Multi-cell Thin-walled Structures Research Articles

Crashworthiness and gradient optimization of multi-cell thin-walled structures inspired by leaf venation in royal water lily

As a key component of lightweight impact-protection devices, thin-walled structures with marvelous specific energy absorption (SEA) have attracted wide attention. Inspired by leaf venation in royal water lily, a hybrid multi-cell thin-walled structure with fractal and hierarchy architectures is proposed. Its crashworthiness is compared with traditional cylinder by combining finite element simulation and experiment, and corresponding mechanism is revealed. The results show that due to more folds and smaller folded wavelength, the venation-like structure exhibits better crashworthiness than the cylinder. Increasing the initial bifurcation number and hierarchy level of venation-like structure will introduce massive corner constraints, especially the hierarchy level, which benefits folding deformation and improving effectively crashworthiness. Further, a fully hybrid venation-like structure is designed by introducing gradient architecture. With the increase of length-gradient or thickness-gradient, the SEA first linearly increases and then slightly decreases. Under the optimal length-gradient, majority of area exhibits high internal energy. By taking the gradient length and thickness simultaneously, a kind of hybrid deformation mode with quasi-uniform small folding and overall large folding appears, where multiple small folds interacts strongly, achieving good load-bearing capacity. The optimal SEA of venation-like structure is 81.5% higher than that of the cylinder.

Effects of undulating printing paths on axial compressive behaviors of 3D-printed continuous fiber-reinforced multi-cell thin-walled structure

Thin-walled structures are widely used in passive safety systems of the vehicles because of their excellent lightweight and stable progressive deformation behavior. Recently, continuous fiber 3D printing technique has been successfully applied in the manufacturing of thin-walled structures, providing a promising path to meet increasing requirements for energy absorbers as vehicle speed increases. This paper proposed a range of novel undulating printing paths to fabricate two kinds of continuous Kevlar fiber reinforced multi-cell thin-walled structures (CFMSs) with different cross-section shapes, named MT1 and MT2, respectively. For each type of CFMS, three different printing paths (moving back and forth between two layers) were designed to manufacture CFMS with the wall thickness comprised of only a single deposited line. The axial compressive tests were conducted to investigate the compressive response of CFMSs. It was found that undulating printing paths affect both the mechanical behavior and collapse mode of CFMSs. During the compression process, MT1 and MT2 printed with path 3 showed progressively folding deformation modes (differed from the progressive crushing mode of composite laminated thin-walled structures). Thus, compared to MT2 printed with path 1 and path 2, which exhibit global buckling, MT1 and MT2 printed with path 3 exhibited more stable energy absorption performance. Besides, although the local failure mode in different CFMSs caused by the same path was similar, the same printing path had different influences on the axial compressive properties of different CFMSs.

Experimental and numerical investigation of crashworthiness of multicell metal/CFRP tubes

Metal/CFRP hybrid thin-walled structures combine low-density and high-strength carbon fibre reinforced plastics (CFRP) with low-cost and stable failure form aluminium, which have drawn increasing attention in the transportation industry. A theoretical model was developed to predict the average crushing force of a hybrid multicell under axial compression. The model captures the main energy dissipation mechanism of the hybrid tube under axial compression, and the average crushing force is determined by a quasi-static compression test. The obtained results show that the average crushing force predicted by the theoretical model is in good agreement with the experimental results. However, the geometry size and configuration of multicell thin-walled structures have important effects on crashworthiness. Therefore, it is necessary to study the parametrization of hybrid multicell tubes. First, the simulation model of the multicell tube is established, and quasi-static experiments verify its accuracy. Second, finite element analysis was used to compare the effects of the geometric size of the cell and the multicell structure of different configurations on the energy absorption characteristics. It is clear that with the increase in the thickness of the large aluminium tube, the specific energy absorption (SEA) and crush force efficiency (CFE) both show an upward trend. In addition, with the increase in the ply number of the CFRP tubes, the SEA also shows a minor monotonic increasing trend. Finally, various hybrid tubes with different configurations are designed, and the C-C4-AL tube (the aluminium tube surrounded by four small-size CFRP tubes being placed inside a CFRP tube.) configuration has the most significant energy absorption (EA) and peak crushing force (PCF).

