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An experimental study of deformation modes of domes and large-angled frusta at different rates of compression
Abstract
Axial compression tests were conducted on a large number of spherical domes and conical frusta of various sizes to study their modes of collapse and energy absorption capacities. The results presented here include aluminium spherical domes of R/t values ranging between 15.3 and 240.9, and large-angled conical frusta of slenderness ratio (t/d) varying from 0.00554 to 0.02152, and semi-apical cone angles from 44.5° to 67.1°. These were chosen because their mode of collapse primarily was due to the formation of rolling plastic hinges. All specimens were made from aluminium sheets of different thicknesses by the process of spinning. Quasi-static tests were conducted on an INSTRON machine at crosshead speeds of 2, 100 and 200 mm/min. Impact tests were conducted on a drop hammer, and the impact velocities varied from 2 to 9 m/s. Their various modes of collapse, load–deformation and energy–compression curves were recorded. Typical results are presented. A comparative study of the modes of collapse and load–deformation curves of the spherical domes and conical frusta, obtained from quasi-static and impact tests, is also presented.
... While a shell is subjected to collision, its deformation is a dynamic process, but under relative low impact velocity (less than 30 m/s), the inertia effects may be considered negligible [4,12]. Thus a majority of both theoretical and experimental studies in the field are focused on quasi-static deformation. ...
... In recent years, the behavior of spherical shells under dynamic loading has been related to possible strain rate and inertia effects. Easwara Prasad and Gupta [12] reported dynamic tests conducted on aluminum spherical domes, but they were mainly interested in the dependence of collapse mode on the thickness of the shells. The experimental results exhibited that the modes of collapse of spherical domes and conical frusta are similar to those appearing in quasi-static tests, but the modes of deformation of spherical domes are sensitive to the rate of compression. ...
Experimental studies on dynamic behavior of thin-walled spheres and sphere arrays in response to different impact velocity are presented. Ping pong balls are selected to study the collapse of thin-walled spheres. The tests were carried out by a modified Split Hopkinson Pressure Bar (SHPB) test system. The experimental results show that the deformation of thin-walled spherical shells depends on the impact velocity. The dynamic force in the range of small elastic deformation is larger than its quasi-static counterpart, but significantly below the latter after snap-through of the shell. The deformation and buckling mode are sensitive to the loading rate. It is noted that the strain rate effect of the materials and the inertia effect of the shell should be considered in the analysis of the shells response to dynamic loading.
... The gradual varying cross-sectional area of the structure influenced their energy absorption capability. Further at the time of the impact, the taper tubes produced less inertia effect [14] which helped to minimize the Eulerbuckling deformation mode Prasad and Gupta [17] analyzed large angle frusta against both quasi-static and dynamic loading conditions. The load displacement plot and the collapse behavior of frusta were found similar for both loading conditions, whereas for the dome shell it was different as different strain rates. ...
An experimental and numerical investigation was carried out to know the crashworthiness performance of layered frusta tube structures against axial impact loading. The configuration of AA-1080 frusta tubes was varied as single, double, triple and four layers, whereas the mass and velocity of the impactor were kept 20 kg and 6.7 m/s, respectively. For three-dimensional finite element analysis, commercial code Ansys/Ls-Dyna was employed and experiments were carried out through drop weight impact tester. The failure modes obtained through experiments and numerical simulations were compared and found similar for different multiwall frusta structures. The different configurations of layered frusta tubes were evaluated based on crashworthiness parameters in terms of peak force (PF), mean force (MF), crushing load efficiency (CLE) and energy absorption capability (EAC). Moreover, a parametric analysis was carried out by maintaining a constant taper angle of 5.71° with a slight variation in height, thickness, diameter and mass of impactor to analyze the dynamic response of layered frusta tube structures. The volume of all sets of layered frusta tube structures was kept approximately the same. Compared to double- and four-layered frusta tubes, the three-layered frusta tube proved to be more efficient against dynamic loading condition.
... Although some experimental, computational, and theoretical studies have explored the quasi-static or dynamic behavior and energyabsorption characteristics of some hollow sphere-based structures (e. g., ping-pong ball arrays) and cellular foams (e.g., aluminum foams, honeycomb, syntactic foams) [21][22][23][24], little effort has been made to investigate the energy-absorption behavior of MHSS under impact loading, particularly for its potential use as an anti-collision material to protect bridge piers from vehicle impact. This paper presents an integrated experimental and computational study of the MHSS as an energyabsorption material to be potentially used in bridge pier protection against vehicle collision. ...
An integrated experimental and computation study is presented of the energy-absorption behavior of metallic hollow sphere structures (MHSS) as an innovative anti-collision material to protect bridge piers from vehicle impact loading. Quasi-static compression and dynamic split Hopkinson pressure bar impact testing were first conducted to compare different deformation and energy-absorption characteristics of MHSS subjected to different loading modes, followed by more realistic laboratory downscaled model impact testing and finite element modeling (FEM) of collisions between real-scale bridge piers and vehicle to further examine the energy-absorption capability of MHSS under dynamic loading. Results show that the MHSS exhibits an increased structural stiffness (e.g., by ~20 times), yield strength (by 4-5 times), and toughness (by 200%) with increasing loading rate (i.e., from static to impact loading). When used as a protective layer on bridge piers, the downscaled model tests and FEM simulations validated the MHSS can provide remarkable anti-collision function to concrete structures: MHSS can substantially reduce the horizontal accelerations (by 63-68%), displacements (by 56.6%), and surface strains of bridge piers, and there reductions further increases with impact velocity. The high energy-absorption capability of MHSS may originates from the exceptionally high, multiscale porosity as well as the excellent mechanical properties of the MHSS material. The findings suggest that MHSS can be an effective energy-absorptive material for anti-collision protection of bridge structures.
