Multi-cell Tubes Research Articles

Crashworthiness design for multi-cell circumferentially corrugated thin-walled tubes with sub-sections under multiple loading conditions

Multi-cell, multi-corner and adding edge-junctions structures are widely used approaches to enhance the crash characteristic of the thin-walled structures. In this study, the crashworthiness of twenty-one structures combining these three structures is examined under axial and oblique loading angles. The finite element models under axial loading are validated by experimental data from the literature and theoretical approach. In the theoretical approach, removing the corner elements in the inner structure from the theoretical calculation in multi-cell tubes has increased the accuracy. With the validations performed in axial loadings, it is predicted that the finite element model will be accurate also in oblique loadings. On the other hand, rupture strain has not been used in finite element models, which may cause some errors. Crashworthiness performance has improved as the cell number increases under all loading conditions except the C2 tube under 20-degree oblique loading. Also, the sub-sections added to the inner wall corners of the tubes significantly increase the energy absorption capacity. The complex proportion assessment (COPRAS) method and the technique for order of preference by similarity to ideal solution (TOPSIS) are utilized to get the tube with the best crashworthiness performance. The entropy method is used for weighting to avoid human intervention. The best tube varies depending on the weighting and selection method. Finally, the radial basis function (RBF) approximation approach and four multiobjective optimization methods are used to obtain optimum sizes of the C4O tube. The results of the optimizations show that the optimum structure does not differ depending on the optimization method, and the results are very close to each other.

Energy absorption characteristics of bio-inspired hierarchical multi-cell square tubes under axial crushing

In this study, the dynamic crushing behaviour and energy absorption characteristics of a novel bio-inspired hierarchical multi-cell square (BHMS) tubes were numerically and theoretically investigated. The proposed structures were constructed mimicking the gradient distribution of cell sizes in the biological structures such as bone and bamboo. A series of compression tests were numerically carried out for the BHMS structures with different hierarchical orders and mass of the structures. The results indicated that the specific energy absorption (SEA) of the 3rd order BHMS tube is 178.4% higher than that of the 0th order BHMS tube. Comparing with the conventional square and multi-cell square tube, the maximum increment of the SEA of the BHMS tube reaches up to 173.7% and 128.1%, respectively. Moreover, the undulation of the load-carrying capacity (ULC) used for evaluating the stability of the BHMS tubes under dynamic crushing was also considered. The ULC of the 3rd order BHMS tube reduces up to 88.8% and 85.7% compared to the square and multi-cell tubes. It indicates that the BHMS tube has a larger potential to improve energy absorption than the square tube and conventional multi-cell square tube. Finally, a theoretical study for the mean crushing force (MCF) was developed for the proposed tubes, which was in good agreement with the numerical results. This study provides an effective guide for the design of a multi-cell energy absorber with excellent energy absorption efficiency.

Multiobjective crashworthiness optimization of graphene type multi-cell tubes under various loading conditions

Nature is an important source of inspiration for researchers to create better designs. In this study, graphene type multi-cell tubes is inspired by graphene due to its strong and lightweight mechanical properties. Peak crushing force (PCF), energy absorption (EA) and crushing force efficiency crashworthiness indicators have been taken into consideration under different loading angles, and the complex proportion assessment (COPRAS) which is a multicriteria decision-making method has been used to determine the best model. The best model is found to be GTMT5 (second-order and third-order hollow cylinders in the graphene type multi-cell tube) by the COPRAS selection method. The multiobjective optimization, whose objective is to minimize PCF and maximize EA, is applied on the GTMT5 using the multiobjective particle swarm optimization and non-dominated sorting genetic algorithm II methods, and the techniques are compared. The optimization study is carried out on the radial basis function metamodels. This study shows that circular structures placed in multi-cell tubes have a significant effect on the crashworthiness performance.

Crashworthiness Design of Thin-Walled Tubes Reinforced by Triply Periodic Minimal Surfaces.