A comparative study on dynamic compression response of multi-cell thin-walled structures with filling foams and connecting ribs

In order to comparatively study effect of foam filling and connecting ribs on dynamic response of multi-cell thin-walled structure (MTS), high velocity (30–70 m/s) mass block impact tests were performed on empty MTS, polyurethane foam (PUR) filled MTS (FMTS) and 2nd order MTS (MTS-2nd) with connecting ribs between sub-cells. The dynamic enhancement mechanism of energy absorption of three kinds of thin-walled structures was discussed based on experimental and numerical results. The results indicate that the dynamic enhancement coefficient (DEC) of the mean crushing force (MCF) is 1.07–1.23 and 1.08–1.33 for empty MTS and FMTS, respectively. The dynamic enhancement of total energy absorption (EA) is 11.4–26.32% for MTS, 13.83–32.52% for FMTS and 4.3–9.68% for MTS-2nd, compared to the quasi-static compression. The multi-cellularization tends to degenerate the crushing force sensitivity of MTS to the loading rate, while the foam filling increases the sensitivity. The inertia effect is the main reason for the dynamic enhancement of crushing force of thin-walled structures. The coupling effect of FMTS is related to the dimensions of sub-cells, the impact velocity and the foam strength. The folding pattern and deformation stability of MTS can be improved by filling foams and increasing impact velocity. The multi-cellularization by using connecting ribs is still the most effective method to improve the specific energy absorption of thin-walled structures, although it causes a size effect and reduces the robustness of deformation modes.

Performance of hollow and aluminum foam-filled multi-cell thin-walled aluminum alloy tubes (6063-T5) under axial impact

This study investigates a new form of multi-cell thin-walled structures under axial impact. Eighteen multi-cell thin-walled aluminum alloy tubes were tested under drop hammer impacts. Nine of the specimens were hollow tubes and the other nine specimens were aluminum foam-filled multi-cell thin-walled aluminum alloy tubes. This paper presents the entire duration of the impact including the time history curves of forces and vertical displacement. The influence of impact velocity, wall thickness and aluminum foam on the impact resistance of multi-cell thin-walled aluminum alloy tubes were discussed. Then, the energy dissipation performance of multi-cell thin-walled structures tested in this study and single-cell thin-walled structures tested in prior research is compared. The results show that the foam infill improves the energy dissipation capacity of the multi-cell thin-walled aluminum alloy tubes, but the specific energy absorption (the energy absorbed per unit mass) decreases. Although the specific energy absorption is reduced, using foam infill is still an effective method to improve energy dissipation capacity without increasing the size of the member. Compared with the single-cell thin-walled aluminum alloy tubes, the specific energy absorption of the multi-cell thin-walled aluminum alloy tubes is higher by 7.35%–55.51%, which means that multi-cell thin-walled columns are a better energy absorption component compared with single-cell columns.

3G-optimization of multi-cell crash box cross-section of autobody based on crashworthiness

The cross-section, thickness, and material of the autobody structure determine the crashworthiness and lightweight level. Different from the variables in traditional autobody design that are considered separately, the basic theory of 3G-optimization is to simultaneously consider geometric shape (Geometry), the thickness of structure (Gauge), and material grade (Grade) in structural optimization design, which is conducive to maximizing the lightweight potential of the structure. This paper presents a cross-section optimization method for multi-cell thin-walled structures based on 3G-optimization, which is used in the structural design of crash box. Based on full width frontal collision condition, the cross-section shape, thickness, and material variables of the multi-cell crash box are optimized simultaneously. Multiple sets of optimization schemes show obvious weight reduction effect while ensuring safety. Besides, the sub-system decoupling method and hybrid cellular automaton (HCA) method are applied to 3G-optimization process, which is beneficial to improve the calculation efficiency and provide a theoretical basis for the definition of the initial design space for 3G-optimization.

Numerical study on energy absorption characteristics of bio-mimetic multi-cell thin-walled structures with different hierarchy

Horsetail plant is the most primitive terrestrial plant bred by spores. After hundreds of millions of years of evolution, the internal structure of horsetail plant stem is composed of multiple cavity which brings excellent impact resistance. The investigation of the internal thin-walled structure of horsetail plant can be used to improve the energy absorption property of the existing thin-walled structure, and has important significance and application potential for the design of anti-collision structure. In this study, four kinds of bio-mimetic thin-walled models with different shapes of cross-sections were proposed and established based on the horsetail plants, and the energy absorption values of the structures were calculated and analyzed by numerical method. The squ-3rd structure with the highest specific energy absorption value of 49.121 kJ/kg was obtained. Then the specific energy absorption value and crushing force efficiency of the structure under different parameters, including wall thickness, side length height ratio, and impact angle were calculated and discussed. Based on the numerical simulation results, we found that for the third-order form of structure with square cross-section, the structure with the wall thickness between 1 and 1.25 mm showed better crushing resistance. And, the energy absorption characteristics of the structure were found to have better performance when the side length height ratio is 1:1.

