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.     

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.     

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.     

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.     

Quasi-static axial buckling behavior of NiTi thin-walled cylindrical shells

The quasi-static axial buckling response of super-elastic NiTi thin-walled cylindrical shells has been investigated. The results show that the main buckling pattern is the non-axisymmetric mode with various circumferential patterns depending on the geometry of a specimen. The specific energy is strongly related to the geometry and the buckling mode of a specimen. The austenite–martenite phase transition is concentrated in the buckling area to form so-called phase transition hinges. The buckling behavior of a specimen is significantly related to the phase transition and phase transition hinges. After unloading a NiTi specimen can recover to its initial shape, which differs from an elastic–plastic specimen.     

Dynamic torsional buckling of cylindrical shells in Hamiltonian system

By considering the effect of stress waves in a Hamiltonian system, this paper treats dynamic buckling of an elastic cylindrical shell which is subjected to an impact torsional load. A symplectic analytical approach is employed to convert the fundamental equations to the Hamiltonian canonical equations in dual variables. In a symplectic space, the critical torsion and buckling mode are reduced to solving the symplectic eigenvalue and eigensolution, respectively. The primary influence factors, such as the impact time, boundary conditions and thickness, are discussed in detail through some numerical examples. It is found that boundary conditions have limited influence except free boundary condition in the context of the scope in this paper. The localization of dynamic buckling patterns can be observed at the free end of the shell. The new analytical and numerical results serve as guidelines for safer designs of shell structures.     

Creep buckling of cylindrical shells under external lateral pressure

In this paper, the authors present the results of an analysis of creep buckling of cylindrical shells under external lateral pressure. The nature of the material, the dimensions of the specimens and the type of boundary permit an elastic analysis of this phenomenon. The results of tests and calculations show on the one hand that this phenomenon is very sensitive to the presence of initial geometric imperfections; and on the other hand that it is possible to establish a monograph giving the critical time of an electroplated nickel shell as a function of its initial imperfections and of the nominal applied load. In this manner, the same reasoning can be applied to other shells made up of other materials that are sensitive to creep (resins, concretes, wood, metals at high temperatures, etc.).     

Dynamic and static axial crushing of axially stiffened cylindrical shells

The axial impact of cylindrical tubes, which incorporate axial stiffeners, is examined in this paper. For comparison purposes, the effect of static loading is also studied. An examination is made into the influence of stiffener depth (T), number of stiffeners (N) and the effect of placing the stiffeners externally or internally.

The experimental results on mild steel specimens show that there are considerable differences between the static and dynamic modes of failure, and that an optimum T/D ratio may exist for a given value of N.     

Dynamic buckling of stiffened cylindrical shells of revolution under a transient lateral pressure shock wave

A modal method of analysis is used to determine the response of an infinitely long stiffened cylindrical shell of revolution to a transient lateral pressure produced by an underwater explosion and propagating in an acoustic fluid. The shell is initially immersed, hence prestressed by the external hydrostatic pressure. A theory of dynamic buckling is then developed for cylindrical shells subjected to transverse pressure pulses of different durations.     

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.     

A study of elastic-plastic buckling of cylindrical shells under torsion

The elastic-plastic buckling of cylindrical shells under torsion is analysed with a deep thick-shell model under various boundary conditions. The word ‘deep’ means that in the general equations of equilibrium the three non-linear terms that involve the torsional force are all retained for the buckling analysis. In the Donnell-type shallow-shell theory, however, only one of such terms is retained. The word ‘thick’ means that in calculating strains and stress resultants the factor (1+z/R) is retained. This factor results from the trapezoid-like shape of the cross-section and is usually neglected in the thin-shell theory. For boundary conditions, not only the conventional geometrical boundary conditions, which are in terms of displacements and rotations, but also the mechanical boundary conditions, which are in terms of forces and moments, are considered. The numerical results of examples assess the effect of the additional non-linear terms, the effect of the factor (1+z/R), and the effect of the mechanical boundary conditions.     

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.     

轴压功能梯度材料圆柱壳的弹、塑性屈曲分析

功能梯度材料板壳弹性屈曲领域研究已取得许多卓有成效的成果,而弹塑性、塑性屈曲问题的研究却鲜有报道。针对功能梯度材料圆柱壳的弹、塑性屈曲问题,采用有限元软件ABAQUS开展了数值模拟与分析。分析中采用叠层模型,定义材料沿厚度方向的梯度特性,计入材料的物理非线性和前屈曲几何非线性的影响。计算得到弹、塑性功能梯度材料圆柱壳的屈曲临界荷载和变形模式,给出了壳体从弹塑性屈曲到塑性屈曲的转化过程,并对屈曲类型对应的区域进行划分,研究了壳体厚度、组分参数对屈曲临界状态的影响。     

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.     

