Design of thin wall structures for energy absorption applications: Enhancement of crashworthiness due to axial and oblique impact forces

This paper describes a computationally aided design process of a thin wall structure subject to dynamic compression in both axial and oblique directions. Several different cross sectional shapes of thin walled structures subjected to direct and oblique loads were compared initially to obtain the cross section that fulfills the performance criteria. The selection was based on multi-criteria decision making (MCDM) process. The performance parameters used are the absorbed crash energy, crush force efficiency, ease of manufacture and cost. Once the cross section was selected, the design was further enhanced for better crash performances by investigating the effect of foam filling, increasing the wall thickness and by introducing a trigger mechanism. The outcome of the design process was very encouraging as the new design was able to improve the crash performance by an average of 10%.     

Multiobjective optimization of orthogonally stiffened cylindrical shells for minimum weight and maximum axial buckling load

In the present research, the weight and axial buckling optimization of orthogonally stiffened cylindrical shells is carried out by the Genetic Algorithm. Constraints include two nondimensional functions of weight and buckling load in such a way that the stiffened shell has no increase in the weight and no decrease in the buckling load with respect to the initial unstiffened shell. In analytical solution, the Rayleigh–Ritz energy procedure is applied and the stiffeners are treated as discrete members. The optimization is implemented for shells with simply supported end conditions stiffened by four shapes of stiffeners including rectangular-, cee-, I-, and hat-shaped ones. The results show that the I-section and rectangular-section stiffeners are, respectively, the most and the least efficient in designing stiffened cylindrical shells for minimum weight and maximum critical axial buckling load.     

Experimental studying of buckling of stringer cylindrical shells under axial compression

Results of tests on axial compression of small-sized quality steel cylinder shells strengthened by 24 and 36 longitudinal thin-walled stiffeners are presented. The shell length was varied. Shells both with inside and outside stiffening were tested at simply supported and clamped edges. The shell carrying capacity that was governed in the tests by overall buckling in the elastic range was compared with the estimated critical loads based on structural-orthotropic theory. The satisfactory quantitative correlation has been received only for the long simply supported shells with 36 inner stiffeners, which demonstrated insignificant effect of local undulation that preceded overall deflections. The experimental and the theoretical results differed significantly (twice as much) when the actual mechanism of lateral deflection caused by the intensive local undulation differed from the adopted model.     

Transient dynamic response of composite circular cylindrical shells under radial impulse load and axial compressive loads

Free and forced vibration of composite circular cylindrical shells are investigated based on the first love's approximation theory using the first-order shear deformation shell theory. The boundary conditions (BCs) are considered as clamped-free edges. The dynamic response of the composite shells is studied under transverse impulse and axial compressive loads. The axial compressive load was less than critical buckling loads. The modal technique is used to develop the analytical solution of the composite cylindrical shell. The solution for the shell under the given loading conditions can be found using the convolution integrals. The effect of fiber orientation, axial load, and some of the geometric parameters on the time response of the shells has been shown. The results show that dynamic responses are governed primarily by natural period of the structure. The accuracy of the analysis has been examined by comparing results with those available in the literature and experiments.     

On the buckling of cylindrical shells with through cracks under axial load

Presence of cracks or similar imperfections can considerably reduce the buckling load of a shell structure. In this paper, the buckling of cylindrical shells with through cracks has been studied. A general finite element model has been proposed, verified and applied to some novel cracked shell buckling problems for which documented results are not available. A special purpose program has been developed for generating finite elements models of cylindrical shells with cracks of varying length and orientation. The buckling behavior of cracked cylinders in tension and compression has been studied. The results of the analysis are presented in parametric form when it seems to be appropriate. Sensitivity of the buckling load to the crack length and orientation has also been investigated.     

Dynamic buckling of fiber composite shells under impulsive axial compression

The paper deals with dynamic buckling due to impulsive loading of thin-walled carbon fiber reinforced plastics (CFRP) shell structures under axial compression. The approach adopted is based on the equations of motion, which are numerically solved using a finite element code (ABAQUS/Explicit) and using numerical models validated by experimental static buckling tests. To study the influence of the load duration, the time history of impulsive loading is varied and the corresponding dynamic buckling loads are related to the quasi-static buckling loads. To analyse the sensitivity to geometric imperfections, the initial geometric imperfections, measured experimentally on the internal surface of real shells, are introduced in the numerical models. It is shown numerically that the initial geometric imperfections as well as the duration of the loading period have a great influence on the dynamic buckling of the shells. For short time duration, the dynamic buckling loads are larger than the static ones. By increasing the load duration, the dynamic buckling loads decrease quickly and get significantly smaller than the static loads. Since the common practice is to assume that dynamic bucking loads are higher than the static ones, which means that static design is safe, careful design is recommended. Indeed, taking the static buckling load as the design point for dynamic problems might be misleading.     