... The taper angle in the range of 65 � -80 � , deformed with the formation of a new folding named as folding crumpling mode [5] and absorbed maximum energy compared to the other reported mode. Prasad and Gupta [6] studied the deformation behaviour of domes and large angle frusta with the variation in slenderness ratio against both quasi-static and dynamic loading. The obtained load deformation curve and the collapse modes of frusta tubes showed similarities against both loading conditions. ...
In the present study crashworthiness performance of monolithic and co-axial multi-wall (double, triple, and four layered) frusta tube structures was investigated under the quasi-static axial loading. The developed layered frusta tubular structures having a total equivalent thickness of 2.3 mm were made of aluminium alloy AA-1080 sheet. A series of layered configurations were simulated and analysed using non-linear finite element analysis code LS-DYNA, keeping volume approximately the same as the monolithic frusta tube. For the effectiveness of the simulated results, double-tubular structure was examined through experimental results. A parametric study was performed by keeping taper angle constant as 5.71° with the variation in height (91.6 and 82 mm for double layered, 91.6, 86 and 78 mm for triple layered and 91.6, 87, 82 and 77 mm for four layered), thickness (2.3–0.4 mm) and diameter (smaller end diameter in the range of 42.8 mm–48.4 mm while larger end diameter varied from 61 mm to 64 mm) to analyse the crushing performance of layered structures. The crashworthiness performance indicator like peak force (PF), mean force (MF), energy absorbing capacity (EAC), specific energy absorption (SEA) and crush load efficiency (CLE) which is defined as the ratio of MF to the PF, were studied for the various layered frusta tubular structures. Moreover, optimization technique GRA (Grey Relational Analysis) was employed to obtain a better combination of multi-wall layered structures. With the increase in the layer, the initial peak force was reduced compared to the monolithic frusta. The optimization technique suggested the triple-layer configuration showed better crashworthiness performance.
... A cap surface also reduced the initial maximum force. In this context, modifications in geometry with variations in angle and structure were studied by Prasad and Gupta [72]. The authors conducted a comparative study of collapse modes and load deformation behavior of aluminum spherical domes and tube under quasi-static and dynamic impact conditions. ...
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.
... It can be seen that numerical results can predict reasonable values compared to the experimental ones. The appeared discrepancy may be attributed to the presence of imperfections in the frustum test specimens and the variation in thickness along the meridian direction of the spun frusta [17]. These imperfections were produced from the spinning process used in manufacturing of the frustum specimens. ...
... Gupta et al. extended the investigation of quasi-static compression of large hollow aluminum spheres (D = 40-125 mm with a mixed range of t/D = 0.002-0.03) to compression at high loading rates of up to 10 m/s [13][14][15]. Besides, several papers have reported the dynamic behavior of hollow spheres. Ruan et al. reported the crushing behavior of a single ping-pong ball compressed by point loading, rigid ball, rigid plate, rigid cap, and double rigid balls, as well as the one-dimensional (1D) and 2D loaddeformation behavior compressed by rigid plates [6]; Dong et al. studied the collapse behavior of selected ping-pong ball arrays under different impact velocities using a split Hopkinson pressure bar (SHPB) system [16]; Li et al. conducted high loading-rate experiments and finite element modeling (FEM) to investigate the underlying deformation and failure mechanisms of thin-walled hollow nickel spheres [17]. ...
This paper presents an integrated experimental and computational study of the compression behavior of individual thin-walled metallic hollow spheres (MHS) with patterned distributions of microporosity. Quasi-static compression testing, including purely elastic loading, was conducted on two groups of individual MHS with two different sizes to examine the entire deformation process as well as the purely elastic response. Three-dimensional finite element modeling was then performed to investigate the effects of different microporosity distribution patterns on the MHS compression behavior and to understand the pertinent deformation and failure mechanisms. Results show that the Young's modulus and collapse stress of individual MHS with a uniform microporosity distribution decrease nonlinearly with porosity, which follows the same power-law functions developed for the porous wall material. For other patterned (i.e., vertical, horizontal, and random) distributions of microporosity involving localized weak wall sections, buckling commences at the weak sections, generating “buckling lines” followed by buckling failure along these adjacent or converged “buckling lines”. Moreover, among the “buckling lines” generate some hinges that contribute to the increased load-bearing capability during the densification process. These findings can shed lights on the design, manufacturing, and modeling of individual MHS and MHS-based materials with specifically tailored engineering performance.
... The size of folded area and the variation of crushing load are theoretically found in this paper. An experimental study on the deformation modes of domes and large-angled truncated cones subjected to axial loading was studied by Prasad and Gupta (Prasad and Gupta 2005). ...