This article aims to propose a kind of internally reinforced square tube based on triply periodic minimal surfaces (TPMSs), which can be obtained by computer-assisted techniques and additive manufacturing. To achieve this goal, a finite element simulation model is exploited to simulate the collision situation of reinforced thin-walled tubes. The design of reinforced tubes can be formulated into a multiparameter and multiobjective optimization problem, which can be solved using the well-known non-linear programming by quadratic Lagrangian (NLPQL) optimization method. Three types of TPMS-based tubes and two multicell tubes are compared under the same conditions to show the effectiveness of our method. Through the methods mentioned above, TPMS-reinforced tubes are found to be superior in crashworthiness. This means that the safety performance of the automobiles with lighter weight can be effectively improved. The optimal parameters of three types of TPMS-reinforced tubes under different conditions were obtained, providing the foundations and references for subsequent related studies. In addition, TPMS is first explored in the design of crashworthiness for automobiles in this article. Due to the controllability and implicit functional expression of TPMSs, TPMS-reinforced tubes can be easily controlled and optimized. Meanwhile, it is easy to manufacture them by three-dimensional printing technologies.

Improving Blast Performance of Reinforced Concrete Panels Using Sacrificial Cladding with Hybrid-Multi Cell Tubes

The utilization of sacrificial layers to strengthen civilian structures against terrorist attacks is of great interest to engineering experts in structural retrofitting. The sacrificial cladding structures are designed to be attached to the façade of structures to absorb the impact of the explosion through the facing plate and the core layer progressive plastic deformation. Therefore, blast load striking the non-sacrificial structure could be attenuated. The idea of this study is to construct a sacrificial cladding structure from multicellular hybrid tubes to protect the prominent bearing members of civil engineering structures from blast hazard. The hybrid multi-cell tubes utilized in this study were out of staking composite layers (CFRP) around thin-walled tubes; single, double, and quadruple (AL) thin-walled tubes formed a hybrid single cell tube (H-SCT), a hybrid double cell tube (H-DCT), and a hybrid quadruple cell tube (H-QCT). An unprotected reinforced concrete (RC) panel under the impact of close-range free air blast detonation was selected to highlight the effectiveness of fortifying structural elements with sacrificial cladding layers. To investigate the proposed problem, Eulerian–Lagrangian coupled analyses were conducted using the explicit finite element program (Autodyn/ANSYS). The numerical models’ accuracy was validated with available blast testing data reported in the literature. Numerical simulations showed a decent agreement with the field blast test. The proposed cladding structures with different core topologies were applied to the unprotected RC slabs as an effective technique for blast loading mitigation. Mid-span deflection and damage patterns of the RC panels were used to evaluate the blast behavior of the structures. Cladding structure achieved a desired protection for the RC panel as the mid-span deflection decreased by 62%, 78%, and 87% for H-SCT, H-DCT, and H-QCT cores, respectively, compared to the unprotected panels. Additionally, the influence of the skin plate thickness on the behavior of the cladding structure was investigated.

Experimental and numerical investigation on the crashworthiness optimization of thin-walled aluminum tubes considering damage criteria

This paper aims to investigate the crashworthiness performance of thin-walled tubes under quasi-static conditions both experimentally and numerically. Single-cell and multi-cell tubes made of aluminum were tested under quasi-static compressive loading. A three-dimensional finite element (FE) model accounting for the damage in the constitutive equations was developed. It was validated through experiments based on the force–displacement behavior and the deformation views of the tubes. The sensitivity of the initial peak force, total energy absorption, specific energy absorption, and crush force efficiency to different model parameters such as the tube height and thickness, velocity of the rigid upper plate, and the type of the constitutive equations used were investigated in detail. It was observed that the element type used (shell/solid) in the FE model and the element size in the thickness direction played an important role in simulating the tests accurately. In addition, surrogate-based optimization of the single-cell tubes (T0) and two different types of multi-cell tubes (T4E, T8E) is performed to maximize crush force efficiency (CFE) and specific energy absorption (SEA). It is found that CFE of the optimum T4E design is 8.5% greater than CFE of the optimum T8E design and 30% greater than CFE of the optimum T0 design. It is also found that SEA of the optimum T4E design is 9.8% greater than SEA of the optimum T8E design and 213% greater than SEA of the optimum T0 design.

Crashworthiness analysis and optimization of standard and windowed multi-cell hexagonal tubes