Tailoring the elastic postbuckling response of thin-walled cylindrical composite shells under axial compression

The buckling of cylindrical shells has long been regarded as an undesirable phenomenon, but increasing interests on the development of active and controllable structures open new opportunities to utilize such unstable behavior. In this paper, approaches for modifying and controlling the elastic response of axially compressed laminated composite cylindrical shells in the far postbuckling regime are presented and evaluated. Three methods are explored (1) varying ply orientation and laminate stacking sequence; (2) introducing patterned material stiffness distributions; and (3) providing internal lateral constraints. Experimental data and numerical results show that the static and kinematic response of unstable mode branch switching during postbuckling response can be modified and potentially tailored.     

Effects of openings of the buckling of cylindrical shells subjected to axial compression

Experimental and numerical methods are used to study the stability problem of cylindrical shells with cut-outs. The paper presents parametric research of the shape (square, rectangular, circular), the dimensions (axial and circumferential sizes, diameter) of the hole. The effect of the location and the number of the holes are also studied. The analysis indicates that the critical load is sensitive to the opening angle or circumferential size of the hole. The function (critical load-opening angle) is linear for large openings and independent of the geometrical imperfections of the shell. However for small openings, it is necessary to take into account the coupling between the initial geometrical imperfections and the openings. The linear approach does not fit because of the importance of the evolution of the displacements near the openings. These results will be used for the development of European rules.     

Stability of circular cylindrical steel shells under combined loading

Circular cylindrical shells made of steel are used in a large variety of civil engineering structures, e.g. in off-shore platforms, chimneys, silos, tanks, pipelines, bridge arches or wind turbine towers. They are often subjected to combined loading inducing membrane compressive and/or shear stress states which endanger the local structural stability (shell buckling). A comprehensive experimental and numerical investigation of cylindrical shells under combined loading has been performed which yielded a deeper insight into the real buckling behaviour under combined loading . Beyond that, it provided rules how to simulate numerically the realistic buckling behaviour by means of substitute geometric imperfections. A comparison with existing design codes for interactive shell buckling reveals significant shortcomings. A proposal for improved design rules is put forward.     

Dynamic local and global buckling of cylindrical shells under axial impact

In this paper, the local and global buckling of cylindrical shells under axial, compressive impact loads is studied. A Hamiltonian system is introduced in the problem. The fundamental problem in the system can be described mathematically by the Hamiltonian dual equations, which are expressed in four pairs of dual variables. The problem is reduced to a problem of eigenvalues and eigensolutions for critical loads and buckling modes, respectively. The buckling modes can be described by their respective orders and they are grouped into two classes, the short-wave or local buckling and the long-wave or global buckling. The solutions are obtained analytically and numerically, and some rules observed are indicated.     

Buckling of intermediate ring supported cylindrical shells under axial compression

This paper is concerned with the elastic buckling of axially compressed, circular cylindrical shells with intermediate ring supports. The simple Timoshenko thin shell theory and the more sophisticated Flügge thin shell theory have been adopted in the modeling of the cylindrical shells. We used these two representative theories to examine the sensitivity of the buckling solutions to the different degree of approximations made in shell theories. By dividing the shell into segments at the locations of the ring supports, the state-space technique is employed to derive the solutions for each shell segment and the domain decomposition method utilized to impose the equilibrium and compatibility conditions at the interfaces of the shell segments. First-known exact buckling factors are obtained for cylindrical shells of one and multiple intermediate ring supports and various combinations of boundary conditions. Comparison studies are carried out against benchmark solutions and independent numerical results from ANSYS and p-Ritz analyses. The influence of the locations of the ring supports on the buckling behaviour of the shells is examined.     

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.     

