Stability analysis of a cylindrical shell with axially symmetric defects under axial compression based on the reduction stiffness method

Calculating the modes of cylindrical shell, then embed them into ideal perfect cylindrical pressure-resistant shell as the initial geometric imperfections to form the modal. According to the characteristics of each mode, the first 30 modes can be classified into four types, and it is found that the mode of the first type is the worst defect form. By calculation, the cylinder shell has the minimum ultimate strength when the 23rd mode happened. The sensitivity analysis of cylindrical shells with initial geometric defects shows that the critical buckling load has approximate linear relationship with different thickness radius ratio and defect amplitude. Six cylindrical shells of different materials are selected for research, and it is found that although the modal orders of the worst geometric defects of various materials are not the same, they all belong to the first type of mode. The comparison showed that the 921 steel and 909 steel materials are economic.

Buckling of cracked cylindrical thin shells under combined internal pressure and axial compression

Elastic buckling analysis of imperfect FGM cylindrical shells under axial compression in thermal environments is carried out, using two different models for geometrical imperfections. The material properties of the functionally graded shell are assumed to vary continuously through the thickness of the shell according to a power law distribution of the volume fraction of the constituent materials, also temperature dependency of the material properties is considered. Derivation of equations is based on classical shell theory using the Sanders nonlinear kinematic relations. The stability and compatibility equations for the imperfect FGM cylindrical shell are obtained, and the buckling analysis of shell is carried out using Galerkin’s method. The novelty of the present work is to obtain closed form solutions for critical buckling loads of the imperfect FGM cylindrical shells, which may be easily used in engineering design applications. The effects of shell geometry, volume fraction exponent, magnitude of initial imperfections, and environment temperature on the buckling load are investigated. The results reveal that initial geometrical imperfections and temperature dependency of the material properties play major roles in dictating the bifurcation point of the functionally graded cylindrical shells under the action of axial compressive loads. Also results show that for a particular value of environment temperature, critical buckling load is almost independent of volume fraction exponent.

Cylindrical shells under uniaxial compression and spherical shells under equi-biaxial compression display the most extreme buckling sensitivity to imperfections. In engineering practice, the reduction of load carrying capacity due to imperfections is usually addressed by use of a knockdown factor to lower the critical buckling stress estimated or computed without accounting for imperfections. For thin elastic cylindrical shells under uniaxial compression and spherical shells under equi-biaxial compression, the knockdown factor is typically as small as 0.2. This paper explores the alleviation of imperfection-sensitivity for loadings with a reduced circumferential (transverse) membrane stress component. The analysis of Koiter (1963) on the effect of an axisymmetric imperfection on the elastic buckling of a cylindrical shell under uniaxial compression is extended to both cylinders and spheres for loadings that produce general combinations of biaxial membrane stresses. Increases in the knockdown factor due to a reduction of the transverse membrane component are remarkably similar for cylindrical and spherical shells.

This paper presents an analytical approach to analyze the nonlinear stability of thin closed circular cylindrical shells under axial compression with material properties varying smoothly along the thickness in the power and exponential distribution laws. Equilibrium and compatibility equations are obtained by using Donnel shell theory taking into account the geometrical nonlinearity in von Karman and initial geometrical imperfection. Equations to find the critical load and the load-deflection curve are established by Galerkin's method. Effects of buckling modes, of imperfection, of dimensional parameters and of volume fraction indexes to buckling loads and postbuckling load-deflection curves of cylindrical shells are investigated. In case of perfect cylindrical shell, the present results coincide with the ones of the paper [13] which were solved by Ritz energy method.

