Multi-cell Structures Research Articles

Energy absorbing ability of rectangular self-similar multi-cell sandwich-walled tubular structures

Thin-walled tubes (TWTs) have been widely applied as energy absorbers in engineering. The energy absorbing property of rectangular TWTs can be substantially enhanced by changing the ultra-thin solid walls into sandwich walls. Sandwich wall has great bending rigidity and it improves the energy absorption through two aspects: shortening the wave length or improving the plastic bending moment. Competition of these two mechanisms endows the rectangular sandwich-walled tube (SWT) with excellent energy absorbing ability and the best performance is achieved when the two mechanisms appear simultaneously. Mean crushing force (MCF) of the rectangular SWT could be 2.5 times of that of the TWT. The MCF of optimally designed rectangular SWT is even greater than the yield load of the tubular structure.

Energy absorption performance of concentric and multi-cell profiles involving damage evolution criteria

Many advantages are attributed to concentric and multi-cell columns, respect to single cell structures, which made them useful for applications in automobile design. The current paper analyzes the effect of cross-section on the crashworthiness performance of concentric and multi-cell profiles. Numerical analyses were performed considering damage evolution criteria using Abaqus/Explicit. Structures with triangular, square, hexagonal and circular base cross-sections were considered. In all cases, the structures were made of aluminum alloy EN AW-7108 T6 and modelled with ductile, shear and Müschenborn-Sonne Forming Limit Diagram (MSFLD) damage initiation criteria. The structures were axially loaded/impacted using a striker of 500kg with an initial velocity of 10m/s. Booth concentric and multi-cell structures showed an increase in energy absorption (Ea) as their cross-section tend to form a circular shape. The best performance was obtained by the profiles with circular cross-sectional base. In regard to profiles with triangular shape, an increase in crush force efficiency of 76.4% and energy absorption of 60.32%, was observed. Likewise, a better performance of specific energy absorption (SEA) for multi-cell profiles, relative to concentric structures, was obtained in the range from 33% to 57.92%. Finally, we end our study with a typical application in automotive crashworthiness design.

Multi-objective optimization of multi-cell tubes with origami patterns for energy absorption

Three novel types of multi-cell tubular structures with pre-folded origami patterns were proposed in this paper, aimed at reducing the initial peak force and the crushing force fluctuation while maintaining or increasing the specific energy absorption during uniaxial crush. Experimentally validated finite element modelling was conducted to study the influence of geometric parameters on the mechanical properties. Optimal designs were obtained through multi-objective optimization. The results showed that predesigned origami patterns governed the buckling process of the tubes and quintuple-cell origami tubes could absorb the highest energy in crush with significantly reduced initial peak force and the crushing force fluctuation.

A novel multi-cell tubal structure with circular corners for crashworthiness

Multi-cell structures have proven to own excellent energy absorbing capability and lightweight effect in the automotive and aerospace industries. The cross-sectional configuration of the multi-cell structure has a significant effect on crashworthiness. Unlike existing multi-cell tubes, a new type of five-cell profile with four circular elements at the corners (C5C) was proposed in this study. To investigate the crashworthiness of the new C5C tube, finite element (FE) models were first established by using the nonlinear finite element code LS-DYNA and validated with experimental results. Following that, the comparison of the C5C tube and other multi-cell tubes with the same mass was conducted to quantify the relative merits of the C5C tube. Then, a detailed study was performed to analyze the effect of the corner-cell size and wall thickness. Finally, the optimization design was carried out to seek the optimal structure. The results showed that the new multi-cell structure can absorb much more crash energy than other four types of tubes. Moreover, the energy absorption of this new multi-cell tube C5C was affected by the corner-cell size and wall thickness significantly. A proper corner-cell size and slightly thicker internal ribs were recommended. In addition, the multi-objective particle swarm optimization (MOPSO) algorithm and radial basis function (RBF) surrogate model can optimize the structure effectively. The outcomes of the present study will facilitate the design of multi-cell structures with better crashworthiness.

