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.     

Free vibrations of fluid-filled cylindrical shells on elastic foundations

The free vibration characteristics of fluid-filled cylindrical shells on elastic foundations are presented by a semi-analytical finite element method. A shell is discretized into cylindrical finite elements where shell governing equations based shape functions in the longitudinal direction are used instead of the usual simple polynomials. Non-uniformities of the foundations in the circumferential and longitudinal directions are handled by the Fourier series and an element mesh strategy, respectively. The fluid domain is described by the potential flow theory. The hydrodynamic pressure acting on shells is derived from the condition for dynamic coupling of the fluid-structure. The effect of fluid in a shell, shell geometries, and foundation parameters on the dynamic behavior of fluid-containing shells is investigated. Numerical results based on the present method converge more rapidly than those obtained by the simple polynomial formulation. The method is suitable for the problem considered due to its generality, simplicity, and potential for further development.     

Nonlinear free vibration analysis of prestressed circular cylindrical shells on the Winkler/Pasternak foundation

Nonlinear free vibration analysis of prestressed circular cylindrical shells placed on Winkler/Pasternak foundation is investigated in the present paper. The nonlinearity is considered due to large deflections. Simultaneous effects of prestressed condition and elastic foundation on natural frequencies of the shells under various boundary conditions are examined extensively in this study. The nonlinear Sanders–Koiter shell theory is employed in order to derive strain–displacement relationships. The nonlinear classical Love's thin shell theory is also applied in some specific cases due to contrast the results. Beam modal functions are used to approximate spatial displacement field. The governing equations in linear state are solved by the Rayleigh–Ritz procedure. Perturbation methods are used to find the relationship between vibration amplitude and frequency in nonlinear state. Prestress state includes the effects of internal hydrostatic pressure and initial uniaxial tension. Results are compared with published theoretical and experimental data for some specific cases.     

有多条轴对称焊接凹陷的钢圆柱薄壳在内压力和轴压力共同作用下的强度

钢筒仓中圆柱薄壳承受内压力和轴压力共同作用:在轴压和低内压作用下,壳可发生弹性失稳;在轴压和高内压作用下,壳可发生塑性破坏.内压轴压共同作用下的圆柱薄壳对几何缺陷比较敏感:单条轴对称焊接凹陷可使壳的承载力降低;而多条轴对称凹陷由于相邻凹陷的相互作用,可使壳的强度进一步降低;对于小间距的凹陷,这种相互作用更为明显.本文首次对有多条小间距轴对称凹陷轴压圆柱薄壳的整体结构在不同水平内压作用下的强度进行了有限元分析,并将计算结果与欧洲规范EC3的设计曲线进行比较,对EC3的设计曲线提出了修改意见,从而达到安全设计的目的.     

Buckling and postbuckling behaviors of imperfect cylindrical shells subjected to torsion

Buckling and postbuckling behaviors of imperfect cylindrical shell subjected to torsion are investigated. The governing equations are based on the Karman–Donnell-type nonlinear differential equations. A boundary layer theory of shell buckling is applied to obtain the analytic solutions that meet the boundary conditions strictly. A singular perturbation technique is employed to determine the buckling loads and postbuckling equilibrium paths. Numerical results reveal that the current theory gives quite good estimates of the postbuckling paths of cylindrical shells. The effects of the geometric parameters on the buckling and postbuckling behaviors of the cylindrical shells are analyzed. It is confirmed that the postbuckling equilibrium paths of cylindrical shells subjected to torsion are unstable and the relatively shorter shells have higher postbuckling equilibrium paths. Finally, the effects of the initial imperfections on the buckling and postbuckling behaviors of the cylindrical shells are clarified. The illustrated results of the imperfect shells with different initial transverse deflections show that extremely small imperfections do indeed reduce the buckling loads and make the postbuckling equilibrium paths be lower. The buckling and postbuckling of cylindrical shells under torsion exhibit obvious imperfect sensitivity. Furthermore, the effects become greater following with the larger imperfections.     

Postbuckling analysis of stiffened cylindrical shells under combined external pressure and axial compression

A new approach is extended to investigate the buckling and postbuckling behaviour of perfect and imperfect, stringer and ring stiffened cylindrical shells of finite length subject to combined loading of external pressure and axial compression. The formulations are based on a boundary layer theory which includes the edge effect in the postbuckling analysis of a thin shell. The analysis uses a singular perturbation technique to determine the buckling loads and the postbuckling equilibrium paths. Some interaction curves for perfect and imperfect stiffened cylindrical shells are given and compared well with experimental data. The effects of initial imperfection on the interactive buckling load and postbuckling behaviour of stiffened cylindrical shells have also been discussed.     