This paper proposes a new type of shell, similar to a cylindrical shell, which has significantly higher buckling strength when subjected to an arbitrary combination of uniform external pressure and axial compression. The underlying principle consists in a slight modification of the perfect cylinder in order to counteract the natural deformations which get larger and larger and lead to the collapse of the structure. Such shells are called ASTER shells. The concept has been validated through experiments, then analyzed numerically in order to explain what was observed and to propose avenues for improvements. The shells were made of electrodeposited nickel. The material was characterized. The chosen specimens were carefully measured to characterize their thickness and initial imperfections, then tested under the various types of loading. Then they were analyzed using finite elements. Thus, we were able to compare the finite element predictions with the experimental results. This comparison shows that plasticity has a decisive influence on the critical load and that linear elastic dimensioning leads to a serious overestimation of the experimental critical load. Contrary to perfect cylindrical shells, this type of shell is not significantly affected by geometric imperfections: this is another advantage of this type of design. Finally, we propose a numerical analysis in order to optimize the choice of the shape and propose shapes which resist buckling much better than a smooth cylinder when subjected to uniform external pressure, axial compression or a combination of both.

Compressed cylindrical shells are common in our daily life, such as rolled-up sleeves and a retreated package of drinking straws. The deformations on these cylindrical shells with a rigid core are often random and unpredictable. In contrast, compressed beer can exhibit uniform arrays of diamonds, called the Yoshimura pattern. To elucidate the difference between these systems, we combine molecular dynamics simulations and experiments to study the deformation on a compressed cylindrical shell with a rigid core. By thoroughly exploring different material parameters, we are able to pin down the mode diagram.

Thin cylindrical shells in axial compression are known to be highly sensitive to geometric imperfections. Previous theoretical and experimental investigations have mostly concentrated on imperfections of small amplitude extending over the whole surface or at least over the whole circumference of the cylinder. Local imperfections occurring naturally are often found to be similar in form to the diamond-shaped facets of the buckle pattern of the collapsed cylinder. The current study is aimed at investigating experimentally the effect of such facet-shaped dimples on the load bearing capacity of the axially loaded circular cylindrical shell and evaluating the applicability of the space frame theory in predicting the same. The space frame theory predicts the secondary collapses observed in cylindrical shells under axial compression in terms of the buckling strengths of the diagonal members of an equivalent space frame having the geometry of the Yoshimura pattern. The proposed application of the space frame model to estimate the load carrying capacity of shells with diamond-shaped defects is based on the hypothesis that the effect of such a defect is similar to that of a facet of the same size in a buckled cylinder. Central to this model is the effective width of the flanges of the diagonal members of the space frame. In the present work modifications are introduced in the space frame theory to accommodate an analytical determination of the effective width of the flanges. Geometric constraints on the buckled configuration of the axially loaded cylinder are also investigated.

Initial geometric imperfections have a great effect on the buckling strength of thin-walled cylindrical shells under axial compression, and the circumferential weld-induced imperfection is usually the most deleterious imperfection form. Two axisymmetric imperfection forms proposed by Rotter and Teng have widely been employed in the buckling analysis of cylindrical shells. However, the applicability of the two forms for tapered-wall cylinders needs further study, since they are derived from the elastic bending theory for long thin-walled cylinders with a constant wall thickness. This paper presents a modified form of circumferential imperfection for tapered-wall cylinders. Finite element analyses are carried out by employing the trapezoidal strain field approach to model the welding process, and the obtained circumferential depression shapes are used to evaluate the availability of the modified imperfection form. It is shown that the modified imperfection form is reasonable for any wall thickness ratio bet...

The composite cylindrical shell pressure structure is widely used for autonomous underwater vehicle (AUV). To analyze the critical buckling problem of variable stiffness (VS) composite pressure structure of AUV, a discrete finite element (DFE) method based on the curve fiber path function is developed in this work. A design and optimization method based on the radial basis function surrogate method is proposed to optimize the critical buckling pressure for a VS composite cylindrical shell. Both the DFE and surrogate methods are verified to be valid by comparison with the experimental data from the listed references. The effects of the geometric parameter and fiber angle on the critical buckling pressure are studied for different cylindrical shell cases. The results indicate that the proposed simulation model and optimization method are accurate and efficient for the buckling analysis and optimization of a VS composite cylindrical shell. Optimization result shows that the optimum critical buckling pressure for the VS cylindrical shell is improved and is 21.1% larger than that of the constant stiffness cylindrical shell under the same geometric and boundary condition.