Configurational optimization of multi-cell topologies for multiple oblique loads

Multi-cell thin-walled structures exhibit significant advantages in maximizing energy absorption and minimizing mass during vehicle crashes. Since the topological distribution of wall members has an appreciable effect on the crashworthiness, their design signifies an important area of research. As a major energy absorber, multi-cell tubes are more commonly encounter oblique loading in real life. Thus, this study aimed to optimize multi-cell cross-sectional configuration of tubal structures for multiple oblique loading cases. An integer coded genetic algorithm (ICGA) is introduced here to optimize topological distribution of multi-celled web members for single/multiple oblique impacting conditions. Specifically, material distribution in a form of allocating web wall thickness, starting from zero, is considered as design variables and maximization of energy absorption (EA) as the design objective under the predefined peak crushing force and structural mass constraints. The optimization allows generating uniform or non-uniform thickness distribution in different web wall configurations to maximize usage efficiency of material. Compared with the baseline structure, the optimized configurations largely improved the energy absorption in both single and multiple load cases. The examples demonstrate that the proposed ICGA-based design method not only provides a useful approach to searching for novel crashworthy structures in a systematic fashion, but also develops a series of novel multi-cell topologies for multiple oblique loading cases.

Shape memory composite cellular plan-forms for shape and area morphing

In this paper we demonstrate a two-dimensional deformation mechanism with shape memory alloy (SMA) wire reinforced composite unit cell based plan-form structure which can produce various combinatorial effects of shape change and area change. Active deformation is realized using thermal SMA wire thermoelectric actuators. Compliant topological constructs are arrived at by consider passive and active load path decoupling and sub-optimal shape change and area change. Out-of-plane bending and buckling of the cellular membrane is restricted with the help of first auxiliary rib type stiffeners and later with monolithic elastic thermoplastic fabricated by laser machining. Systematic incorporation of various small-scale deformation features lead to large improvement in actuation efficiency. Structural compliance without and with the actuators are analyzed based on finite element simulation and experimental validation. A super-cell plan-form is characterized which shows interesting possibilities in structural morphing applications. The proposed multi-cell structures have potential applications membrane like structural morphing which can be integrated with transverse load carrying members.

Topological design of multi-cell hexagonal tubes under axial and lateral loading cases using a modified particle swarm algorithm

• Topology optimization of multi-cell hexagonal tubes was studied under both axial and lateral loading cases. • A modified PSO algorithm was proposed to improve the success rate. • The design requirements for cross-sectional configurations were discussed. Multi-cell structures have widely been studied due to their excellent energy absorption ability. However, few systematic studies have been conducted on the topological design of cross-sectional configurations of thin-walled tubes. To make full use of the material, topology optimization of multi-cell hexagonal tubes was conducted under both axial compression and lateral bending loadings. A binary particle swarm optimization (PSO) was enhanced by introducing the mass constraint factor to guide the movement of particles, which could improve the success rate of obtaining the global optimum. It was found that the optimum designs under the axial load placed the material outward to strengthen the interaction between the outer and inner walls and created more partitions between the inside rib walls. While under the lateral load, all the optimum designs have diagonally-connected elements to resist local deformation, and the material was also placed outward to increase the moment of inertia and thus to resist the global deformation. For the multiple loading cases, the final optimal designs are similar to the compression designs or combined designs from the two loading cases.

Crushing analysis and multiobjective optimization design for rectangular unequal triple-cell tubes subjected to axial loading

Multi-cell thin-walled tubes have proven to be better in energy absorption than plain square tubes subjected to axial compression. Therefore, square multi-cell structures have been extensively utilized as energy absorbers in automobiles. This paper provides an investigation on the crashworthiness of rectangular single-, double- and triple-cell columns under axial loading and an optimization design of rectangular unequal triple-cell tubes. First, a theoretical solution is derived for the mean crushing force (MCF) of tubes with unequal triple-cell configuration. Second, quasi-static crushing experiments and finite element analyses (FEA) are conducted on single-, double- and unequal triple-cell columns. Theoretical predictions compare well with experimental and numerical data, and all results show that the triple-cell tubes exhibit the best crashworthiness among all the samples. Third, in order to study effects of wall thickness distribution and the layout of internal ribs on crashing behavior, multiobjective optimization design is implemented combining Radial Basis Function (RBF) model with Non-dominant sorting Genetic Algorithm II (NSGA-II). The optimal solution obtained from Pareto frontier indicates that unequal triple-cell tube with appropriate thickness distribution and arrangement of internal ribs is superior in energy absorption to initial design.