Recently, multi-cell structures have received increased attention for crashworthiness applications due to their superior energy absorption capability. However, such structures were featured with high peak collapsing force (PCL) forming a serious safety concern, and this limited their application for vehicle structures. Accordingly, this paper proposes windowed shaped cuttings as a mechanism to reduce the high PCL of the multi-cell hexagonal tubes and systemically investigates the axial crushing of different windowed multi-cell tubes and also seeks for their optimal crashworthiness design. Three different multi-cell configurations were constructed using wall-to-wall (WTW) and corner-to-corner (CTC) connection webs. Validated finite element models were generated using explicit finite element code, LS-DYNA, and were used to run crush simulations on the studied structures. The crashworthiness responses of the multi-cell standard tubes (STs), i.e., without windows, and multi-cell windowed tubes (WTs) were determined and compared. The WTW connection type was found to be more effective for STs and less favorable for WTs. Design of experiments (DoE), response surface methodology (RSM), and multiple objective particle swarm optimization (MOPSO) tools were employed to find the optimal designs of the different STs and WTs. Furthermore, parametric analysis was conducted to uncover the effects of key geometrical parameters on the main crashworthiness responses of all studied structures. The windowed cuttings were found to be able to slightly reduce the PCL of the multi-cell tubes, but this reduction was associated with a major negative implication on their energy absorption capability. This work provides useful insights on designing effective multi-cell structures suitable for vehicle crashworthiness applications.

Energy absorption analysis of square-circle hybrid section tubes under axial loading

Square-circle hybrid section (SCHS) tubes under axial loading which combine the advantage of square tubes and circular tubes are investigated. Firstly, effective finite element models of SCHS tubes are established to study the crashworthiness characteristics. Through a series of finite element models, the influence of the geometry on the behaviour of crashworthiness is studied, including relative size of square and circular sections in SCHS tubes and the position of connecting plates. The results show that compared with corresponding traditional multi-cell tubes, SCHS tubes improve the performance in energy absorption, with a maximum increase of 40.49%, while reducing peak force and improving crushing load efficiency. Moreover, the deformation of elements constituting the SCHS tube is analysed, and deformation of arc-plate elements could be classified into three typical modes. According to the observed deformation modes, the theoretical model is proposed to predict the mean crushing force of SCHS tubes. The theoretical results show that it is in good agreement with the numerical results.

Energy absorption performance of hybrid cross section tubes under oblique loads

Compared with the excellent energy absorption performance under axial loading, thin-walled tubes are vulnerable to unstable global bending under oblique loading. To improve the energy absorption performance of tubes under oblique loads, a novel designed tube with hybrid cross section is studied in this paper by adding ribs at the bottom end of the tube. Quasi-static compression experiments of square (single-cell) tube, single-double hybrid tube, double-cell tube under three oblique loads were performed to verify the finite element model. Based on the verified finite element model, the energy absorption performance was compared between the single cell tube (SCT), double cell tube (DCT) and single-double hybrid tube (SDHT) under seven oblique loads. Results showed that the SDHT has the best energy absorption performance. The influence of the height, direction and number of the ribs on the energy absorption performance of the hybrid cross section tubes is also discussed in this paper. The hybrid cross-section tubes could get the best energy absorption performance when the direction and height of the ribs were appropriate. And the energy absorption performance could be further improved by increasing the number of the ribs to compose the multi-cell hybrid cross section tube. The results also showed that the multi-cell hybrid cross section tube is more stable than the traditional multi cell tube under oblique loads. This will promote the application of multi-cell tubes in vehicles.

On crashing behaviors of bio-inspired hybrid multi-cell Al/CFRP hierarchical tube under quasi-static loading: An experimental study

Bio-inspired structures have gained more and more concerns attributed to their unique enhancement in energy absorption capacity. This paper experimentally investigates the axial crushing behavior and energy absorption of a second-order hybrid multi-cell aluminum and CFRP (Al/CFRP) hierarchical tube under quasi-static loading. Five different configurations of the hierarchical tubes packing CFRP hollow tubes were designed. The quasi-static compression test was employed to investigate their crushing characteristics, axial collapse and energy absorption behaviors, and further compared with the Al hollow counterparts. The effects of different configurations involving the radial topology, the sub-tube number, the wall thickness, and the packing configuration were discussed in detail. The results reveal that the multi-cell tubes undergo a specific progressive folding collapse, and the energy absorption capability can be significantly improved for the hierarchical sections. The radial topology hardly affects the crashworthiness with the constant outer-tubular diameter and thickness. Additionally, both packing number and wall thickness conduce to improving the load-bearing capacities. By comparison with the specific multi-cell tube packing Al/CFRP sub-tubes, the hybrid tube packing net CFRP tubes own better crashworthiness and conduce to a wider range of applications in the design of automobile frames and energy absorbers.

