Dynamic effects on buckling and energy absorption of cylindrical shells under axial impact

The crushing behaviour of aluminium and steel cylindrical shells, when subjected to an axial impact, is examined using a numerical simulation. The influence of the material properties, shell geometry, boundary conditions and loading techniques on the energy absorbed and the buckling shapes is explored. Various shell response characteristics, such as the peak load, fold lengths, axial compression and energy absorption are studied. An examination is also made of the influence of filtering on the accuracy of data obtained usually in dynamic tests.     

Computer simulation and energy absorption of tapered thin-walled rectangular tubes

Tapered thin-walled tubes have been considered desirable energy absorbers under axial loading due to their relatively stable crush load and deformation response compared with straight tubes. This paper compares the energy absorption response of straight and tapered thin-walled rectangular tubes under quasi-static axial loading, for variations in their wall thickness, taper angle and number of tapered sides. Overall the study highlights the advantages of using tapered tubes as energy absorbers. In particular, the peak load required to crush the tubes decreases with the introduction of a taper, and as the taper angle increases. This is desirable for minimising the impact loads transmitted to the protected structure. The practical outcome of the study is design information for the use of tapered thin-walled rectangular tubes as energy absorbers in impact loading applications. Analysis has been undertaken using a finite element model, validated using existing theoretical and numerical models.     

Optimization of thin conical frusta for impact energy absorption

Experimental and numerical investigations were carried out to optimize thin-walled conical shells for their use in design for energy absorption. Geometrical parameters, such as bottom diameter, height, and semi-apical angle were considered to obtain the design space. The numerical analysis and impact experiments were designed using design of experiments (DOE). A three-level, second-order Box–Bhenken technique was used to select the design points from the design space. Various set of numerical simulations were carried out using LS-DYNA. To investigate the influence of flow stress of the material on the energy absorption, numerical simulations were carried out using frusta made of aluminium, zinc, and mild steel. From the numerical results, mathematical models were created using response surface methodology (RSM). With the help of impact experiments carried out on specimens made of zinc on a drop mass test rig, a mathematical model has been developed using RSM. The mathematical models developed using experimental data and the numerical data were used as objective functions for optimization of the design. The non-dominated sorting genetic algorithm code NSGA II was used to optimize the design. The mathematical models were also used to predict the energy absorbed and deformation. The influence of various design parameters on energy absorption has been analysed and is discussed.     

Multiobjective crashworthiness optimization of hollow and conical tubes for multiple load cases

Much attention of current design analysis and optimization of crashworthy structures have been largely paid to the scenarios with single load case in literature. Nevertheless the designed structures may often have to be operated in other load conditions, thus raising a critical issue of optimality. This paper aims to understand and optimize the dynamic responses and energy absorption of foam-filled conical thin-walled tubes under oblique impact loading conditions by using multiobjective optimization method. The crashworthiness criteria, namely specific energy absorption (SEA) and crushing force efficiency (CFE), are related to loading parameters and design variables by using D-optimal design of experiments (DoE) and Kriging model. To obtain the optimal Pareto solutions of hollow and foam-filled conical tubes, design optimization is first performed under different loading case (DLC) using multiobjective particle swarm optimization (MOPSO) algorithm separately. The optimal designs indicate that hollow tube has better crashing performance than the foam-filled tube under relatively high impacting velocity and great loading angle. To combine multiple load cases (MLC) for multiobjective optimization, a double weight factor technique is then adopted. It is found that the optimal foam-filled tube has better crashing performance than empty conical tube under any of overall oblique loading cases concerned. The study gains insights in deriving multiobjective optimization for multiple load cases, providing a guideline for design of energy absorber under multiple oblique loading.     

Relative merits of single-cell, multi-cell and foam-filled thin-walled structures in energy absorption

The axial crushing of hollow multi-cell columns were studied analytically and numerically. A theoretical solution for the mean crushing force of multi-cell sections were derived, and the solution was shown to compare very well with the numerical predictions. Numerical studies were also carried out on foam-filled double-cell and triple-cell columns. Based upon the numerical results, closed-form solutions were derived to calculate the mean crushing strength of these sections. It was found that the interaction effects between the foam core and the column wall contribute to the total crushing resistance by the amounts equal to 140% and 180% of the direct foam resistance for double cell and triple cell respectively. Finally, the relative merits of single-cell, multi-cell and foam-filled sections were discussed.     