Steel conical shells have long been used in various parts of different structures. Sensitivity to the initial geometrical imperfection has been one of the most significant issues on the stability of these structures, which has made them highly vulnerable to the buckling. Most attention has been devoted to structures under normal fabrication related imperfections. Notwithstanding, the challenges of large local imperfections - presented herein as dent-shaped imperfections - have not been a focus yet for these structures. This study aims to provide experimental data on the effect of such imperfections on the buckling capacity of these shells under axial compression. The results show changes in the buckling mode and the capacity for such damaged thin specimens as is outlined in this paper, with an average overall capacity reduction of 11%.
... The simulated results from the two models explained above show good agreement with the experimental data and indicated the high accuracy from the modelling output, which demonstrates the high accuracy results from thickness defined shell elements for modelling solid parts. Similar models have also been constructed out by other researchers to evaluate the stress distribution and deformation of the thin-walled structures[27,28,29] Lamers et al.[30] constructed an FE model of large deformation simulating the forming of woven fabric reinforced composite product using DIEKA. The thermal mechanical behaviour was modelling by firstly predicting the fibre orientations of the product from the forming simulation; a Classic Laminate Theory based model was then was then applied to obtain the local changed thermo-mechanical properties of the composite laminates. ...
... The size of folded area and the variation of crushing load are theoretically found in this paper. An experimental study on the deformation modes of domes and large-angled truncated cones subjected to axial loading was studied by Prasad and Gupta (Prasad and Gupta 2005). Over the past few years the buckling of conical shells with different geometries was discussed by (Błachut 2011, Ifayefunmi 2011, Sofiyev 2011, Zhao and Liew 2011, Błachut 2012 al. 2013) and different aspects of stability problems in these structures were examined. ...
A new composite comprising steel tubes, timber and CFRP confinement was studied. The weight of the composite only increased 86%. The capacity considerably enhanced, around 2.5 times more than bare steel specimen. Practical benefits of the new composite are remarkable. The timber-filled specimens can potentially gain attentions of the researchers. a b s t r a c t This paper discusses the structural behavior of an innovative composite column through an experimental study. The new composite comprised steel cylindrical hollow sections known as CHS, solid timber infill and CFRP confinements. The present stub columns were under pure axial compression. Plastic buckling, failure modes and deformational response of the mentioned elements were assessed. The ultimate capacity enhancement was evaluated for specimens with different conditions and comprehensive discussions were made in order to clarify the effect of each material on the structural behavior of different specimens.
... Details about experiments of axially compressed unstiffened cones can be found in (Arbocz, 1968;Blachut et al., 2011;Blachut and Ifayefunmi, 2010;Chryssanthopoulos and Poggi, 2001;Easwara Prasda and Gupta, 2005;El-Sobky and Singace, 1999;Foster, 1987;Gupta et al., 1997Gupta et al., , 2006Lackman and Penzien, 1961;Mahdi et al., 2002;Mamalis and Johnson, 1983;Mamalis et al., 1984Mamalis et al., , 1986Ramsey, 1977;Tong, 1999;Weingarten et al., 1965aWeingarten et al., , 1965b. Seide (1956Seide ( , 1961 first derived an expression based on Donnelltype shell theory for the critical elastic buckling load for an axisymmetric mode in a conical shell subjected to axial compression. ...
... N.K. Gupta and his group have made a series studies (e.g. [1][2][3]) on quasi-static compression and impact on thin-walled aluminum spherical shells of various radii and thicknesses. The impact loading was made by a drop hammer and the load histories were obtained in all the cases. ...
The dynamic behavior of a thin-walled hollow sphere colliding onto a rigid wall has been studied by experiments, numerical simulation and analytical modeling, as reported in our previous papers. In the present paper, the impact crushing of metallic thin-walled hollow spheres onto rigid plates and the subsequent rebound are analyzed using finite element method. The effects of hollow sphere’s thickness-to-radius ratio, the material properties and the impact velocity on the dynamic responses are systematically investigated. The transition from axisymmetric dimpling to non-axisymmetric lobing is found to depend on the relative thickness of spheres and impact velocity; while the coefficient of restitution almost merely depends on impact velocity.
... Specimens were made from aluminium Ref [42], steel Ref. [43], and from polyvinylchloride (PVC) Ref. [44]. Gupta and Easwara Prasad [45,46], studied experimentally the plastic behavior of aluminium conical frusta for large cone angles under axial compression. Whereas, in Ref. [47], aluminium cones with smaller cone angle were investigated. ...
The paper reviews literature on buckling of conical shells subjected to three loading conditions: (i) axial compression
only, (ii) external pressure only and (iii) combined loading. The review is from the theoretical as well as experimental
points of view. This review covers known experiments on cones from (1958 – 2012). The literature review is split
thematically into the following categories: theoretical prediction of axially compressed cones, theoretical prediction of
externally pressurized cones, theoretical prediction of cones under combined loading, buckling experiments on axially
compressed cones, buckling experiments on externally pressurized cones, buckling experiments on cones subjected to
combined loading, buckling experiments on composite conical shells, equivalent cylinder approach, effect of initial
geometric imperfection on the buckling behaviour of cones and effect of imperfect boundary conditions on the buckling
behaviour of cones.