Energy absorption characteristics of multi-cell tubes with different cross-sectional shapes under quasi-static axial crushing

Energy absorption characteristics of polygonal multi-cell tubes with different cross-sectional shapes under quasi-static axial crushing are investigated systematically. Based on the SSFE theory and CE method, theoretical models for predicting mean crushing force of tubes are proposed, and theoretical expressions of normalized mean crushing force (NFm) and normalized special energy absorption (NSEA) of tubes are derived. Numerical models for predicting the energy absorption characteristics also are established using the software ABAQUS/Explicit. The results of theoretical predictions and numerical simulations about 36 design conditions are in good agreement with experimental results those obtained by previous authors. Adding inner panels can improve the energy absorption characteristics of thin-walled tubes. And adding Cross-type inner panels in S, H and O single-cell tubes has more remarkable improvement than that of adding X-type and Y-type inner panels. The NFm increases with the increase of wide-thickness ratio, and NSEA decreases with the increase of wide-thickness ratio.

Effects of sections added to multi-cell square tubes on crash performance

Abstract In this study, the effects of sections added to multi-cell square tubes on crash performance are examined. Square, hexagonal and circular sections are added to multi-cell square tubes and their results are examined. Finite element analyses under axial loading are performed to examine the crash performance of the multi-cell tubes. Analyses show that by adding a section to the multi-cell square tubes. the crash behavior of the tubes is improved. According to the results, S5H multi-cell square tube reveals the best crash performance. The optimization of S5H is carried out by using genetic algorithms and radial basis functions. The S5H tube presents a good crashworthiness performance and could be used as an energy absorber.

Crushing analysis and crashworthiness optimisation for a novel bioinspired multicell filled tubular structure

In this article, a novel multicell filled tubular structure (MFTS) consisting of a multicell tube (MT) and filled circular tube (FCT) is proposed based on the microstructure of the lady beetle elytron. Systematic crashworthiness studies for MFTS under axial crushing have been performed using Abaqus/Explicit. The numerical results show that the MFTS substantially improves for three important indicators, the specific energy absorption (SEA), initial peak force (F max) and crush force efficiency (CFE), compared to the sum of the MT and FCT under crushing alone due to the coupling effect. The SEA and CFE values were improved by as much as 62.22% and 80.49%, respectively. The F max value is reduced by as much as 10.12%. A parametric study was performed and the main and interaction effects were analysed. Finally, the non-dominated sorting genetic algorithm II was used to optimise two different multiobjective problems with no constraints and constraints.

Study on the crashworthiness of bio-inspired multi-cell tube under axial impact

In recent years, thin-walled energy-absorbing structures have attracted more and more attention due to their excellent structural mechanical properties. In this article, one new kind of multi-cell bionic intersecting thin-walled tube inspired by the structure of the pine cone was designed. In order to fully study the crashworthiness of this new multi-cell tube under axial impact, the effectiveness of the simulation analysis is verified by the verification test of the circular thin-walled tube. Then, the crashworthiness of the circular tube and a series of multi-cell tubes were compared by means of simulation analysis. The simulation results show that the new multi-cell tube can effectively improve the efficiency of energy absorption, specific energy absorption, and crushing force efficiency under the premise of sacrificing part of the peak load. Finally, the response surface method was used to find the optimal design parameters. Response surface model (RSM) was used to represent specific energy absorption (SEA), peak force (PF), crushing force efficiency (CFE), and mass (M). Optimisation results show that the overall impact performance of the three-cell bionic tube under the axial impact load is better than that of the ordinary circular tube and several other multi-cell tubes. Therefore, the three-cell bionic tube can be used as an excellent absorption structure of collision energy under axial impact.

Crashworthiness performance of corrugation- reinforced multicell tubular structures

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.

Axial crushing of self-lock multi-cell tubes with foam filler and tube envelope

A type of self-lock multi-cell tubes assembled by open section components is recently proposed to serve as energy absorbing devices. Due to the open feature of the section, the self-lock tubes with large width may develop global buckling mode under axial crushing and show much worse energy absorption performances. To overcome this drawback, expanded polystyrene (EPS) foam fillers are firstly employed to improve the stability of the structural deformation and to increase the energy absorption efficiency. Experiment results show that a 4% increase in mass by EPS foam leads to about 20% increase in energy absorption of the self-lock tube. Numerical analyses are also carried out to simulate the tests and analyze the structures with other enhancement methods including Al foam filling and tube enveloping. They may be employed separately or simultaneously. The combination method of Al foam filling and tube enveloping gets the highest energy absorption capacity and efficiency. Theoretical analysis is performed to predict the mean crushing force of self-lock tubes enhanced by Al foam filling and tube enveloping, and the theoretical results compare well with numerical results. Finally, crashworthiness optimization problems are proposed and solved to explore the optimal enhancement configurations of the self-lock multi-cell tubes.

