Non-linear buckling behavior of FGM truncated conical shells subjected to axial load

In this study, the non-linear buckling behavior of truncated conical shells made of functionally graded materials (FGMs), subject to a uniform axial compressive load, has been investigated using the large deformation theory with von the Karman-Donnell-type of kinematic non-linearity. The material properties of functionally graded shells are assumed to vary continuously through the thickness of the shell. The variation of properties followed an arbitrary distribution in terms of the volume fractions of the constituents. The fundamental relations, the modified Donnell type non-linear stability and compatibility equations of functionally graded truncated conical shells are obtained and are solved by superposition and Galerkin methods and the upper and lower critical axial loads have been found analytically. Finally, the influences of the compositional profile variations and the variation of the shell geometry on the upper and lower critical axial loads are investigated. Comparing the results of this study with those in the literature validates the present analysis.     

Torsional buckling of spherical shells under circumferential shear loads

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Experimental studies on dynamic plastic buckling of circular cylindrical shells under axial impact

In the present paper, experimental studies on dynamic plasticbuckling of circular cylindrical shells under axial impact are carried out. Hopkinson bar and drop hammer apparatus are used for dynamic loading. Three groups of circular cylindrical shells made of copper are tested under axial impact. From the experiments, the first critical velocity corresponding to the axi-symmetric buckling mode and the second critical velocity corresponding to the non-axisymmetric buckling mode are determined. The present results come close to those of second critical velocity given by Wang Ren^[4–6]. Two different kinds of non-axisymmetric buckling modes oval-shaped and triangle shaped are founded. The buckling modes under two loading cases, viz. with small mass but high velocity and with large mass and low velocity using Hopkinson bar and drop hammer, are different. Their critical energies are also discussed. The project is supported by the National Natural Science Foundation of China (19672039) and the Foundation for Returned Scholar from Abroad of Shanxi Province     

Thermal buckling and free vibration of FG truncated conical shells with stringer and ring stiffeners using differential quadrature method

In this paper, thermal buckling and free vibration of orthogonally stiffened functionally graded truncated conical shells in thermal environment is investigated. Conical shell has been stiffened by rings and stringers, and the influences of the stiffeners are evaluated by the aid of smearing method. The material properties of the structure are assumed to be changed continuously in the thickness direction. First, the initial thermal stresses are obtained accurately by solving the thermoelastic equilibrium equations. Then, by taking into account the initial thermal stresses, equations of motion as well as boundary conditions are obtained, applying the Hamilton’s principle and the first-order shear deformation theory. The natural frequencies of the system have been achieved, solving these governing equations with considering Differential Quadrature Method (DQM). In addition to Eigen frequency analysis, the critical buckling-temperature of the conical shell has been computed. Moreover, the effects of geometrical parameters, number of stiffeners, thermal environment and various boundary conditions on natural frequency of the system have been investigated. Finally, in order to validate the present work, the results are compared with those of other researches available in literature.     

Studies on the torsional buckling of elastic cylindrical shells

The experimental phenomenon and theoretical analysis are given for the torsional buckling of elastic cylindrical shells. From the experiment, it is found that the postbuckling deformation doesn't occupy the whole length when the shell is longer. In the theoretical calculation, only the normal displacement boundary condition is taken into account. By comparing the present calculation results with the accurate result of Yamakis theory and the results of the present experiment, it is shown that the influence of the axial and circumference boundary condition is less important.     

薄壳失稳机理浅析

对薄壳失稳问题研究的理论与实验成果进行了总结和讨论，对薄壳后屈曲理论研究结果提出了不同的看法，同时应用动力学原理对薄壳失稳问题进行了探讨，并建立了计算模型。文中应用动力学原理描述了从加载初期的一个呈现静力学特征的薄壳随荷载的增加而逐渐成为一个呈现动力学特征的薄壳的过程，从薄壳受扰振动乃至共振的角度解释了失稳临界荷载实验数据值及其离散并低于失稳临界荷载理论值的原因。     

轴向应力波作用下圆柱壳塑性轴对称动力屈曲

运用有限元特征值分析方法对应力波作用下圆柱壳塑性轴对称动力失稳问题进行了研究。基于应力波理论和相邻平衡准则导出了圆柱壳轴对称动力失稳时的特征方程,在分析中同时考虑了应力波效应及横向惯性效应,把圆柱壳塑性动力失稳问题归结为特征值问题。通过引入圆柱壳动力失稳时的波前约束条件实现了此类问题的有限元特征值解法。计算结果揭示了圆柱壳塑性轴对称动力屈曲变形发展的机理,以及轴向应力波和屈曲变形的相互作用规律。     

各向异性矩形板的剪切屈曲分析

根据各向异性矩形薄板剪切屈曲横向位移函数的微分方程建立了一般性的解析解。该一般解包括三角函数和双曲线函数组成的解,它能满足四个边为任意边界条件的问题;该一般解还包括代数多项式解,它能满足四个角的边界条件问题。因此,这一解析解可用于精确地求解任意边界的各向异性矩形板的剪切屈曲问题。其中待定常数可由四边和四角的边界条件来确定,由此得出的齐次线性代数方程系数矩阵行列式等于零可以求得各阶临界载荷及其屈型。结合配点法,利用变形的对称和反对称性,以及对称迭层正方形板均可使计算更简单。以四边平夹的对称角铺设复合材料迭层板为例进行了计算和讨论。     

Stability of cylindrical shells with one plane of elastic symmetry under axial compression and torsion

A numerical technique is developed for stability analysis of laminated cylindrical shells with one plane of symmetry subject to axial compression and torsion. Shells filament-wound in directions other than the coordinate axes are considered as a special case. These shells are analyzed for stability under axial compression, external pressure, and torsion. It is shown that shells with a great number of plies and different ply angles may be considered orthotropic __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 8, pp. 115–121, August 2006.     