The dynamic performance of vertical cylindrical storage tanks under lateral impact of explosive fragments is important for its safe loading. In this paper, the method of combining experiments and numerical simulation is employed. Based on the simplified scaled model of thin-walled cylindrical containers, the lateral impact model experiments are carried out by using the drop hammer impact tester. Typical deformations and failure modes of the structure are then obtained. After processing the experimental data to obtain the load-deformation curve and the absorption energy curve, the curves are analyzed to study the dynamical response characteristics for cylindrical containers under impact as well as the influences for container length and impact velocity on the structural dynamical response. Then, the LS-DYNA program is applied for simulating the impact procedure and its dynamic response. With the reliability of the numerical model being verified, the stress distribution of the cylindrical container during the impact process is analyzed. Through finite element parametric analyses, combined with experimental results, the influences of impact velocity, length-to-radius ratio and radius-to-thickness ratio on dynamical responses as well as failure modes of the structure are investigated. It is shown that the failure mode of the cylindrical container changes with impact velocity and radius-to-thickness ratio, but is not affected by length-to-radius ratio. The variation of peak deformation and average force of the structure with parameters such as impact velocity are obtained.
This paper studied the energy absorption performance of conical tubes subjected to dynamic axial loading based on numerical finite element calculations. The influence of geometric parameters and material properties on the collapse behavior and energy absorption was discussed. The results showed that the two materials considered in this study have little effect on deformation mode of conical tubes, while the taper angle has a significant effect on deformation mode of conical tubes, and a classification chart of deformation modes for conical tubes was proposed. It was found that the conical tubes with TM mode have the best energy absorption characteristics, and the aluminum alloy conical tubes is more effective than similar tubes made from mild steel. Based on dimensional analysis, a model was proposed to predict the dynamic response of conical tubes under axial loading, including deformation displacement, energy absorption, specific energy absorption and mean crushing force. The results predicted by the proposed model were found to match well with the finite element analysis results. Furthermore, the equivalent substitution method between the aluminum alloy and mild steel conical tubes was studied, which concluded that the energy absorption equivalence method is better for lightweight design of energy-absorbing conical tubes.
Thin-walled hollow structures capable of large plastic deformations are ubiquitously present in sacrificial, high-capacity energy absorbers. A significant challenge in the field of structural crashworthiness is the myriad of loading conditions that an entity can experience. For example, bumper frames are equally vulnerable to direct and oblique impacts, where the latter cases are particularly prone to instability, under a broad range of loading rates and geometric and mechanical properties of the target structure. Traditional energy absorbers are designed with a single, characteristic force–displacement response which must be carefully tuned to accommodate a comprehensive range of loading conditions. This review highlights and summarizes the extensive research efforts directed towards the development of more advanced, adaptive energy absorbers with tailored mechanical responses and specialized characteristics, including prescribed steady-state loading regimes, load-limiting behavior and multi-to omnidirectional load bearing capabilities.
The novel concept of adaptive energy dissipation has recently emerged as a design philosophy intended to combat the diverse challenges in the field of structural crashworthiness by manipulating the structural and/or material properties of energy absorbers to enable more ideal, sophisticated mechanical responses. Passive adaptive energy absorbers are typically comprised of structures with varied (graded) dimensions, localized material refinement and/or compounded materials to yield structures which exhibit force responses with precisely designed corridors. The development efforts for active adaptive systems which can readily alter their geometry based upon data collected by external sensors to implement the preferred mechanical response for a given scenario, either before or during an impact event, are also showcased.
The primary objective of this present investigation is to study the
axial crushing characteristics of aluminium and composite wrapped
aluminium combined geometry tubes when subjected to static and impact loading conditions. The combined geometry tubes consist of cylindrical portion harnessed with plain end-cap, shallow spherical end-cap, and
hemispherical end-cap. Quasi-static compression and dynamic impact tests were conducted experimentally. The entire crushing process, including the initial stage of crushing, its localization, and the subsequent progressive folding has been carefully investigated by experiments. The axial crash performance of the various proposed end-capped tubes was also compared with non-capped cylindrical tubes and it was found that the initial peak force of the end-capped tubes is significantly reduced by 15–30% than the non-capped cylindrical tube without compromising the energy absorption
capacity.
For a good energy absorber, specific energy absorption (SEA) is also an influencing parameter to be considered and it should be high for better crashworthiness. Hybridization is one of the techniques to improve the SEA and hence hybrid composite wrapped aluminium tubes were also fabricated and tested. Further, the performance of the hybrid composite wrapped aluminium tubes were compared with bare aluminium combined geometry tubes and it was found that the specific energy absorption capacity of the hybrid tubes is 10-20% higher than the aluminium bare tubes.
It is evident that both the aluminium and composite wrapped aluminium combined geometry tubes significantly reduce the initial peak force and stabilize the crushing response without compromising the energy absorption capacity for both static and impact loading conditions. This is practically beneficial when large impact energy needs to be absorbed, thus attenuating the impact force transmitted to the protected structure and occupants. The significant outcomes of this study highlighted the advantages of using combined geometry cylindrical tubes in the automotive industry to design a convenient passive crash protection system for absorbing energy during car crash events.