Numerical studies on STFD-HAT sections under axial dynamic impact

A new type of spot-weld double-hat section with symmetrically distributed tilt flanges (STFD-HAT) is introduced in this paper to improve the crushing performance, especially crushing stability. LS-DYNA code has been employed here to analyze the effect of several parameters on the collapse modes of STFD-HAT sections under axial dynamic impact loading condition. Some variables, such as tilt angle, size of core cross-section and thickness of sheet shell, have been proved to be effective in controlling the collapse mode and crushing performance of STFD-HAT sections by analysis on energy absorption and RSS of result curves. Compared with traditional double-hat sections, the STFD-HAT sections with reasonable designed profiles can effectively improve the crushing resistances and stabilities, especially, the bending mode.     

Experimental and numerical study of circular,stainless thin tube energy absorber under axial impact by a control rod

In this study, several crashworthiness parameters of a circular, thin tube energy-absorbing structure, which is used in a high-temperature, gas-cooled reactor (HTR), are studied experimentally and numerically at various tube thicknesses, temperatures and impact velocities. The average crushing force is fundamentally dependent on strain hardening, strain rate hardening, and, particularly, temperature softening of the material. The peak forces during buckling are significantly affected by the local strain rate in the material and exhibit a decreasing trend in sequentially formed folds. Reducing the tube thickness is an effective method to weaken the average crushing force, but it does not weaken the maximum crushing force. Additionally, the stress concentration at the edge of the backplate–graphite contact surface is evaluated in detail to ensure the structural security of the energy absorber.     

Energy absorbtion and mean crushing load of thin-walled grooved tubes under axial compression

In the present study, crashworthiness characteristics of thin-walled steel tubes containing annular grooves are studied. For this purpose, the grooves are introduced in the tube to force the plastic deformation to occur at predetermined intervals along the tube. The aims are controlling the buckling mode and predicting energy absorption capacity of the tubes. To do so, circumferential grooves are cut alternately inside and outside of the tubes at predetermined intervals. Quasi-static axial crushing tests are performed and the load-displacement curves are studied. Theoretical formulations are presented for predicting the energy absorption and mean crushing load. It is found a good agreement between the theoretical results and experimental findings. The results indicate that the load-displacement curve and energy absorbed by the axial crushing of tubes could be controlled by the introduction of grooves with different distances. Also, grooves can stabilize the deformation behavior and thus, the proposed method could be a good candidate as a controllable energy absorption element.     

Numerical and experimental study of crashworthiness parameters of honeycomb structures

Crashworthiness parameters of aluminum hexagonal honeycomb structures under impact loads are investigated by using finite element methods and conducting experiments. To validate the finite element models, numerical results are compared with experimental measurements and theoretical results reported in literature. In numerical simulations of honeycomb structures, out-of-plane loads are considered while the aluminum foil thickness, cell side size, cell expanding angle, impact velocity and mass are varying, and dynamic behavior and crashworthiness parameters are examined. It is observed that there are good agreements between numerical, experimental and theoretical results. Numerical simulations predict that crashworthiness parameters depend on cell specification and foil thickness of the honeycomb structure and are independent of impact mass and velocity.     

Attempts to improve energy absorption characteristics of circular metal tubes subjected to axial loading

In this paper, experimental investigation of two new structural design solutions with the aim of improving crashworthiness characteristics of cylindrical metal tubes is performed. In the first design method, a rigid steel ring is press-fitted on top of circular aluminum tubes. When this arrangement of dissipating energy is subjected to axial compression, the rigid ring is driven into the cylindrical tube and expands its top area; then, plastic folds start shaping along the rest of the tube length as the compression of the structure continues. In the second design method, wide grooves are cut from the outer surface of steel thick-walled circular tubes. In fact, this method converts thick-walled tubes into several thin-walled tubes of shorter length, being assembled together coaxially. When this energy absorbing device is subjected to axial compression, plastic deformation occurs within the space of each wide groove, and thick portions control and stabilize collapsing of the whole structure. In the present study, several specimens of each developed design methods with various geometric parameters are prepared and compressed quasi-statistically. Also, some ordinary tubes of the same size of these specimens are compressed axially to investigate efficiency of the presented structural solutions in energy absorption applications. Experimental results show the significant efficiency of the presented design methods in improving crashworthiness characteristics and collapse modes of circular tubes under axial loading.     

