Stability Of Cylindrical Shells Research Articles

Ring Stiffened Cylindrical Shell Structures: State-of-the-Art Review

The cylindrical shell is a widely used structure in engineering practice, and its main form of failure is instability due to buckling. As a classical problem in the field of mechanics, the stability of cylindrical shells has been studied extensively. However, the large difference between the theoretically predicted results of the critical buckling load and the experimental results for the cylindrical shells subjected to uniform axial pressure has contributed to the continuous development of the shell stability theory. This paper briefly reviews the development of the shell stability theory, then presents an overview of the current status and trends of stability research on the stiffened cylindrical shell widely used in cylindrical shell structures in real engineering, and finally presents the difficulties and directions of future stability research on cylindrical shell structures in engineering applications.

Dynamic Stability of a Cylindrical Shell Reinforced by Longitudinal Ribs of Piecewise-Constant Thickness under Axial Loading

A model is proposed for studying the simultaneous parametric and longitudinal vibrations of an orthotropic cylindrical shell reinforced by longitudinal ribs of piecewise-constant thickness under the action of an axial time-harmonic load. The discrete location and changes in the thickness of the ribs are taken into account using generalized functions. The basic stages of solving the problem are considered with the combination of methods proposed. Using a numerical example, the dependences of the principal instability region on the geometric parameters of the ribs are plotted for the first time, and a comparison is made with the instability regions for the ribs with a mean-integral thickness. The model developed makes it possible to correct significantly the solutions of problems on calculation of the dynamic stability of orthotropic cylindrical shells with the ribs of piecewise-constant thickness.

Impact of High-Frequency Vibrations on Metal Items Resistance to Cyclic and Axial Loads

It was shown that the forced vibrations of objects on resonance frequencies could significantly change resistance of these objects to cyclic loads in a low-cycle loading range and decrease critical compression load under axial compression. We carried out a procedure of fatigue testing performance with simultaneous application of high-frequency vibrations. We developed and produced a device allowing carrying out testing aimed to check shape stability of cylindrical shells and their resistance to forced vibrations. Dependence of fatigue life capability within the low-cycle range on the frequency of applied forced vibrations in four harmonics of resonance frequency was experimentally determined. Fatigue life capability decreased by 1,6 times. Decrease of life capability particularly occurs on frequencies which are presumably connected with minimum in size elements of hierarchy of polycrystalline material structures. It was found out that the forced vibrations on resonance frequency contribute the increase of a number of vibrations, that leads to decrease of critical axial compression force value. Decrease can be by up to 40%. Experimental determination of critical load during application of vibrations allowed obtaining formula for adjusting factor calculation in the formula for permitted compression force calculation.

04.17: Cylindrical shell buckling under a hydraulic constraint: Numerical study

ABSTRACTSteel cylindrical shell structures are used in a large variety of civil engineering applications such as off‐ shore platforms, tanks, silos, wind turbine towers, etc. The local stability of such structures and their sensitivity to imperfections is a well‐known problem. In current engineering practice the design method is based on the selection of an imperfection class for the shell and subsequently calculating a reduction factor,χ, to the resistance of the shell. One such methodology is supplied by the EN1993‐1‐6; special conditions are given to pressurized tubes subjected to meridional compression.Past studies have focused on the stability of cylindrical shells with internal pressure. The stability problem of a long cylinder considering the internal pressure as a simple static load was addressed. Thus, the approaches considered the fluid as compressible.The purpose of the present work is to investigate numerically the potential benefit of using an incompressible fluid fully enclosed in a circular cylindrical shell. The constraint imposed by the presence of the liquid in the interior of a shell will be referred to as “hydraulic constraint”. As liquids are nearly incompressible, the buckling of a liquid‐filled shell has to satisfy the condition that the integral of all the displacements normal to the shell surface is equal to the volume variation of the contained liquid. The volume variation of the shell interior has to be equal to the dilation of the shell due to liquid pressure increments associated to the onset of geometrical instability. Additionally, the weight of the contained liquid causes additional circumferential tension in the cases of vertically placed cylinders.The methodology followed is the numerical analysis of cylindrical shells by means of the ABAQUS Finite Element code and a comparison with the methods given in the Eurocode.