In the present study, the energy absorption capacity of thin-walled end-capped conical geometries is taken into consideration and the collapse of the absorbers under different loading types and strengths is investigated. First, the manual spinning method is utilized in order to manufacture the specimen. The manufacturing geometry quality of the parts is then evaluated. Next, quasi-static load-deflection tests are employed to investigate the collapse process as well as the calculation of energy absorption for conical tubes. Drop experiments are carried out using a free flight drop tower on the conical tubes to obtain the acceleration time-history of the hammer. The time history of hammer velocity change during its collision with the energy absorber, the mean collapse load of the absorber and absorbed energy are calculated. The explicit FE code Abaqus/explicit is employed and validated using dynamic experimental data. Finally, a multi-objective optimization method is used to find the tube geometry which has the maximum energy absorption and specific energy absorption. The results show that the impactor's velocity, as well as the geometrical characteristics of the end-capped conical tubes, have significant effects on the energy absorption and specific energy absorption capacity.
Geometric imperfections and lower-bound methods used to calculate knockdown factors for composite cylindrical shells: This chapter provides a general overview of the important role that geometric imperfections play on degrading the load carrying capacity of cylindrical shell structures. The developments carried out during the European Project DESICOS will pivot the discussion, which will start with early and classic developments on the field and finish with early contributions that form the state-of-the-art techniques for calculating knockdown factors that can be applied during the design phase of cylindrical shells.
A geometrical model has been proposed to guarantee the axisymmetric axial crumpling of thin-walled 6061-T6 aluminum alloy frusta tubes. In this new design, to facilitate the axisymmetric collapse mode in frusta tube, circumferential grooves are cut from the outer and inner surfaces of the frusta at variant chosen positions along the tube. In the present study, several numerical simulations are carried out to study the energy absorption characteristics of the grooved frusta tubes. In order to verify these numerical results, some quasi-static axial compression tests are performed. Moreover, load–displacement curves and deformation mechanism of these structures under axial compression are described precisely. In addition, a series of experimental tests are conducted on thin-walled grooved cylinders and their crashworthiness characteristics are compared with grooved frusta tubes. The results show that the grooves can stabilize the collapse mode and control energy absorption of the frusta tubes.
Results of an experimental and numerical study on rib reinforced square cross-section thin wall extruded aluminium tubes formed by TIG welding process subjected to axial compression are presented in this paper. The distance between the ribs plays a vital role in modifying the energy absorption capacity of structure. Ribs assist the formation of more number of plastic hinges. As the rate of loading increases, the mean crushing force and energy absorption also increases for the same axial crushing distance. Results of the numerical study were found to be within 5-8% variation with the experimental results.
This paper experimentally investigates the crash responses of the empty and polyurethane foam-filled conical tubes with shallow spherical caps under quasi-static axial loading. To find more details about the energy absorption mechanism, finite element methods is used to simulate the crush process. In terms of finding more efficient and lighter crash absorbers particularly, the energy absorption and specific energy absorption and load ratio have been considered. The influences of the tube geometrical and material parameters such as radius of spherical region, wall thickness, length, semi-apical angle and foam density on the energy absorption mechanism have been investigated. This study provides practical information for the use of thin-walled tubes with shallow spherical caps as energy absorbers in aerospace applications to design reentry of sounding rocket based on foam-filled conical tube with shallow spherical caps.
Recent interest in lightweight metallic hollow sphere foams for aerospace applications requires a better physical understanding of dynamic properties of single spheres. Finite element modelling supported by high rate experiments was developed to investigate the underlying deformation and failure mechanisms of electrodeposited nickel thin-walled hollow spheres. Parametric simulation was performed to further explore the effect of sphere geometry (wall thickness to diameter ratio) and loading rate. It was found that decreasing the ratio of wall thickness to diameter tends to transit the side wall failure mode from bending to buckling. For a thin-walled sphere (the thickness to diameter ratio less than a critical value), the macroscopic dynamic behaviour is primarily dominated by the two deformation and failure mechanisms: (1) buckling failures of wall materials and (2) self-contacts of wall surfaces and wall-anvil contacts. At higher impact velocity (greater than a critical velocity), inertia effect due to dynamic localisation of wall crushing arises and significantly influences the deformation/failure mode of the sphere, resulting in an increased initial crushing strength and asymmetric deformation. Finally, the behaviour of hollow spheres was correlated to explore the power law behaviour of bulk foams with respect to the relative density; it was found that metallic thin-walled hollow sphere foams can be better approximated as open-cell rather than closed-cell foams.
This research deals with experimental and numerical axial quasi-static crash tests on end-capped cylindrical and conical tubes. Axial quasi-static crush tests have been generated for end-capped cylindrical and conical tubes. Furthermore, in order to gain more detailed knowledge about the crash process, finite element (FE) simulations of the experiments have been performed. The explicit FE code Abaqus/explicit was used and the results have been validated by experimental data. The elastic–plastic material model was used for the aluminium tubes. In terms of finding more efficient (higher energy absorption) and lighter crash absorbers particularly, the energy absorption, E, and specific energy absorption, SEA, have been considered. The influences of geometrical parameters of the tubes on their collapse response have also been investigated. Finally, a multiobjective optimisation method is used to find the tube geometry which has the maximum energy absorption and specific energy absorption.