Crushing behaviors of novel multi-cell square tubes and its hierarchical multi-cell structures under axial loading

This study proposed a novel multi-cell square tube and its hierarchical structures to improve the energy absorption efficiency of multi-cell thin-walled structures. The finite element model is built and validated with experiment result. The crushing behaviors of novel multi-cell square tubes and its hierarchical structures are compared with the traditional multi-cell square tubes under the same weight. Furthermore, the theoretical model is derived and validated to predict the energy absorption behaviors of the designed multi-cell tubes. The results indicate that the novel multi-cell square tubes and its hierarchical structures exhibit superior crashworthiness performance than corresponding traditional multi-cell square tubes.

Optimization for multi-cell thin-walled tubes under quasi-static three-point bending

Approaches such as changing the cell number, changing the rib direction, and adding internal structure are utilized to acquire a multi-cell thin-walled structure, and these approaches have meaningful effects on the crashworthiness performance of multi-cell thin-walled tubes. In this study, a comprehensive review is done by using and comparing these approaches together under quasi-static three-point bending conditions. A different crashworthiness indicator is better for each of the produced multi-cell thin-walled structures. The overall best tubes are determined by the complex proportion assessment (COPRAS), a multi-criteria decision-making technique. The weights used in the COPRAS technique are calculated by the entropy method. Thus, two different tubes are chosen as the best ones. Then, multi-objective optimization is performed on these tubes with the multi-objective genetic algorithm (MOGA). The surrogate models of PCF and SEA, which are defined as the objectives in multi-objective optimization studies, are obtained by the (radial basis functions) RBF. Multi-objective optimized multi-cell thin-walled W1L1 and W1L1S1 tubes achieved the same SEA values as the W0L0 square tube at 13.1% and 15.4% lower PCF values, respectively.

Simulation and Optimization Design for Energy Absorption Characteristics of Multi-cell Thin-walled Structures

Abstract Based on muti-cell thin-walled structures, construct variety of circular, octagonal, hexagonal multi-cell thin-walled tubes, energy absorption characteristics were studied. Used ANSYS to 12 different cross-sectional shapes of thin-walled tubes axial compression characteristics to nonlinear numerical simulation. The best cross-sectional shape was determined by comparing the energy absorption of different cross-sectional shapes. The thickness of inner and outer walls of thin-walled tubes and stiffened ribs were taken as design variables. Taking the strain energy density and peak force as targets, a response surface model was fitted and multi-objective optimization was performed. The optimization results show that strain energy density and compression efficiency are improved under premise of small peak force.

Study on Impact Resistance of Composite Reinforced Thin-Walled Tubes

In order to further improve the impact resistance of composite multi-cell thin-walled structures under axial loading, a new type of composite multi-cell sandwich tubular structure is proposed. Based on the MAT54 material model and the Chang-Chang failure criterion, a composite laminated shell modeling method was developed to simulate the failure behavior of the material under axial compression load and verified by quasi-static compression tests. The effectiveness of the simulation model is verified by comparing the parameters of peak load and specific energy absorption. The impact-resistance sensitivity of cell number and sandwich structure in composite multicellular structure was studied by this model. The results show that number of cells have a significant effect on the specific energy absorption of the composite multi-cell structure.

Energy absorption parameters of multi-cell thin-walled structure with various thicknesses under lateral loading

Energy absorbers are widely used in many engineering structures, especially mobile ones to prevent or alleviate the impact damages. Thin-walled structures are employed as an important category of energy-absorbing systems. In this study, the effect of thickness variations in different parts of a particular structure is investigated on the energy absorption behavior. The geometry of the considered structure is a four-cell squared-section of aluminum alloy 6061 that is subjected to the lateral loading and the thicknesses of the sides are defined as the input variables. For the systematic investigation of the input variables effect, design of experiments procedure is utilized. The simulations are performed by the LS-Dyna software using the finite element method based on the output data of design of experiments. Moreover, in order to ensure the accuracy and validity of the simulations, an experimental investigation has been conducted for one of the scenarios and the results are confirmed. According to the results of numerical investigations, it was found that all the input variables of the problem are effective with distinct and considerable trend in energy absorption of the structures. These trends are generally nonlinear and relative extremum can be observed in some of them. Finally, by analyzing the energy absorption process of the structures by response surface methodology, an optimal sample is selected and simulated; moreover, the identical sample is also subjected to experimental tests. The results showed approximately 272% enhancement in the specific energy absorption of the optimal sample in design of experiments table compared to the weakest one.