Reduced stiffness buckling of sandwich cylindrical shells under uniform external pressure

A reduced stiffness lower bound method for the buckling of laterally pressure loaded sandwich cylindrical shell is proposed. Also, an attempt is made to assess the validity of the proposed reduced stiffness lower bound with FEM numerical examples. In addition, the proposed method is compared with classical and Plantema's approaches of the buckling of the laterally pressure loaded sandwich cylindrical shell. Comparison of the proposed reduced stiffness lower bound with that obtained from non-linear FEM analysis verifies that it indeed provides a safe lower bound to the buckling of laterally pressure loaded sandwich cylindrical shells. The attractive feature of the proposed reduced stiffness method is that it can be readily used in designing laterally pressure loaded sandwich cylindrical shells without being concerned about geometrical imperfections.     

下部支承柱受冲击作用时单层柱面网壳的动力响应分析

为研究单层柱面网壳在下部支承结构受到冲击荷载作用时的动力响应,建立带有下部支承柱的36m×20m三向网格网壳,根据结构的应力和变形,将结构在冲击荷载作用下的动力响应分为3种模式.分析了网壳在不同响应模式下的变形特征,并对冲击荷载作用下的网壳结构塑性发展规律进行了研究.通过改变冲击物的质量、冲击速度和冲击作用点的位置,讨...     

Deflection and buckling behavior of thin,circular cylindrical shells under wind loads

Some wind-tunnel tests have been conducted on the buckling behavior of closed-ended, thin cylindrical shells such as silos. Detailed measurements of the prebuckling deflections as well as of the buckling pressures were made with a variety of elastic cylinders in both smooth and turbulent flows.The results indicate that the prebuckling deflection is extremely sensitive to the wind pressure distribution, while the buckling pressure is less sensitive to it. It was also found that the pressure—deflection relationship exhibits a marked nonlinearity as the wind pressure approaches the buckling pressure. The experimental results were compared with the results of a stability analysis based on Donnell's theory, and a relatively good agreement was derived with respect to the buckling pressure.Furthermore, on the basis of the experimental results, an empirical formula for the buckling pressure was proposed as function of the height/radius ratio and the radius/ thickness ratio of the cylindrical shell.     

Elephant's foot buckling in pressurised cylindrical shells

Metal cylindrical bins, silos and tanks are thin shell structures subject to internal pressure from stored materials together with axial compression from the frictional drag of stored materials on the walls and horizontal loads. The governing failure mode is frequently buckling under axial compression. The internal pressure exerted by the stored fluids or solids can significantly enhance the buckling strength, but high internal pressures lead to severe local bending near the base. Local yielding then precipitates an early elastic‐plastic buckling failure. This failure mode, commonly known as “elephant's foot buckling”, has received relatively little attention to date and until recently was often ignored in tank and silo design. This problem is an unusual buckling condition, because it involves very high tensile stresses in one direction, coupled with rather small compressive stresses in the orthogonal direction. Thus, although it is a buckling failure involving considerable plasticity, it occurs at low buckling stresses and under conditions that appear to be classically “slender”. The normal concatenation of “slender” with “elastic” in buckling formulations does not apply at all here. This paper describes alternative approaches to the formulation of design rules for the elastic‐plastic instability and collapse of axially‐loaded internally‐pressurised thin cylindrical shells adjacent to the base support. The differences between the different approaches arise from different conceptual models for the manner in which an elastic‐plastic slender structure instability should be treated.     

Behaviour of FRP-jacketed circular steel tubes and cylindrical shells under axial compression

Fibre-reinforced polymer (FRP) jackets have been widely used to confine reinforced concrete (RC) columns for enhancement in both strength and ductility. This paper presents the results of a recent study in which the benefit of FRP confinement of hollow steel tubes was explored. Axial compression tests on FRP-confined steel tubes are first described. Finite element modelling of these tests is next discussed. Both the test and the numerical results show that FRP jacketing is a very promising technique for the retrofit and strengthening of circular hollow steel tubes. In addition, finite element results for FRP-jacketed thin cylindrical shells under combined axial compression and internal pressure are presented to show that FRP jacketing is also an effective strengthening method for such shells failing by elephant’s foot collapse near the base.     

Plastic buckling of axially compressed circular cylindrical shells

For elastic-plastic cylindrical shells with initial axisymmetric imperfections bifurcation into a non-axisymmetric shape is analysed. The shell material is represented by a phenomenological plasticity theory that accounts for the formation of a vertex on subsequent yield surfaces. The influence of various geometric and material parameters is investigated for a wide range of radius-to-thickness ratios. It is shown that for the thicker shells bifurcation generally occurs beyond the maximum axial compressive load. A few analyses for shells with additional non-axisymmetric imperfections show the unstable post-bifurcation behaviour and the sensitivity to imperfections of more general shapes.