Study on the crashworthiness of windowed multi-cell square tubes under axial and oblique impact

Abstract The crumpling of aluminium alloy AA6060 T4 thin-walled tubes when subjected to axial and oblique impact is often experienced in collisions. Tubes with holes (so-called windows) and multi-cell tubes are efficient in terms of the structure's energy absorption. This paper proposes a combination of rectangular windows and multi-cell square tubes to improve the structure's crashworthiness. The advantages of the introduction of windows into the structure can diminish the initial peak collapsing load. This can also improve the crashworthiness performance and the mechanism of a folding formation. However, this introduction causes cracks in the tube and thus reduces the plastic zone area of the fold. The decrease in the plastic zone area and the cracks reduce the tube's energy absorption capacity. The specific energy absorption (SEA) and mean collapsing load (Pmcl) of WMCT-I and WMCT-III under axial impact is higher by about 20% and 16% compared to those of MCT-I and MCT-III, respectively. Relating to MCT-II having a wall-to-corner (WTC) one, the tube with holes does not improve in either case of axial and oblique impact. Extensive theoretical solutions are proposed to predict the mean collapsing loads of the windowed multi-cell tubes. The results of the theoretical predictions are compared to those of the numerical simulation. The Multi-Criteria Decision Making (MCDM) method is applied to select the better structure for the energy absorber application.

An investigation on the energy absorption characteristics of a multi-cell hexagonal tube under axial crushing loads.

A multi-cell tube enhances the energy absorption considerably compared to the absorption of a single tube under the same conditions. A novel tube configuration, namely, a multi-cell hexagonal tube, was proposed in this paper. The multi-cell tubes consist of three basic elements: a 2-panel element and two 3-panel elements (I and II). Simplified super folding element theory was utilized to estimate the energy dissipation of the basic elements. Based on this estimation, a theoretical expression for the mean crushing force was developed for the proposed tubes. The relative errors between a simulation, an experiment and theoretical results were no more than 5%. The effects of the hexagonal tube size and wall thickness on the crashworthiness of the multi-cell tubes were investigated. To a certain extent, the energy absorption and peak crushing force increased as the tube size and thickness increased. The response surface method (RSM) and the multi-objective non-dominated sorting genetic algorithm (NSGA-II) were used to improve the crashworthiness of the tube, and Pareto fronts were achieved. Finally, it was concluded that the optimal solution is C = 45 mm, t1 = 3.0 mm, and t2 = 2.35 mm, and the corresponding SEA and PCF were 16.52 kJ/kg and 411.36 kN, respectively.

Effects of sections added to multi-cell square tubes on crash performance

Abstract In this study, the effects of sections added to multi-cell square tubes on crash performance are examined. Square, hexagonal and circular sections are added to multi-cell square tubes and their results are examined. Finite element analyses under axial loading are performed to examine the crash performance of the multi-cell tubes. Analyses show that by adding a section to the multi-cell square tubes. the crash behavior of the tubes is improved. According to the results, S5H multi-cell square tube reveals the best crash performance. The optimization of S5H is carried out by using genetic algorithms and radial basis functions. The S5H tube presents a good crashworthiness performance and could be used as an energy absorber.

Review of the crushing response of collapsible tubular structures

Studies on determining and analyzing the crushing response of tubular structures are of significant interest, primarily due to their relation to safety. Several aspects of tubular structures, such as geometry, material, configuration, and hybrid structure, have been used as criteria for evaluation. In this review, a comprehensive analysis of the important findings of extensive research on understanding the crushing response of thin-walled tubular structures is presented. Advancements in thin-walled structures, including multi-cell tube, honeycomb and foam-filled, multi wall, and functionally graded thickness tubes, are also discussed, focusing on their energy absorption ability. An extensive review of experimentation and numerical analysis used to extract the deformation behavior of materials, such as aluminum and steel, against static and dynamic loadings are also provided. Several tube shapes, such as tubes of uniform and nonuniform (tapered) cross sections of circular, square, and rectangular shapes, have been used in different studies to identify their efficacy. Apart from geometric and loading parameters, the effects of fabrication process, heat treatment, and triggering mechanism on initiating plastic deformation, such as cutouts and grooves, on the surface of tubular structures are discussed.