Study of multi-cell thin-walled tube with various configuration under lateral loading

Thin-walled structure is one of the common structures that is widely used as an energy absorber due to inexpensive, high availability and lightweight. Moreover, the multi-cell structure is known as a useful method to elevate the effectiveness of thin-walled structures in crashworthiness. Energy absorber performance of multi-cell thin-walled tube structure is known to be greater than the single thin-walled tube. This is due to the limitation of plastic hinge zones of single tube during lateral loading condition. This paper presents the effect of multi-cell configuration on energy absorption responses under lateral loading condition. Experiment and numerical approach were used in this research. The validation of finite element model (FEM) was conducted by comparing the load-displacement responses and deformation mode of a quasi-static compression test. Multi-cell configuration study was performed to identify the energy absorption performance of multi-cell thin-walled tube with different arrangements. The results reveal that an increasing number of cells will increase the energy absorption capacity of multi-cell structure. The additional number of tube cells contribute to the increases of the contact joint between each tube consequently this generate additional permanent plastic-hinges.

Theoretical estimation of axial crushing behavior of multicell hollow sections

This research, which is a continuation of the previously published paper, develops the idea for estimating the behavior of axially crushed multicell thin walled structures. This approach employs new crushing mechanisms or simply crushing modes for different configurations of multiweb corner elements based on simulation, geometric, and kinematic observations. Furthermore, a new model is introduced named as “Induced Curvature Model” or ICM which includes the curvature of the sheet during progressive crumpling and also the hardening effect of the material under plastic deformation, instead of simple assumptions of perfect plastic material and hinge lines for the folds in case of previously offered plastic hinge model (PHM). Both ICM and PHM are employed to capture crushing properties based on the offered crushing modes and the results suggested by them are compared to each other. Different aspects of crushing behavior were studied and discussed. To show the validity of the proposed models, FE simulation studies were also conducted. Results show an average error around 7% which indicates a good agreement between theoretical and simulation findings and the applicability of the proposed novel model to a wide range of thin walled structures.

Multi-cell energy-absorbing structures with hollow columns inspired by the beetle elytra

In this work, we propose a new type of thin-walled energy-absorbed structure with hollow columns that possesses a design inspired by the beetle elytra. The failure mode of the bionic thin-walled structures is firstly discussed by developing a theoretical model. The energy absorption properties of these bio-inspired multi-cell thin-walled structures have been then investigated using nonlinear finite element simulations. The values of the specific energy absorption and the crushing force effectiveness have been evaluated for different structures with parametrized column nested configurations. Dynamic impact simulations of multi-cell tubes with different columns nested modes, wall thickness and impact angles have been performed, and the results discussed.

Multi-objective optimization of crashworthiness of vehicle front longitudinal beam

Front longitudinal beam (FLB) is an important structure for the analysis of force transmission and energy absorption path in different crashing scenarios. In the present paper, the finite element (FE) model of a full-scale vehicle yun-100 Zotye is employed to explore the energy absorption of FLB, and aiming at its poor energy absorption problem, circular beam was used as the original topology optimization space of FLB. The advantages of both static and dynamic topology optimization methods are fully considered, and a variable density method is combined with a hybrid cellular automaton (HCA) method. The substructure dissipated energy and force for frontal crash in a full-scale vehicle are obtained at a speed of 13.8 m/s. The maximum stiffness in axial is obtained through the static topology optimization method and the maximum energy-absorbing structure of FLB which is satisfied with axial strength obtained through the dynamic topology optimization method. According to the results of topology optimization, a multi-cell thin-walled structure is interpreted as the novel FLB. A parametric study on geometric parameters is also performed to explore their effects on crashing characteristics of novel FLB, and it is found that they significantly influenced the crashworthiness of multi-cell thin-walled structure (especially the absorption of energy). Furthermore, in order to maximize the characteristics of novel FLB, a multi-objective optimization process is carried out using non-dominated sorting genetic algorithm (NSGA-II). The optimized FLB after multi-objective optimization is applied to Zotye of 100% vehicle frontal crash. The results showed that the peak value of acceleration decreased by 10.3% and the mass of the optimized FLB reduced to 0.59 kg. It indicated that the optimized FLB manifested excellent crashworthiness and better protective characteristics.