We performed experimental and theoretical analyses that show a thin-walled cylinder with stiff ribs can be used as a structural element to improve or adjust energy absorption characteristics. We conducted impact crushing tests using several different cylinders with ribs. The experimental results showed that the axisymmetric and non-axisymmetric crushing modes were dependent on not only the cross-section size but also on the distances between the ribs. A critical distance between the ribs was found to exist for generating axisymmetric and non-asxisymmetric crushing modes and it was more than double the wavelength of axisymmetric wrinkles regardless of cylinder size. The mean crushing forces of the axisymmetric modes were found to be roughly 1.3 times larger than those of the non-axisymmetric modes. The theoretical results based on plastic hinge behavior showed good agreement with the experimental results. The effects of material and cylinder size on the crushing behavior of a cylinder with ribs were expressed using approximate mathematical equations. The critical distance between ribs for generating axisymmetric or non-axisymmetric crushing mode was also expressed approximately. Stiff ribs appropriately spaced in a cylinder were found to be effective in absorbing a large amount of energy with a short crushing deformation.
Collapse behaviour of aluminium thin conical frusta with shallow spherical caps (shells of combined geometry) is studied both experimentally and numerically. These shells were of four different thicknesses and were subjected to axial compression between two rigid platens under both quasi-static and impact loading. The R/t values of the spherical portion of the shells were varied between 27 and 218, and for the conical frusta portion, mean diameter-to-thickness (Dm/t) values were varied between 79 and 190. Quasi-static tests were performed on a UTM of 100T capacity with digital recording facility. Impact experiments were carried out on a drop mass set-up. A three-dimensional non-linear finite element analysis was carried out using LS-DYNA. Numerical results thus obtained were validated with the experimental results. Typical time histories of the specimen deformation and load compression curves were obtained. The behaviour of these shells of combined geometry is compared with the response of the shells of spherical or conical geometries. A discussion on their deformation behaviour, mean buckling load and energy absorbed is presented, and influence thereon of various parameters is discussed.
Experiments were performed wherein conical frusta of aluminium of thicknesses between 0.7 and 1.62mm 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.
Stamping processes induce plastic strain and changes in the thickness, shape and mechanical behaviour of sheet metal parts. Simulated crash tests on vehicles should theoretically take these changes into account in order to be as realistic as possible, but this is not actually feasible because the calculations required would be too time-consuming. Crash-modelling calculations, therefore, have to be based on simplifying hypotheses about the geometry and the mechanical behaviour of body parts. This study deals with the influences of such hypothesis on the impact behaviour of a 1-mm-thick steel dome bulged plastically at different thick strain levels ranging from −37% to −6% and impacted by an instrumented projectile with 13 m/s initial speed. Experimental results are compared to several impact finite element simulations based on different simplifying hypotheses about the geometry of the bulge and the strain hardening of the sheet metal and performed with the LS-DYNA finite element code.
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.
No standardised device is available yet to measure contact forces continuously during transverse impacts caused by a projectile on a metal plate or a thin-walled structure. This study describes the design and validation phases of an instrumented projectile (mass = 1 kg) that can be used to achieve such measurements. The impact force, indeed, is computed from the strain data collected by some strain gauges glued on to a projectile part, which remains elastic during shock. Under numerically defined conditions, the projectile geometry makes it possible to record signals that are not disturbed by the reflections of the compressive and tensile strength waves appearing inside the projectile during and after shock. Gauge signal post-filtering is then virtually useless. The strain gauge-instrumented projectile sensitivity is used to study the effects of small clamping pressure variations during the transverse impact study on shipbuilding steel plates. A second application deals with the impact of an automotive steel dome initially drawn with a bulge test apparatus.
Topics discussed at this symposium include the following: (1) Ship impacts: bow collisions; (2) New design-analysis techniques for blast loaded stiffened box and cylindrical shell structures; (3) Maximum strength of square thin-walled sections subjected to combined loading of torsion and bending; (4) Damage assessment of cylinders due to impact and explosive loading; (5) The crash response of circular tubes under general applied loading; (6) Dynamic response and failure of fully clamped circular plates under impulsive loading; (7) Deformation and rupture of blast loaded square plates-predictions and experiments; (8) Dynamic energy absorption characteristics of sandwich shells; (9) Residual tensile strength of ballistically damaged aluminum-based laminates; (10) High-speed impact response of particulate metal matrix composite materials- an experimental and theoretical investigation; (11) Dynamic response of the Space Station Freedom due to a module perforation by a hypervelocity impact; (12) The measurement of Mode I dynamic shear crack resistance in 50D structural steel using Double Cantilever Beam specimens; and (13) Ship-ramming after 1859.