Natural vibrations of loaded noncircular cylindrical shells containing a quiescent fluid

The paper deals with a solution of three-dimensional problems of natural vibrations and stability of loaded cylindrical shells with circular and arbitrary cross sections containing a quiescent ideal compressible fluid. A mathematical formulation of the problem has been developed based on the variational principle of virtual displacements taking into account the pre-stressed undeformed state caused by the action of static forces on the shell. The motion of potential compressible non-viscous fluid is described by a wave equation, which is transformed using the Bubnov–Galerkin method. The solution of the problem reduces to the computation of complex eigenvalues of a coupled system of two equations. Based on the developed finite element algorithm several numerical examples have been considered to analyze the influence of fluid levels, ratio of ellipse semi-axes, shell thickness and boundary conditions on the natural frequencies and vibration modes of circular and elliptical cylindrical shells loaded by mechanical forces. It has been found that the value of the external uniformly distributed pressure giving rise to instability does not depend on the level of fluid in the shell. The results allow us to conclude that the dynamic characteristics of the system are specified not only by the equivalent added mass of the fluid but also by hydroelastic interaction at the wetted surface.     

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

Linear eigenvalue analysis of cracked cylindrical shells under combined internal pressure and axial compression is carried out to study the effect of crack type, size and orientation on the buckling behavior of cylindrical thin shells. Two types of crack are considered; through crack and thumbnail crack. Our calculations indicate that depending on the crack type, length, orientation and the internal pressure, local buckling may precede the global buckling of the cylindrical shell. The internal pressure, in general, increases the buckling load associated with the global buckling mode of the cylindrical shells. In contrast, the effect of internal pressure on buckling loads associated with the local buckling modes of the cylindrical shell depends mainly on the crack orientation. For cylindrical shells with relatively long axial crack, buckling loads associated with local buckling modes of the cylindrical shell reduce drastically on increasing the shell internal pressure. In contrast, the internal pressure has the stabilizing effect against the local buckling for circumferentially cracked cylindrical shells. A critical crack length for each crack orientation and loading condition is defined as the shortest crack causing the local buckling to precede the global buckling of the cylindrical shell. Some insight into the effect of internal pressure on this critical crack length is provided.     

真空引起的薄壁圆筒屈曲压力预测

研究均匀外压力下初始缺陷对圆柱形薄壳结构屈曲性能的影响。对缩尺薄壁圆筒的外形进行分析以测量壳体表面的几何缺陷。有限元分析时将这些初始缺陷考虑在内,并进行静态几何非线性分析。在实验室进行圆筒的倒塌试验,并将试验结果和有限元分析结果进行比较。结果表明,有限元分析能够准确预测圆筒的破坏坍塌压力和后屈曲模态。     

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.     

The prediction of the elastic critical load of submerged elliptical cylindrical shell based on the vibro-acoustic model

Based on the vibro-acoustical model, an effective new approach to nondestructively predict the elastic critical hydrostatic pressure of a submerged elliptical cylindrical shell is presented in this paper. Based on the Goldenveizer–Novozhilov thin shell theory, the vibration equations considering hydrostatic pressures of outer fluid are written in the form of a matrix differential equation which is obtained by using the transfer matrix of the state vector of the shell. The fluid-loading term is represented as the form of Mathieu function. The data of the fundamental natural frequencies of the various elliptical cylindrical shells with different hydrostatic pressure and boundary conditions are obtained by solving the frequency equation using Lagrange interpolation method. The curve of the fundamental natural frequency squared versus hydrostatic pressure is drawn, which is approximately straight line. The elastic critical hydrostatic pressure is therefore obtained while the fundamental natural frequency is assumed to be zero according to the curve. The results obtained by the present approach show good agreement with published results.     

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.     

Static buckling analysis of thin cylindrical shell with centrally located dent under uniform lateral pressure

One of the common failure modes of thin cylindrical shell subjected to external pressure is buckling. The buckling pressure of these shell structures are dominantly affected by the geometrical imperfections present in the cylindrical shell which are very difficult to alleviate during manufacturing process. Dent is one of the common geometrical imperfections present in thin shell structures which may be formed due to mechanical damage caused by accidental loading or impact. In this work, influence of various dent parameters (dent length, dent width, dent depth and angle of orientation of the dent) on the critical buckling pressure of thin cylindrical shells with a centrally located dent is studied using non-linear static finite-element analysis of ANSYS under external pressure with simply supported boundary conditions at the top and bottom edges of the thin cylindrical shell.     