Crashworthiness study for multi-cell composite filling structures

ABSTRACTLightweight cellular materials such as honeycombs and foams can absorb energy efficiently, and are therefore used as filler materials in thin-walled structures. This paper aims to explore the merits of various filling fashions on the crashworthiness of multi-cell square structures, namely honeycomb filling, foam filling and compound filling of honeycomb and foam. First, finite element models of different filling structures are validated by the theoretical model. Then, the numerical analysis is carried out using nonlinear finite element code LS-DYNA. The results reveal that partially filling the corner cells of the multi-cell square tube using honeycombs (H40) yields best crashworthiness performance. While for foam filling, filling two diagonally opposed corner cells (F20) produces the best results. Finally, the compound filling schemes were implemented, and found that filling the corner cells with honeycombs, and the central cell with foams (H40F01) generates promising crashworthiness performance. Finally, multi-objective particle swarm optimisation algorithm is adopted to maximise the specific energy absorption and minimise peak crushing force of the three novel structures. The results show that partially filling the four corner cells with honeycombs (H40) yields the most desirable crashworthiness performance.

COLLAPSE BEHAVIOR OF DYNAMICALLY CRASHED HEXAGONAL THIN WALLED STRUCTURES WITH MULTI-CELL CROSS-SECTION GEOMETRY

<p>In previous studies, the cross-section geometries were either single cell (circular, prismatic) or multi-cell structures with identical cell properties. In the present research the collapse characterization of multi-cell structures consisting of three different types of cell formation defined by either two wide or two narrow angles separating the ladders is conducted. The shape characteristics of interest sum up the layout of the interior walls and their constraints over the outer structure walls. To study the control of cross-section geometry over the crashing mechanism, local or global progressive buckling response, energy absorption and crash load for the structures in discussion FEA simulations of the impact were performed.</p>

A New Reduced-Component Hybrid Flying Capacitor Multicell Converter

This paper presents a new multicell topology based on flying capacitor (FC) structure suitable for multilevel converters. The proposed topology employs the concept of phase-shifted carrier pulse width modulation (PWM) with modified modulating signals to generate appropriate PWM signals. The modulation strategy along with all possible switching states are explained. The implementation of the proposed PWM technique is shown by the help of illustrating waveforms. To show the advantages of the proposed structure, different performance criteria are compared with other FC multicell (FCM) structures. Simulation results are used to further evaluate the potential merits of the proposed topology. It is shown that the proposed structure is superior to other FCM-based structures from different standpoints. Specifically, it reduces the number of high-frequency switches, the number of FCs, and at the same time improves the quality of output voltage. A laboratory-type experimental setup is used to validate the modulation strategy and other theoretical findings.

Numerical simulations of crashworthiness performance of multi-cell structures considering damage evolution criteria

In this paper finite element software Abaqus was used to analyse the effect of cross-sectional shape on the crashworthiness performance of multi-cell profiles. An emphasis was placed on the modelling of the damage initiation criteria and its evolution during the crash event. The structures evaluated included square and circular multi-cell cross-sections fabricated with aluminium alloy EN AW-7108 T6. During the crash simulations, the structures were subjected to axial impact loads using a 500-kg rigid body striker with an initial velocity of 10 m/s. Accordingly to our results, profiles with circular cross-section base presented better crashworthiness performance than square profiles. An increase in crush force efficiency to 36.9% and specific energy to 35.4% was observed when a circular cross-section has been reinforced in the transversal and longitudinal directions. Finally, it was corroborated that the addition of the damage initiation criteria allowed for more reliable crash simulations of the structures.