This review is principally concerned with the relatively slow speed (of the order of, say, 50 m/sec) dynamic impact of metallic structures and dwells on the large deformation plasto-mechanics of the simple structure elements frequently used as parts of complete devices. The design aim is to dissipate kinetic energy irreversibly rather than convert and store it elastically and in particular, restitution is to be avoided. The aim is to safeguard people, cargo, machinery or even the vehicle itself from suffering an excessively high rate of retardation or degree of damage. Devices used to this end are usually one-shot items, i. e. , once having been deformed, they are discarded and replaced. The implication of designing an energy-absorbing device on the basis of its quasi-static loading response is that inertia effects within the device itself are unimportant and hence the kinetic energy is considered converted into plastic work in a quasi-static deformation mode. Exceptions to this behavior will be mentioned where appropriate. Besides a brief statement concerning strain-rate effects and other general features, we conclude with some comments concerning nonmetallic systems for absorbing impact energy.
The behavior of a rigid perfectly plastic spherical shell loaded by means of contact with a flat rigid surface is investigated. The predictions of the analysis are restricted to overall displacements lying between a few thicknesses and about one tenth the shell radius. At each stage of deformation an approximate limit load and corresponding velocity field are found for an assumed deformed shape of the shell, which later is shown to be very close to the calculated deformed shape. A simple formula relating the total axial force on the shell to the displacement of the shell is derived, and its range of validity is investigated. Finally, the results of some static tests of shells are shown to agree favorably with the theory.
Part 1: Simple struts have been impacted between travelling and stationary masses and the collapse found to consist of two distinct phases. The pre-failure phase, being primarily an elastic region, has been analysed by stability criteria and the post-failure phase by consideration of the plastic collapse of the strut. Associated with the pre-failure phase is a large transient deceleration which is found, among other parameters, to be a function of the strut shape.
Part 2: A series of sheet-metal structures have been impacted and, like struts, the collapse found to consist of pre- and post-failure phases of separate identities. The pre-failure phase is again associated with the shape of the structure and may give rise to a large transient deceleration. This analysis has led to the consideration of more complex elements, such as might be found in an automobile frontal structure, and finally to a complete automobile analogue. Conclusions are drawn about the structural parameters required to bring about specific deceleration characteristics in a vehicle crash.
Analysis and experimental results are presented on the plastic axisymmetric buckling of steep, truncated conical shells under axial compression. Specimens of 6061-T6 aluminum and type 416 stainless steel were tested; in spite of the considerable difference in the stress-strain curves for the two materials, the buckling modes observed in the experiments for geometrically identical cones were the same. Perturbation analysis, which takes account of the continuous change in direction of the plastic strain rate vector during buckling, is found to describe the essential features of the observed buckling deformation.
This paper provides a review of recent research advances and trends in the area of thin shell buckling. Only the more important and interesting aspects of recent research, judged from a personal view point, are discussed. In particular, the following topics are given emphasis: (a) imperfections in real structures and their influence; (b) buckling of shells under local/non-uniform loads and localized compressive stresses; and (c) the use of computer buckling analysis in the stability design of complex thin shell structures.
This paper considers the crushing which occurs in a spherical shell made of ductile material on striking a rigid wall. A static analysis is developed which allows for strain hardening, while for relatively low impact velocities, such as to permit the effect of inertia to be neglected, strain rate sensitivity is allowed for in an empirical manner.
The analysis presented is applicable to spherical shells with a mean radius to thickness ratio exceeding seven, constructed in ductile material obeying a simple power law work hardening relationship. The deformation is assumed to occur in two phases. In the first phase a local flattening of the shell in contact with the rigid wall occurs, while in the second, an axisymmetric dimpling of the previously flattened portion takes place.
Other workers have discovered that at radius to thickness ratios exceeding one hundred, a third mode of behaviour takes place when a number of non-axisymmetric nodes can be formed. The analysis in this paper, however, is only applicable to lower ratios when the crushing deformation, although reaching a value of half the radius, remains axisymmetric, as is borne out in all the experimental results examined for correlation.
A number of assumptions and simplifications are made, all of which are clearly stated below. Reference is made to earlier papers on this subject and a comparison is made of correlations by such earlier work and by the present analysis in respect of a group of quasi-static tests carried out by the Civil Engineering Department of the Queen's University of Belfast under a Leverhulme Trust fellowship funding: this is described in detail in Appendix 1.
The result of a moderate velocity impact test on a spherical shell of 625 mm diameter is utilized to examine the correlation given by the present analysis taking strain rate effect into account.
Note: the first author was mainly concerned with the analysis, while the co-authors carried out the experimental work detailed in Appendix 1.
The crushing analysis of rotationally symmetric plastic shells undergoing very large deflections is presented. A general methodology is developed and simple closed-form solutions are derived for the case of a conical shell, a spherical shell under point load, a spherical shell crushed between rigid plates and under boss loading, and a spherical cap under external uniform pressure.
The quasi-static loading of an open hemispherical shell along its axis of symmetry through a rigid flat plate is considered with particular reference to large deformations and buckling.
Experiments were conducted wherein aluminium conical frusta of different semi-apical angles varying over a wide range from 16.5° to 65° and different slenderness ratios (t/d), were subjected to axial compression. Their various modes of collapse, load-deformation and energy-compression behaviour, and initial peak and mean collapse loads are studied from the experiments. Typical results are presented. An analytical model is proposed for the prediction of load-deformation and energy-compression curves. The influence of semi-apical angle and the slenderness ratio of the conical frusta on the modes of collapse and load-deformation curves is discussed. The results predicted from the proposed analytical model are found to match well with the experiments.