Effects of hinges and deployment angle on the energy absorption characteristics of a single cell in a deployable energy absorber

Numerical simulation is carried out to investigate the crushing characteristics of a single cell in a fan-shaped deployable energy absorber (FDEA) under quasi-static axial loading. FDEA can effectively improve the crashworthiness behavior of aircrafts with the advantages of saving space and deploying actively. Hinges are added to the single cell to meet the need of fan-shaped deployment. The finite element model is established to study the effects of hinge׳s parameters, including material properties such as Young׳s modulus, yield strength and the tube thickness, on the single cell׳s energy absorption characteristics. The relationship between the deployment angle and the specific energy absorption (SEA) of the single cell is also studied. The numerical results indicate that the energy absorption increases rapidly as yield strength and the hinge׳s thickness increase, while it only has minor correlation with Young׳s modulus of the material. Three different modes of the cell appear during its axial crushing as the deployment angle increases. Besides, experiments were conducted to observe the crushing mode of the straight single cell, and the results are compared with the numerical simulation results. Finally, a theoretical model of a straight single cell with hinges is proposed to predict the mean crushing force, which is in good agreement with the numerical simulation.     

Quasi-static axial compression of concentric expanded metal tubes

Previous studies have demonstrated that the failure mechanism and energy absorption capacity of expanded metal tubes strongly depends on the orientation of the cells. This paper presents an experimental investigation on the collapse of concentric expanded metal tubes subjected to quasi-static axial compression. Square tubes with two different cell orientations are tested to failure, and the energy absorption characteristics are calculated. The results show that the combination of cell geometries lead to a complex buckling mode interaction, which enhances the energy absorption capacity of expanded metal tubes.     

Theoretical prediction and crashworthiness optimization of multi-cell triangular tubes

The triangular tubes with multi-cell were first studied on the aspects of theoretical prediction and crashworthiness optimization design under the impact loading. The tubes׳ profiles were divided into 2-, 3-, T-shapes, 4-, and 6-panel angle elements. The Simplified Super Folding Element theory was utilized to estimate the energy dissipation of angle elements. Based on the estimation, theoretical expressions of the mean crushing force were developed for three types of tubes under dynamic loading. When taking the inertia effects into account, the dynamic enhancement coefficient was also considered. In the process of multiobjective crashworthiness optimization, Deb and Gupta method was utilized to find out the knee points from the Pareto solutions space. Finally, the theoretical prediction showed an excellent coincidence with the numerical optimal results, and also validated the efficiency of the crashworthiness optimization design method based on surrogate models.     

Experimental and numerical crashworthiness investigation of empty and foam-filled end-capped conical tubes

Foam-filled thin-wall structures exhibit significant advantages in light weight and high energy absorption. They have been widely applied in automotive, aerospace, transportation and defense industries. Quasi-static tests were done to investigate the crash behavior of the empty and polyurethane foam-filled end-capped conical tubes. Non-linear dynamic finite element analyses were carried out to simulate the quasi-static tests. The predicted numerical crushing force and fold pattern were found to be in good agreement with the experimental results. The energy absorption capacities of the filled tubes were compared with the empty end-capped conical tubes. The results showed that the energy absorption capability of foam-filled tube is somewhat higher than that of the combined effect of the empty tube and the foam alone. Finally, the crash performance of the empty and foam filled conical and cylindrical tubes were compared. Results from this study can assist aerospace industry to design sounding rocket carrier payload based on foam-filled conical tubes.     