Numerical study of destruction phenomena for punch-through IGBTs under unclamped inductive switching

In this paper, a numerical description of the ruggedness of punch-through (PT) IGBTs under the unclamped inductive switching (UIS) has been proposed using two-dimensional (2D) simulations with the calibration to experimental results. The UIS capability is an important design factor of device structures for the purpose of screening defects produced during the wafer process. The local hot spot due to the current filament three-dimensionally (3D) distributed over the chip area requires 3D simulations to reproduce the current density of the filament and its behavior leading to the device destruction; however, it is difficult to simulate such a large area with an appropriate mesh size and a boundary condition. To provide a possible solution of this technical issue, 2D simulations using large scale multi-cell structures with the increased current density has been proposed to reproduce experimental results without resorting to 3D simulations. With this approach, not only destructive phenomena including the UIS ruggedness and the latch-up failure mode have been reproduced, but also the device internal state leading to the destruction has been revealed. The spatial distribution of the electric potential and the lateral electric field during the UIS condition is shown to be a key role determining the current filament width and the UIS ruggedness. Besides, the high frequency oscillation of the collector voltage during the UIS observed by experiments has been analyzed and has found to be related with the hopping motion of the current filament from a cell to its neighboring cell of the device.

Ultralow frequency acoustic bandgap and vibration energy recovery in tetragonal folding beam phononic crystal

This paper investigates ultralow frequency acoustic properties and energy recovery of tetragonal folding beam phononic crystal (TFBPC) and its complementary structure. The dispersion curve relationships, transmission spectra and displacement fields of the eigenmodes are studied with FEA in detail. Compared with the traditional three layer phononic crystal (PC) structure, this structure proposed in this paper not only unfold bandgaps (BGs) in lower frequency range (below 300 Hz), but also has lighter weight because of beam structural cracks. We analyze the relevant physical mechanism behind this phenomenon, and discuss the effects of the tetragonal folding beam geometric parameters on band structure maps. FEM proves that the multi-cell structures with different arrangements have different acoustic BGs when compared with single cell structure. Harmonic frequency response and piezoelectric properties of TFBPC are specifically analyzed. The results confirm that this structure does have the recovery ability for low frequency vibration energy in environment. These conclusions in this paper could be indispensable to PC practical applications such as BG tuning and could be applied in portable devices, wireless sensor, micro-electro mechanical systems which can recycle energy from vibration environment as its own energy supply.

Bending resistance of thin-walled multi-cell square tubes

The bending resistance of multi-cell square tubes under three-point bending is investigated in this study. Partition plates are introduced in longitudinal direction and cross-section of square tubes to form multi-cell structures. Numerical simulation of the three-point bending test is carried out by nonlinear finite element code and experimental test is conducted to validate the numerical model. Parametric studies are then performed to investigate the influence of the number of cells, load conditions and other geometrical configurations on the bending resistance. Results reveal that the number of partition plates has important influence on the bending resistance of the structure and more partition plates do not necessarily lead to high energy absorption efficiency. The optimum configurations of the structures are found out and some valuable suggestions are offered for multi-cell structures under transverse loading.

STUDY ON A MULTICELL BOX CULVERT TAKING SPAN TO HEIGHT RATIO AND DYNAMIC VEHICULAR LOAD

Box culverts are very important part of a transportation network as they provide an economical alternative to heavy bridges. Box culverts do not require a separate extensive foundation system and they are ideally suited for medium spans. Structurally, box culverts are complicated structures as they are buried completely in soil and because of their self-stabilizing nature. Hence, there is need to for a detailed parametric study on multi-cell box culvert structures in order to understand their structural behavior and to study the influence of various parameters effecting its structural behavior. In the present study span to height ratio of the culvert is analyzed by taking 3D analysis and dynamic vehicular analysis result is compared to a simplified static analysis. An attempt is made to carry out a parametric study on the behavior of a multi cell box culvert subjected to dead loads as well as IRC wheel loadings. The box culverts are modelled using SAP 2000 software using effective width method. IRC 70R loading is used for the analysis and design of culverts. The results of the study reveal that the dynamic study has significant influence on the result of the analysis and should be carefully considered.