On lower-bound estimates of critical loads for cylindrical shells

The paper proposes a new approach to estimate the lower bounds of critical loads for circular cylindrical shells. These bounds are compared with the ordinary lower bound of critical load under which a shell with initial deflections loses stability. The lower bound produced by the approach is higher than the ordinary bound and can be used in design __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 10, pp. 78–85, October 2006.     

A note on the determination of critical loads for flexible noncircular cylindrical shells with clamped edges

An approach is proposed to determine the upper and lower bounds of the critical load for flexible noncircular long cylindrical shells with clamped longitudinal edges under nonuniform loading. An exact analytical solution is designed. Its critical points are analyzed __________ Translated from Prikladnaya Mekhanika, Vol. 41, No. 11, pp. 78–87, November 2005.     

在轴向应力波传播和反射过程中弹性有限长圆柱壳非对称动态屈曲

本文讨论弹性有限长圆柱壳端部受冲击载荷作用，在轴向应力波传播和反射过程中的非对称动态屈曲问题。通过建立和求解扰动方程得到了动态屈曲的分叉条件，临界载荷和屈曲模态。数值结果表明：当壳壁厚不很薄时，轴对称屈曲临界载荷比非轴对称临界载荷高；反之，轴对称临界载荷会比非对称临界载荷低；由于应力波的反射，临界载荷降低，因而更容易发生屈曲，屈曲模态也有其不同特点。     

Forced nonlinear oscillations of cylindrical shells interacting with fluid flow

The dynamic interaction of thin cylindrical shells with the fluid flow inside them under external periodic loads is studied. A technique is proposed to calculate the parameters of forced nonlinear oscillations of shells with a fluid moving with nearly critical velocities. The amplitude-frequency characteristics of the fluid-shell system under steady-state oscillation are plotted __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 4, pp. 91–99, April 2006.     

Stability of composite shells of revolution

An approach to solving the buckling problem for shells made of a composite material with one plane of elastic symmetry is presented. The approach employs complex Fourier series. The prebuckling stress-strain state is assumed to be geometrically nonlinear. The stability of a cylindrical shell under axial compression and uniform side pressure is analyzed using the Runge-Kutta method with discrete orthogonalization. The numerical results are compared with analytical solutions __________ Translated from Prikladnaya Mekhanika, Vol. 44, No. 3, pp. 109–124, March 2008.     

On the stability analysis of plates and shells using a quadrilateral, 16-degrees of freedom plat shell element DKQ16

The linear buckling problems of plates and shells were analysed using a recently developped quadrilateral, 16-degrees of freedom flat shell element ( called DKQ16 ). The geometrical stiffness matrix was established. Comparison of the numerical results for several typical problems shows that the DKQ16 element has a very good precision for the linear buckling problems of plates and shells.     

Stability of longitudinally corrugated cylindrical shells under uniform surface pressure

The buckling problem for longitudinally corrugated cylindrical shells under external pressure is solved. The solution makes practically exact allowance for the geometry and buckling modes of the shell. The inaccuracy of the results is due to the assumption that the subcritical state is momentless. Shells consisting of cylindrical panels of smaller radius and noncircular shells with sinusoidal corrugations are analyzed for stability. The practical applicability of such shells is demonstrated __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 11, pp. 66–79, October 2007.     

Nonlinear dynamic buckling of symmetrically laminated cylindrically orthotropic shallow spherical shells

Summary In this paper, a model of cusped catastrophe at nonlinear dynamic buckling of a symmetrically laminated cylindrically orthotropic shallow spherical shell is presented. The shell is subjected to an axisymmetrical load. Effects of transverse shear are taken into account. Effects of the shear modulus, geometry and parameters of the material on the nonlinear dynamic buckling are discussed. Received 2 April 1997; accepted for publication 27 November 1997     

Influence of axisymmetric dents in ribbed shells on minimum critical loads

The effect of axisymmetric dents in ribbed shells on the minimum critical loads is studied analytically. The upper and lower bounds for the critical stresses in imperfect cylindrical shells reinforced with stringers, rings, and both are estimated. The upper bounds are compared with those obtained from the known solutions for perfect ribbed momentless shells and with experimental data. The effect of the amplitude of initial dents and their number on the upper and lower bounds of critical stresses is examined. The procedure used is the most efficient to determine the load-bearing capacity of ring-reinforced and ribbed shells __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 5, pp. 73–79, May 2007.     

Dynamics of reinforced compound shells under nonstationary loads

The nonstationary behavior of reinforced compound structures is analyzed within the framework of the geometrically nonlinear Timoshenko theory of shells and rods. The numerical method used to solve the problem is based on the finite-difference approximation of the original differential equations. The dynamic behavior of a reinforced compound structure under nonstationary loading is demonstrated by way of a numerical example. The numerical results are compared with experimental data __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 4, pp. 100–107, April 2006.     

Analytic upper-bound estimates for the critical loads of perfect ribbed shells

A new approximate approach is proposed to find upper-bound estimates for the critical loads of ribbed shells. Seventeen cases are considered, and the minimum critical load parameter is determined __________ Translated from Prikladnaya Mekhanika, Vol. 41, No. 12, pp. 74–83, December 2005.