Experimental and numerical results on seven 580 mm diameter, spun steel, hemispherical shells subjected to external pressure are discussed in the paper. The average wall thickness of the shells varied from 0·37mm to 2·5mm. Careful shape and thickness measurements on all the shells were obtained and utilised in several types of analysis (2-D Finite Element, bestfit axisymmetric, axisymmetric with a local fattening, etc.). None of the analysis techniques employed proved to be entirely reliable insofar as predicting the collapse strength of the spun steel hemispheres. For example, the ratios of the experimental to the 2-D FE numerical collapse pressures were between 0·56 and 1·21.The test results were also compared with the ECCS design curve and it is shown that one should use the minimum shell thickness for design purposes and not rely on the average wall thickness (three test results plotted below the design curve when the average wall thickness was used).
A theoretical model describing the progressive extensible plastic collapse of thin-wall conical and cylindrical shells is presented. The proposed theory enables the load-deflection curves during axial compression following the deformation history of the shell to be evaluated. The comparison of theoretical curves with experimental ones shows a fair degree of accuracy.
Thin-walled circular cylinders, and frusta (truncated circular cones) of aluminium alloy were subjected to axial static loading. Their initial axial length and the outside diameter of the cylinders and frusta (the larger top end) were kept constant whilst their wall thickness was varied. The load-deformation or compression behaviour of the cylinder and frusta of various thicknesses and semi-apical angles were recorded and the modes of collapse were observed and studied. The main purpose of results for circular cylinders is to give a basis of comparison for the frusta. Relatively thick tubes fail by collapsing into circumferential axisymmetric rings and thin ones by folding progressively into diamond-shaped lobes after assuming an initially axisymmetric ring mode of deformation. In the latter case the initial axisymmetric rings developed into nonsymmetric diamond patterns (elliptic, triangular and square, etc.) as loading progressed. Also, initially non-symmetric diamond buckle patterns were observed to be characteristic modes of frustum collapse.Initial peak failure loads and mean post-buckling loads for the various modes of deformation were obtained experimentally. It is shown that buckling loads for both cylinders and frusta increase with increasing slenderness‡ ratio ( for cylinders and for frusta) following, broadly, a parabolic law. Empirical expressions for the post-buckling load required to effect crumpling have been obtained.
Uniformly thin circular cylinders and frusta (truncated circular cones) of low carbon steel were subjected to axial loading at elevated strain-rates. Their initial axial length and the outside diameter of the cylinders and frusta (the larger top end) were kept constant whilst their uniform wall thickness was varied. The load-deformation or compression behaviour of the cylinders and frusta for the two semi-apical angles used, 5° and 10°, were recorded and the modes of collapse were observed and are discussed. Initial axisymmetric rings (‘ring’, ‘bellows’ or ‘concertina’ buckling) developed into non-symmetric ‘diamond’ patterns (elliptic, triangular and square, etc.) as loading progressed and initially non-symmetric diamond buckle patterns were observed to characterise the modes of frustum collapse.
An experimental investigation has been carried out to study the collapse mechanisms and the energy absorption capacities of the glass/polyester composite hemi-spherical shells under both quasi-static and drop hammer loading. The shells were made of randomly oriented glass fibre mats and polyester resin. Quasi-static tests were conducted at speed of 2 mm/min. and the impact velocities varied from 5 to 9 m/s. The radii of the shells varied from 53.5 to 106.1 mm and their thicknesses from 1.10 to 2.84 mm. Influence of these variables on the mechanism of deformation has been discussed. Experiments on 45 shells showed that their progressive crushing occurred due to the formation of successive zones of fracture. Based on these observations an analytical model has been developed for the prediction of load-deformation and energy-compression curves. The results thus obtained are found to match well with the experiments. It is seen that the ratio of the mean collapse loads recorded in impact and quasi-static tests for a given shell is greater than one but it decreases with the increase in thickness of the shell.
Aluminium spherical shells of R/t values between 15 and 240, were axially compressed in an INSTRON machine between flat plates. The modes of their collapse, load-compression and energy-compression curves, and mean collapse loads are presented. A simple analytical model has been developed for the prediction of load-compression and energy-compression curves for the metallic spherical shells, by using the concepts of stationary and rolling plastic hinges. The results thus obtained match well with the experimental results. These results have also been compared with the solutions proposed in earlier studies. Behaviour of these shells is compared with the response of spherical shells (aluminium, mild steel and galvanised steel) of shallow depth, which were also subjected to axial compression between rigid plates. Their load-deformation curves are presented, and their energy-compression behaviour and mean collapse loads are discussed.
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Comparison of mean collapse loads of conical frusta of different t=d values ðY
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ARTICLE IN PRESS Fig. 14. Comparison of mean collapse loads of conical frusta of different t=d values ðY ¼ 53 Þ: G.L.E. Prasad, N.K. Gupta / International Journal of Impact Engineering 32 (2005) 400–415
Buckling of thin shells
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Update to metallic energy dissipating systems
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An assessment of energy absorbing devices for prospective use in aircraft impact situations
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