Crushing mechanism of hierarchical lattice structure

Hierarchy greatly enhances anti-crushing behavior of thin-walled tubular structures. To reveal the energy-absorbing mechanism, hierarchical triangular lattice structures with lattice-core sandwich walls were designed. Crushing experiments were carried out to reveal the progressive collapse modes and folding mechanisms. Compared with single-cell and multi-cell lattice structures, hierarchical structures possess greater mean crushing forces (MCFs), three to four times higher. Three mechanisms, including hierarchical folding, shortening wave length and enlarging plastic bending moment of sandwich wall, help hierarchical structure greatly enhance its anti-crushing behavior. Folding styles turning from single fold, multi-fold, hierarchical fold to single sandwich-fold when increasing micro-cells in the wall were revealed by numerical simulation to propose optimized hierarchical lattice structure possessing the best specific energy absorption (SEA). Based on progressive folding mechanism, global bending mechanism and hybrid folding mechanism, theoretical models were built to predict the MCF. The predictions are reasonable.

On design of multi-cell thin-wall structures for crashworthiness

Multi-cell thin-wall structures have drawn increasing attention and been widely applied in automotive and aerospace industries for their significant advantages in high energy absorption and lightweight. The number of cells and the topological configurations of the multi-cell thin-wall structures have a significant effect on the crashworthiness. In order to investigate the effect of the number of cells and the topological configurations of multi-cell structures on their crashworthiness characteristics, this paper first sets up the simulation models of multi-cell tubes and verifies their accuracy with the quasi-static and dynamic impact experiments. Second, it compares the energy absorption characteristics of the multi-cell structures with different numbers of cells and topological configurations under dynamic impact condition using finite element analysis (FEA). The results show that the mean crushing force (MFC) and specific energy absorption (SEA) increase with the increase in the number of cells of the multi-cell tubes, among which the five-cell tube has the best energy absorption characteristics. Third, a parametric study is carried out to investigate the effects of wall thickness and topology configurations on the crashworthiness of five-cell tubes. Finally, the multiobjective Non-dominated Sorting Genetic Algorithm (NSGA-II) is used to further optimize the five-cell tube for maximizing specific energy absorption and minimizing peak crushing force (PCF). The optimal five-cell tube has excellent crashworthiness and is a potential energy absorber.

Dynamic crashing behavior of new extrudable multi-cell tubes with a functionally graded thickness

Multi-cell structures have been extensively studied for their outstanding performance as potential energy absorbers. Unlike existing multi-cell tubes with a uniform thickness (UT), this paper introduces a functionally graded thickness (FGT) to multi-cell tubes under dynamic impact, which can be fabricated by an extrusion process. A numerical model is first established using the nonlinear finite element analysis code LS-DYNA and validated with experimental data. Based on a numerical study, the thickness gradient parameters in different regions have considerable effects on the crashworthiness of the FGT multi-cell tubes. Moreover, the FGT multi-cell tubes are able to absorb more energy while yielding a similar level of peak impact force to the UT multi-cell tubes. Finally, multiobjective optimizations of the UT and FGT multi-cell tubes are then performed to determine the optimal gradient parameters that simultaneously improve the specific energy absorption (SEA) and reduce the maximum impact force. In these optimizations, the multiobjective particle optimization (MOPSO) algorithm and response surface (RS) surrogate modeling technique are adopted. The optimization results demonstrate that the FGT multi-cell tubes produce more competent Pareto solutions than the conventional UT counterparts; similar gradients in the outer walls and stronger internal ribs are recommended for the FGT multi-cell tubes because of their improved interactions.

Some problems on the axial crushing of multi-cells

Multi-cell structures are highly efficient energy absorber under axial crushing. The present work aimed to resolve some problems concerned with energy absorption of a type of quadruple cells. These problems include influence of geometric compatibility among elements, type of trigger, structural parameter or topology change on crush resistance of the structure. Experimental study was conducted first and numerical simulation was then carried out by using commercial explicit finite element code. Theoretical prediction for the mean crushing force of the quadruple cells was also performed by the existing theoretical models. The results showed that when the structural parameter in the section was varied, the geometric compatibility problem became severe if the discrepancy of folding wavelength among constituent elements was large. However, it generally had limited influence on crush resistance of the multi-cell structure and the existing theoretical models can still predict the crush resistance of the section with good accuracy.