Reliability of axially compressed cylindrical shells with random axisymmetric imperfections

Results from an analytical study of the response of composite shells with cutouts and subjected to internal pressure and axial compression are presented. The analytical results are obtained using a geometrically nonlinear finite element code. Results for axial compression and combined internal pressure and axial compression are presented. The effects of varying internal pressure and cutout size on the prebuckling, buckling, and postbuckling responses of the shell are described. Results indicate that the nonlinear interaction between the inplane load distribution and the out-of-plane displacements near the cutout can significantly influence the structural response of the shell. The results also indicate that these local load distributions and displacements can be affected by the size of the cutout and the internal pressure load. Introduction Many modern aerospace shell structures are designed to support combinations of internal pressure and mechanical loads during their service life. With the increasing need to produce lighter weight aerospace structures, the use of advanced composite materials has become more common in the design of these structures. During operation, flight loads and internal cabin pressure are present in all commercial transport aircraft. Some of these loads may be compressive loads and, thus, it is necessary to investigate the buckling characteristics of these structures. In addition, designers will *Ph.D. Candidate, Composite Structures Laboratory, Department of Aerospace Engineering. Student Member, AIAA. tHead, Structural Mechanics Branch. Fellow, AIAA. ^ Associate Professor, Composite Structures Laboratory, Dept. of Aerospace Engineering. Member AIAA. Copyright ©1998 by Mark W. Hilburger. Published by the American Institute of Aeronautics and Astronautics, Inc. with permission. often need to incorporate cutouts or openings in the structure to serve as doors, windows, or access ports. It has been shown by a number of authors that a cutout in a shell structure subjected to axial compression can cause a significant reduction in the buckling load of the shell (e.g., Ref. 1-4). The local response near the cutout in a compression-loaded shell is strongly influenced by the local displacement gradients and the internal load distribution. These local displacements and internal load distribution can be affected by the size of the cutout. Recent studies of the response of cylindrical shells with longitudinal cracks and subjected to internal pressure and axial compression loads (e.g., Ref. 5) indicate that the interaction between the internal pressure load and the axial compression load can have a significant effect on the local response of the structure. The results of an analytical study of the response of composite cylindrical shells with cutouts and subjected to internal pressure and axial compression are presented. First, the governing parameters for the buckling of cylindrical shells with a cutout will be defined. The governing parameters will be used to develop the results of a parametric study presented in the paper. These parameters will help provide insight into the effects of changing geometric and laminate parameters on the buckling response of shells. The parametric study will include three cutout sizes and five internal pressure levels to determine the effects of varying the cutout size and internal pressure loads on the compression response. The predicted results are characterized by load-shortening response curves and contour plots of shell displacements and stress resultants. Finally, design curves based on classical parameters for the buckling of shells with cutouts and subjected to internal pressure and axial compression are presented.

Axially compressed composite cylindrical shells can attain multiple bifurcation points in their post-buckling procedure because of the natural transverse deformation restraint provided by their geometry. In this paper, the post-buckling analysis of functionally graded (FG) multilayer graphene platelets reinforced composite (GPLRC) cylindrical shells under axial compression is carried out to investigate the stability of such shells. Rather than the critical buckling limit, the focus of the present study is to obtain convergence post-buckling response curves of axially compressed FG multilayer GPLRC cylindrical shells. By introducing a unified shell theory, the nonlinear large deflection governing equations for post-buckling of FG multilayer GPLRC cylindrical shells with wide range of thickness are established, which can be easily changed into three widely used shell theories. Load-shortening curves for both symmetric and asymmetric post-buckling modes are obtained by Galerkin's method. Numerical results illustrate that the present solutions agree well with the existing theoretical and experimental data. The effects of geometries and material properties on the post-buckling behaviours of FG multilayer GPLRC cylindrical shells are investigated. The differences in the three shell theories and their scopes are discussed also.

Ultimate state assessment of medium-thick composite cylindrical pressure shells based on progressive damage

Bifurcation creep buckling analysis of circular cylindrical shell under axial compression