A study on buckling of thin conical frusta under axial loads

Experiments were performed wherein conical frusta of aluminium of thicknesses between 0.7 and 1.62 mm and semi-apical angles range of 16–29° were axially compressed in a universal testing machine. The load–deformation curves and deformed shapes of specimens were recorded. These deformed in axisymmetric concertina mode and non-symmetric diamond modes.A three dimensional numerical simulation was carried out for all samples tested under quasi-static loading using ANSYS^®. Various stages of collapse of the shell, including non-symmetrical lobe formation were simulated for the first time, and material, geometric and contact non-linearities were incorporated. The plastic region of the material curve was assumed to be piecewise linear. Tensile tests were performed on standard samples to obtain stress–strain curves. Results thus obtained compared well with the experiments.Based on the formation of rolling and stationary plastic hinges an analysis was also carried out to study the behaviour of shells under axial compression and results were compared with experimental and numerical results.     

Comparative analysis of energy absorption and deformations of thin walled tubes with various section geometries

In this paper, deformations and energy absorption capacity of thin walled tubes with various section shapes (circular, square, rectangular, hexagonal, triangular, pyramidal and conical) are investigated both experimentally and numerically. The tubes have the same volume, height, average section area, thickness and material and are subjected under axial quasi static loading. The results of simulations are in good agreement with the experimental data and show that the section geometry has considerable effect on the energy absorption. The circular tube has the most energy absorption capacity and the most average force among all investigated sections. Since the maximum force is concerned in impact events, pyramidal and conical tubes are recommended, due to their uniform load–displacement curves and therefore, less difference between the maximum and the average forces.     

Quasi-static axial and lateral crushing of radial corrugated composite tubes

This paper presents the effect of corrugation geometry on the crushing behavior, energy absorption, failure mechanism, and failure mode of woven roving glass fibre/epoxy laminated composite tube. Experimental investigations were carried out on three geometrical different types of composite tubes subjected to axial and lateral compressive loadings. On the addition to a radial corrugated composite tube, cylindrical composite tube, and corrugated surrounded by cylindrical tube were fabricated and tested under the same condition in order to know the effect of corrugation geometry. The results showed that the loading carrying capability is significantly influenced by corrugation geometry in axial crushing. However, no affect of corrugation geometry was observed for lateral crushing. Load–displacement curve was plotted for all conducted tests, thus clear comparison between different specimen's geometry was achieved. It is also found that radial corrugation could significantly applicable as a stable and effective energy absorber.     

Theoretical prediction and numerical simulation of multi-cell square thin-walled structures

The axial crushing of square multi-cell columns were studied analytically and numerically. Based on the Super Folding Element theory, a theoretical solution for the mean crushing force of multi-cell sections were derived by dividing the profile into 3 parts: corner, crisscross, and T-shape. Numerical simulations of square multi-cell sections subjected to dynamic axial crushing were conducted and an enhancement coefficient was introduced to account for the inertia effects for aluminum alloy AA6060 T4. The analytical solutions show an excellent agreement with the numerical results. It was found that the crisscross part was the most efficient component for energy absorption and the energy absorption efficiency of a single-cell column can be increased by 50% when the section was divided into 3×3 cells. Finally, the proposed method was extended to analyze the plateau stress of square cell honeycomb subjected to out-plane axial crushing and to some extent validate the mechanical insensitivity of honeycomb to cell size.     

Effects of boundary conditions on the energy absorption of thin-walled polymer composite tubes under axial crushing

Polymer composite tubes can be designed to absorb high levels of impact energy by progressive crushing. When a tube is crushed onto a flat platen, energy is absorbed by bending failure of the plies, delamination and friction mechanisms. In the present work, significant increases in energy absorption are shown when a shear mode of failure is initiated by crushing the tube onto a radiused plug (or initiator). A study of plug radius, R, normalised with respect to the tube wall thickness, t, in the range of 0R/t5 for circular tube diameter/thickness ratios of 10<D/t<33 was undertaken with continuous filament random mat glass/polyester composite. Different radii plugs lead to significantly different deformed shapes and crush zone morphologies. Large radius initiators (R/t>2) cause the tubes to split and energy is absorbed primarily through friction and axial splitting. As the initiator radius decreases, the amount of through-thickness shear damage in the fronds increases along with specific energy absorption (SEA). When the plug radius becomes small compared to the wall thickness (R/t<0.75) a debris wedge forms between the initiator and the tube and acts like a larger radius initiator. The highest energy absorption was seen to occur at R/t1 when through-thickness shear damage was induced. In this range, under static loading conditions, SEA was seen to be higher than that for tubes crushed onto a flat platen.