К устойчивости цилиндрических оболочек с наполнителем со смешанными граничными условиями.

К устойчивости цилиндрических оболочек с наполнителем со смешанными граничными условиями.

Dynamics and stability of a cylindrical shell subjected to annular flow including temperature effects

Considering thermal loads, dynamics and stability of an outer cylindrical shell conveying swirling fluid in the annulus between the inner shell-type body and the outer shell are investigated by the travelling wave approach. Shell motions are considered based on Donnell-type shell theory. The fluid forces are described by means of the potential flow theory, and thermal loads are determined by the thermo-elastic theory. The numerical analyses are conducted by a zero-level contour method. The study shows the effects of annular gaps and boundary conditions on stability of shells. The influences of angular flow on the critical axial velocity and axial flow on the critical annular velocity are discussed. Moreover, the thermal loads decrease the critical flow velocity markedly and the critical temperature rise is found.

Моделирование динамической устойчивости цилиндрической оболочки при действии внешнего избыточного давления

Моделирование динамической устойчивости цилиндрической оболочки при действии внешнего избыточного давления

Stability of Composite Cylindrical Shells with Added Mass Interacting with the Internal Fluid Flow

The effect of added masses on the quasistatic (divergence) and dynamic (flutter) loss of stability of cylindrical shells interacting with the internal fluid flow is studied. The dependence of the critical velocity of the fluid on the type of attachment of the added masses is analyzed

Multimode interaction in axially excited cylindrical shells

Cylindrical shells exhibit a dense frequency spectrum, especially near the lowest frequency range. In addition, due to the circumferential symmetry, frequencies occur in pairs. So, in the vicinity of the lowest natural frequencies, several equal or nearly equal frequencies may occur, leading to a complex dynamic behavior. So, the aim of the present work is to investigate the dynamic behavior and stability of cylindrical shells under axial forcing with multiple equal or nearly equal natural frequencies. The shell is modelled using the Donnell nonlinear shallow shell theory and the discretized equations of motion are obtained by applying the Galerkin method. For this, a modal solution that takes into account the modal interaction among the relevant modes and the influence of their companion modes (modes with rotational symmetry), which satisfies the boundary and continuity conditions of the shell, is derived. Special attention is given to the 1:1:1:1 internal resonance (four interacting modes). Solving numerically the governing equations of motion and using several tools of nonlinear dynamics, a detailed parametric analysis is conducted to clarify the influence of the internal resonances on the bifurcations, stability boundaries, nonlinear vibration modes and basins of attraction of the structure.

Effects of modal coupling on the dynamics of parametrically and directly excited cylindrical shells

Cylindrical shells exhibit a dense frequency spectrum, especially in the lowest frequency range. In addition, due to the circumferential symmetry, frequencies occur in pairs. So, in the vicinity of the lowest natural frequencies, several equal or nearly equal frequencies may occur, leading to multiple internal resonances. The aim of the present work is to investigate the dynamic behavior and stability of cylindrical shells under lateral and axial forcing with equal natural frequencies. The shell is modeled using the Donnell nonlinear shallow shell theory. A consistent modal solution for this problem is deduced and used to discretize the equations of motion by applying the Galerkin method. A parametric analysis is conducted to clarify the influence of the modal interaction among these nonlinear vibration modes on coexisting solutions, bifurcations, resonances curves and stability boundaries of the shell.

