cosine and triangular corrugations. The crashworthiness of these multi-cell CCSTs were investigated under multiple loading angles. The complex proportional assessment (COPRAS) method was used to select the optimal structures. The results showed that the cosine and triangular multi-cell CCSTs with crisscross ribs, namely, C1 and T1 in this paper, exhibited the best performance. Then, two different multi-objective optimization methods were used to determine the optimal geometric parameters of C1 and T1. The results showed that one optimization method mainly balanced the crashworthiness performance at different loading angles but did not improve the performance, whereas the other optimization method significantly improved the crashworthiness of the tubes. Image, graphical abstract [ABSTRACT FROM AUTHOR]

This paper proposes N-sided polygonal tubes with hierarchical triangular cells (PHTNs) for use as energy-absorbing devices. Different cross sections of the PHTNs are obtained by changing the number of sides and cells of the sandwich wall. Quasi-static compression experiments and finite element (FE) simulations are used to analyse the axial crushing behaviour and energy absorption performance of the PHTNs. The results show that the PHTNs has two deformation modes: when N ≤ 24, the deformation mode is progressive folding, whereas when N > 24, the deformation mode is sandwich folding. The 24-sided PHTN (PHT24) exhibits the best energy absorption performance, and the specific energy absorption (SEA) of PHT24 is 110.37% greater than the minimum SEA , which is exhibit by PHT06. The results also reveal that the energy absorption is improved mainly by shortening the wavelength or increasing the plastic bending moment of the sandwich wall. Finally, theoretical models are established for predicting the mean crushing force in the PHTNs under both deformation modes. The predictions from these models are in good agreement with the FE simulation results, thereby indicating that the predictions are highly accurate. • Novel N-sided polygonal tubes with hierarchical triangular cells (PHTNs) were proposed for energy absorption. • The influences of the novel hierarchical structure on crushing behaviour and energy absorption of the PHTNs were studied. • Theoretical prediction models of mean crushing force for the PHTNs in the different deformation modes were proposed. [ABSTRACT FROM AUTHOR]

• New bio-inspired corrugated tubes with varying vertex configurations (HCTs) were proposed. • The crashworthiness performance of the HCTs were investigated. • The HCTs performed much better than traditional square tube and improved vertex structure tubes. • By applying a complex proportional assessment method, the optimum structure HCT was selected. • The theoretical results showed a good agreement with the experimental and numerical results. Thin-walled metal tubes are the most widely used energy-absorption structures in various industries. Bionics can help engineers to design novel tubular structures to achieve outstanding crashworthiness performance. Inspired by the unique microstructure of a horse-hoof-wall and the concept of vertex-based hierarchy, a novel bio-inspired corrugated tube and its derivative structures with varying vertex configurations were proposed in this paper. Quasi-static compression test and finite element simulation were employed to investigate the mechanical behaviors of these bio-inspired tubes. The results showed that these bio-inspired tubes exhibit good crashworthiness performance, especially in terms of their weight force efficiencies. Moreover, by applying a complex proportional assessment method, the tube with regular octagon vertex configuration was selected as the optimum one among these bio-inspired tubes. A theoretical model was developed to predict the mean crushing force of the proposed tubes. In conclusion, the horse-hoof-wall inspired tubes exhibit a novel perspective on providing superior mechanical properties and pave a way of applications of bio-inspired engineering structures. [ABSTRACT FROM AUTHOR]

Thin-walled tubes are widely used as energy absorption devices in transport vehicles. In this paper, with the goal of improving the energy absorption performance of tubes under quasi-static axial loading, origami tubes with polygonal cross-sections are designed. The geometric characteristics of polygonal origami tubes are controlled by three parameters: the number of sides, the number of modules and the dihedral angle. To investigate the effect of the origami pattern and polygonal structure on the crashworthiness of tubes, a full factorial experiment is adopted, and then parametric analysis is conducted based on eighty-five simulations. The numerical results validate that origami tubes collapsing in the complete diamond mode perform better than conventional tubes. However, this special mode can only be triggered in the crushing process of square and hexagonal origami tubes with smaller dihedral angles. The optimal design leads to a maximum reduction in the initial peak crushing force of 56.96% and a maximum increase in the mean crushing force of 45.49%. The parametric study shows that the initial peak crushing force of tubes with an identical number of modules and edges increases with an increasing dihedral angle, while it decreases with an increasing number of modules when the angle remains the same. Additionally, the influence of geometric parameters on the mean crushing force varies with different collapse modes. Furthermore, a deep insight into the in-extensible deformation mechanism of origami tubes deformed in the complete diamond mode is presented. The theoretical model is subsequently proposed to predict the mean crushing force. • By increasing the number of plastic hinge lines in axial and circumferential directions, origami tubes with polygonal cross-sections are proposed. • The influence laws of the origami pattern and polygonal multicorner structure on the energy-absorbing performance have been investigated. • Theoretical analysis for the crushing process of origami tubes in CDM and theoretical prediction of mean crushing force are carried out. • The analysis result can provide guidance for practical engineering. [ABSTRACT FROM AUTHOR]