Energy absorption mechanism of axially-varying thickness (AVT) multicell thin-walled structures under out-of-plane loading

Multicell columns have becoming increasingly attractive in crashworthiness applications due to their high efficiency of material utilization. Meanwhile, an urgent need exists to develop new structures to achieve the aim of light weight without sacrificing crashworthiness. A novel multicell column with axially-varying thickness (AVT) is proposed in this study. Quasi-static crushing tests were firstly performed experimentally to investigate crushing behaviors. Subsequently, corresponding numerical simulation models were built, validated, and used to conduct a parametric study. Finally, analytical equations for the mean crushing force for AVT multicell columns were derived and used to assess the crashworthiness of multicell columns according to SFE (super folding element) method. The numerical results agreed well with experimental results in terms of deformation mode and crushing forces, and the theoretical predictions were validated by the experimental results. It was concluded that the thickness gradient of AVT multicell columns could effectively reduce the initial peak crushing force while maintaining energy absorption capacity over a long crushing distance. From this perspective, the AVT multicell columns demonstrated competitive advantages over uniform columns as energy absorbers. Moreover, the analytical prediction could be a powerful tool for designing crashworthy structures.

The origami inspired optimization design to improve the crashworthiness of a multi-cell thin-walled structure for high speed train

The initial peak crushing force usually causes catastrophic harm to the passengers once vehicle collision accidents happen. In this study, an origami design is introduced and optimized to improve the initial peak crushing force (IPCF) of a thin-walled energy absorption structure. First, by analyzing the basic idea of origami structure, this paper decides twist angle (φ), height (h) and thickness (t) as the control variables. Then, the crashing characteristics of the thin-walled structure are under study and the FE model is validated by an impact test. Further, parametric analysis on the relationships between design variables and target responses (energy absorption and IPCF) is studied. It is found that the twist angle has a negative influence of IPCF and EA, while the t has a positive influence on the impact responses. Particularly, the increase of h cause the increase of IPCF but a decrease of EA. In further, to minimize the IPCF but do not affect the EA, optimization technology with NSGA-II algorithm is employed. The optimization results (i.e., φ = 3.24°, h = 30 mm, t = 4 mm, IPCF = 934.28 kN, EA = 269.90 kJ) manifest that IPCF reduces by 29.36% without reducing the ability of energy absorption. For the point of train collision safety, the proposed origami inspired structure is introduced successfully and the optimal structure is of great advantages in improving the IPCF for the energy absorption structure.

Collision performance and multi-objective robust optimization of a combined multi-cell thin-walled structure for high speed train

Based on the Simplified Super Folding Element (SSFE) theory, the theoretical prediction of average crushing force (Favg) for multi-cell thin-walled structures is inferred and a combined five-cell thin-walled structure used in high speed train is proposed and investigated in this paper. The finite element model of the proposed structure and the theoretical prediction are validated by a full scaled impact experiment. Then, parametric studies are performed to evaluate the effects of design variables, including the thickness (t) and the side length (a) of the orthohexagonal cell, on collision responses based on the validated FE model and theoretical prediction. It is found that both specific energy absorption (SEA) and the maximum initial force (Fmax) are obviously affected by the design parameters. Particularly, the effect of parameter t on crushing performance is greater than that of parameter a. In further, to minimize the Fmax and maximum SEA under the constraint of Favg, a multi-objective robust optimization methodology is adopted. The Optimal Latin Hypercube Design (OLHD) and orthogonal design are combined to perform Design of Experiment (DoE) and dual response surface models (DRSM) are constructed for the optimization. The optimal results of deterministic optimization indicate that the Fmax decreases by 11.07% compared with the original design while the robust optimization optimal result of Fmax decreases by 10.01%. However, the robust optimization optimal design is more acceptable considering the robustness, which means the robust optimization is more attractive than deterministic optimization in practical engineering application.

Parametric design of multi-cell thin-walled structures for improved crashworthiness with stable progressive buckling mode

Thin-walled single and multi-cell structures are an ongoing topic of interest in the field of crashworthiness, due to their wide range of applications in automotive and aerospace industry as lightweight energy-absorbing structures in crash environments. This work presents a new five-cell cross-section that merges high performance multi-cell and twelve-edge cross-sections from previous research, and compares its performance to four- and nine-cell square cross-sections. Super Folding Element (SFE) theory and Finite Element Analysis (FEA) in LS-DYNA are used to analyze cross-sections and found to have good agreement. The LS-DYNA environment is validated with physical testing. The geometry of the cross-sections is varied in order to find maximal values of the performance parameters specific energy absorption (SEA) and crush force efficiency (CFE) under stable progressive buckling mode and constraints for manufacturability. The nine- and five-cell cross-sections ultimately out-perform the four-cell cross-section, with the nine-cell having the highest SEA and CFE, though the five-cell design has a significantly lower (47%) mean crush force (Pm) for only an 11% and 14% loss in SEA and CFE respectively. As a final refinement, the geometry was varied across these two high-performing cross-sections to create equivalent mean crush forces to the four-cell cross-section, which showed the five-cell cross-section to have an improved SEA and better mass efficiency over the nine-cell under a mean crush force constraint.