Устойчивость цилиндрической оболочки при комбинированном нагружении

Устойчивость цилиндрической оболочки при комбинированном нагружении

Studies of nonlinear deformation and stability of noncircular cylindrical shells in transverse bending

The variational finite element method in displacements is used to solve the problem of geometrically nonlinear deformation and stability of cylindrical shells with a noncircular contour of the cross-section. Quadrangle finite elements of shells of natural curvature are used. In the approximations of element displacements, the displacements of elements as solids are explicitly separated. The variational Lagrange principle is used to obtain a nonlinear system of algebraic equations for the unknown nodal finite elements. The system is solved by the method of successive loadings and by the Newton-Kantorovich linearization method. The linear system is solved by the Crout method. The critical loads are determined in the process of solving the nonlinear problem by using the Sylvester stability criterion. An algorithm and a computer program are developed to study the problem numerically. The nonlinear deformation and stability of shells with oval and elliptic cross-sections are investigated in a broad range of variation of the elongation and ellipticity parameters. The shell critical loads and buckling modes are determined. The influence of the deformation nonlinearity, elongation, and ellipticity of the shell on the critical loads is examined.

Stability of cylindrical shells made of a laminated composite with components subject to long-term damage

Stability of cylindrical shells made of a laminated composite with components subject to long-term damage

Stability of cylindrical shells with initial imperfections under the action of external pressure

We use the equations of nonlinear theory of shallow shells to solve the problem of stability of thin elastic isotropic cylindrical shells, with small initial shape imperfections, that are under the action of external uniform pressure. The problem solution is constructed by the Rayleigh-Ritz method with the approximation of the shell midsurface displacement by double functional sums in trigonometric and beam functions. The system of nonlinear algebraic equations is solved by using the methods of continuation with respect to a close-to-best parameter. For the initial imperfections of the shells, we use their normalized deflections from the limit points of overcritical branches of the loading trajectories. We consider various cases of the shell fixation and support under loading by lateral and hydrostatic uniform pressure. We also construct the range of values of the critical pressure, which, with the maximal deviation of the shell shape from the cylindrical shape up to 30%, covers practically all known experimental data.

К устойчивости цилиндрической оболочки при нормальном давлении.

К устойчивости цилиндрической оболочки при нормальном давлении.

Stability of cylindrical shells with added mass in fluid flow

The paper proposes a technique for the stability analysis of an elastic cylindrical shell with added mass interacting with a flowing fluid. Three cases of mass–shell contact are considered: the added mass (i) is attached to the shell at one point, (ii) has the form of a circular ring, and (iii) is distributed uniformly over the length. For each case, equations to determine the critical speeds of the fluid corresponding to the quasistatic (divergent) and dynamic (flutter) buckling of the shell are derived

Stability of cylindrical shells made of a fibrous composite with components subject to long-term damage

The problem of bifurcational instability of cylindrical shells made of particulate composite materials with components subject to long-term damage is formulated and solved

Stability of cylindrical shells made of a particulate composite with components subject to long-term damage

Stability of cylindrical shells made of a particulate composite with components subject to long-term damage

Nonlinear deformation and stability of reinforced elliptical cylindrical shells loaded by internal pressure under twisting and bending

The problem of stability of cylindrical shells with an elliptical cross-sectional contour reinforced by a set of stringers under combined loading by bending and twisting moments, transverse force, and internal pressure is studied with the use of the variational method of finite elements in displacements. The subcritical stress-strain state of the shells is assumed to be moment and nonlinear. The effect of nonlinearity of deformation of the shells and their ellipticity on the critical loads and buckling type is determined.

The Stability of Cylindrical Shells Containing an FGM Layer Subjected to Axial Load on the Pasternak Foundation

In this study, the stability of cylindrical shells that composed of ceramic, FGM, and metal layers subjected to axial load and resting on Winkler-Pasternak foundations is investigated. Material properties of FGM layer are varied continuously in thickness direction according to a simple power distribution in terms of the ceramic and metal volume fractions. The modified Donnell type stability and compatibility equations on the Pasternak foundation are obtained. Applying Galerkin’s method analytic solutions are obtained for the critical axial load of three-layered cylindrical shells containing an FGM layer with and without elastic foundation. The detailed parametric studies are carried out to study the influences of thickness variations of the FGM layer, radius-to-thickness ratio, material composition and material profile index, Winkler and Pasternak foundations on the critical axial load of three-layered cylindrical shells. Comparing results with those in the literature validates the present analysis.