Numerical and experimental investigations on buckling of steel cylindrical shells with elliptical cutout subject to axial compression

The effect of cutouts on load-bearing capacity and buckling behavior of cylindrical shells is an essential consideration in their design.In this paper, simulation and analysis of thin steel cylindrical shells of various lengths and diameters with elliptical cutouts have been studied using the finite element method and the effect of cutout position and the length-to-diameter (L/D) and diameter-to-thickness (D/t) ratios on the buckling and post-buckling behavior of cylindrical shells has been investigated. For several specimens, buckling test was performed using an INSTRON 8802 servo hydraulic machine and the results of experimental tests were compared to numerical results. A very good correlation was observed between numerical simulation and experimental results. Finally, based on the experimental and numerical results, formulas are presented for finding the buckling load of these structures.     

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.     

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.     

Deformation and buckling of axially compressed cylindrical shells with local loads in numerical simulation and experiments

By means of geometrically non-linear modeling of the test process for high-quality specimens of thin-walled cylinders using a shell finite element implemented in ANSYS, it has been proved that this numerical approach is applicable for design of real axially compressed circular cylindrical shells under external local quasi-static loads.     

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.     

An analytical method for the buckling analysis of cylindrical shells with non-axisymmetric thickness variations under external pressure

This article presents an analytical method for the buckling analysis of laterally pressured cylindrical shells with non-axisymmetric thickness variations. The previous results for thickness variations under external pressure are reviewed firstly. Then, a general analytical method that combines the perturbation method and Fourier series expansion is developed to derive buckling load formulas, which is in terms of thickness variation parameter up to arbitrary order. A classical non-axisymmetric thickness variation is discussed in detail by the presented analytical method. When non-axisymmetric modal thickness variation becomes axisymmetric, the buckling loads degenerate to the known results. Furthermore, the influence of circumferential modal thickness variation with mode corresponding to twice the circumferential buckling mode on the buckling of laterally pressured cylindrical shells is analytically investigated and the results show a great agreement with previous numerical ones by Gusic et al. Thus we confirm the presented method. In addition to theoretical analysis, calculations and comparisons are also performed. The general analytical method presented in the article can be utilized to determine the buckling loads of shells with general thickness variations.     

Buckling of cylindrical shells under transverse shear

This work concerns with experimental studies on buckling of thin-walled circular cylindrical shells under transverse shear. The buckling loads are also obtained from finite element models, empirical formulae and codes and are compared. Experiments are conducted on 12 models made of stainless steel by rolling and longitudinal seam welding. In situ initial geometric imperfection surveys are carried out. The tests are conducted with and without axial constraint at the point diametrically opposite the loading. Theoretical analyses are carried out using ABAQUS finite element code. Two finite element models considered are: (i) geometry with real imperfection (FES-I) and (ii) critical mode imperfect geometry (FES-II). In the former, the imperfections are imposed at all nodes and in the latter, the imperfection is imposed by renormalizing the eigen mode, using the maximum measured imperfection. General nonlinear option is employed in both the cases for estimating the buckling load. Galletly and Blachut’s expressions, design guidelines of Japan for LMFBR main vessel expressions (empirical formulae), ASME and aerospace structural design codes are used for comparing with experimental loads.The comparisons of experimental, numerical and analytical buckling loads reveal the following. The numerical results are always higher than the experimental values; the percentage difference depends on the wall thickness. FES-II predicts somewhat a lower load than that of the FES-I. The Japanese guidelines predict the lowest load, which is conservative. Experimental loads are lower than that predicted by both ASME and aerospace structural design codes.     

Reliable and accurate prediction of the experimental buckling of thin-walled cylindrical shell under an axial load

Reliable and accurate method of the experimental buckling prediction of thin-walled cylindrical shell under an eccentric load is presented. The experimental arrangement and specimens are discussed in detail, including the measurement of the geometric imperfections of the specimen's surface using a coordinate measuring machine. Different FE models, in terms of complexity, are used to simulate the experiment arrangement in an attempt to get a good agreement with the experimental buckling loads and study the effect of measured initial geometric imperfections, load eccentricity, load eccentricity position along the shell's circumferential direction and different experimental arrangement that influence the boundary conditions. It has been demonstrated that FE models with simplified rigid support conditions overestimate the prediction of the experimental buckling load even though these models included the effects of the measured initial geometric imperfections and load eccentricity. By contrast, FE models with realistically modeled support conditions achieved the best result. The average deviation −1.59% from the experimental buckling loads was achieved using the FE model simulating the mounting devices as elastic bodies and with surface-to-surface contact interaction behavior on the support. The presented work also demonstrated the strong influence of the eccentric load position along the imperfect shell's circumferential direction on the buckling of the thin-walled shell.