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.     

Loss of stability of thin, elastic, strongly convex shells of revolution with initial imperfections, subjected to uniform pressure. A probabilistic approach

This paper presents an attempt to evaluate theoretically the influence of initial geometric imperfections in the shell surface on the value of the upper critical load of a strictly convex shell of revolution which is subjected to uniform pressure. Pogorelov's geometric method for nonlinear stability problems of thin shells is applied to obtain an analytical formula for the upper critical load, dependent on the initial imperfections. A probabilistic solution of the problem is presented. As a result, the stochastic influence of the initial deviations in the shell surface on the probability density function of the critical load and on the shell reliability are estimated and presented graphically. An example is given for an ellipsoidal shell of revolution.     

Effect of the presence of fluid on the dynamic response of buried orthotropic cylindrical shells under a moving load

This paper deals with the theoretical analysis of the axisymmetric steady state dynamic response of a buried fluid-filled orthotropic cylindrical shell subjected to a radial line load moving along the axis of the shell. A thin shell is assumed to be perfectly bonded to the surrounding medium of infinite extent, and only the axisymmetric response has been included. A linear acoustic equation has been used for the wave propagation in fluid. The nature of variation of differences between the results of the empty and fluid-filled shells has been studied for varying soil conditions. Changes in results due to variation in the orthotropy parameters have been compared with the difference in results due to the presence of fluid inside the shell.     

Vibration analysis of cylindrical shells in contact with an annular fluid region

An experimental and numerical investigation of the vibratory modal characteristics of a vertical thin-walled cylindrical shell containing water, or oil, in an adjacent coaxial region is presented. A system of two fluid-coupled cylindrical shells is studied. In addition to the effect of increasing liquid level in the shell, the effects of the thickness of the liquid layer in the annular region between the vibrating outer shell and another coaxial rigid cylinder, or between two thin coaxial cylindrical shells, are studied. Experimental results were obtained using the standard modal analysis technique and the time average holographic method. In parallel, computation of natural frequencies and mode shapes of the coupled fluid-structural vibrations were carried out by means of the finite element method operated within the framework of the ANSYS program package. The comparison between experimental results and finite element results was found to be reasonable in most of the cases studied. The fundamental influence of the viscosity of the fluid in the narrow annulus upon the dynamic behaviour of the shell is discussed.     

Experiments on dented cylindrical shells under peripheral pressure

In spite of numerous papers in the literature on the buckling behavior of cylindrical shell structures, the effect of local large imperfections caused by physical contacts has not been exhaustively examined yet. To this end, this paper reports on an experimental program on the buckling and post-buckling response of thin cylindrical shells with local dent imperfections under uniform external pressure. The results of this study can be used in practical structures with similar geometric features, i.e. D/t ratio.     

Free vibration analysis of functionally graded cylindrical shells including thermal effects

Free vibration analysis of simply supported FG cylindrical shells for four sets of in-plane boundary conditions is performed. The material properties are assumed to be temperature-dependant and gradually changed in the thickness direction of the shell. The effects of temperature rise are investigated by specifying arbitrary high temperature on the outer surface and the ambient temperature on the inner surface of the cylinder. Distribution of temperature across the shell thickness is found from steady state heat conduction only in the thickness direction. The equations of motion are based on Love's shell theory and the von Karman–Donnell-type of kinematic nonlinearity. The static analysis is first performed to determine the prestressed state induced by the thermal loadings, using the exact solution of the governing equations and then the equations of motion are solved by Galerkin's method. The results are obtained to indicate the effects of power law index on the natural frequencies and corresponding mode shapes in the thermal environment.     

对称双圆弧柱壳的非线性屈曲

对于潜艇艇体耐压壳结构,屈曲特性在设计中被广泛关注。针对一种新型潜艇耐压艇体结构-对称双圆弧环肋柱壳,推导了相应的弹塑性失稳系数。采用非线性大挠度理论,给出了静水压力作用下含初始缺陷的对称双圆弧环肋柱壳大挠度弹塑性屈曲临界压力计算式。讨论了开口角、周向相当波数和初始几何缺陷对临界压力的影响。计算结果表明,开口角对结构弹塑性屈曲的临界压力影响很小,而周向相当波数是影响临界压力的主要因素。