To the problem of stability of a cylindrical shell under axial compression

The classical problem of stability of a thin elastic cylindrical shell loaded by axial compressions forces is considered. The axially symmetric and non-axisymmetric buckling modes of isotropic and orthotropic shells are studied. In contrast to the traditional approach, the well-known expressions for the critical load are obtained by analyzing the equations for the shell behavior and are independent of the boundary conditions.     

Thermomechanical postbuckling of composite laminated cylindrical shells with local geometric imperfections

The effect of local geometric imperfections on the buckling and postbuckling of composite laminated cylindrical shells subjected to combined axial compression and uniform temperature loading was investigated. The two cases of compressive postbuckling of initially heated shells and of thermal postbuckling of initially compressed shells are considered. The formulations are based on a boundary layer theory of shell buckling, which includes the effects of the nonlinear prebuckling deformation, the nonlinear large deflection in the postbuckling range and the initial geometric imperfection of the shell. The analysis uses a singular perturbation technique to determine buckling loads and postbuckling equilibrium paths. Numerical examples are presented that relate to the performances of cross-ply laminated cylindrical shells with or without initial local imperfections, from which results for isotropic cylindrical shells follow as a limiting case. Typical results are presented in dimensionless graphical form for different parameters and loading conditions.     

Low-Dimensional Galerkin Models for Nonlinear Vibration and Instability Analysis of Cylindrical Shells

This paper discusses the derivation of discrete low-dimensional models for the non-linear vibration analysis of thin shells. In order to understand the peculiarities inherent to this class of structural problems, the non-linear vibrations and dynamic stability of a circular cylindrical shell subjected to dynamic axial loads are analyzed. This choice is based on the fact that cylindrical shells exhibit a highly non-linear behavior under both static and dynamic axial loads. Geometric non-linearities due to finite-amplitude shell motions are considered by using Donnell’s nonlinear shallow shell theory. A perturbation procedure, validated in previous studies, is used to derive a general expression for the non-linear vibration modes and the discretized equations of motion are obtained by the Galerkin method. The responses of several low-dimensional models are compared. These are used to study the influence of the modelling on the convergence of critical loads, bifurcation diagrams, attractors and large amplitude responses of the shell. It is shown that rather low-dimensional and properly selected models can describe with good accuracy the response of the shell up to very large vibration amplitudes.     

Stability of Axially Compressed Noncircular Cylindrical Shells Consisting of Panels of Constant Curvature

The stability problem is solved for an axially compressed cylindrical shell. Its cross section is formed by circular arcs of radius r with ends supported on a closed circle of radius R. The solution is based on the Flügge equations of the classic theory of deep cylindrical shells. It is shown that the critical axial load for shells of medium length and appropriately chosen cross-sectional profile can be increased by a factor of R/r approximately, compared with the circular shell. The shells length affects considerably the efficiency of noncircular shells of this type. This design model allows us to find out how the local properties of the shell and its stiffness are related     

Stability analysis of cylindrical shells containing a fluid with axial and circumferential velocity components

The stability of an elastic circular cylindrical shell of revolution interacting with a compressible liquid (gas) flow having both axial and tangential components is analyzed. The behavior of the fluid is studied within the framework of potential theory. The elastic shell is described in terms of the classical theory of shells. Numerical solution of the problem is performed using a semianalytical finite element method. Results of numerical experiments for shells with different boundary conditions and geometric dimensions are presented. The effects of fluid rotation on the critical flow velocity and the effect of axial fluid flow on the critical angular velocity of fluid rotation were estimated.     

Stability of cylindrical shells subjected to combined axial compression and internal pressure under creep conditions

The critical strain of a cylindrical shell subjected to combined axial compression and internal pressure is computed under creep conditions. A method is proposed to determine values of the initial deflections by means of elastic shell test data for a creep analysis of shells. Data of an experimental investigation of the creep stability of shells are presented, which are compared with the results of the computation.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 5, pp. 109–116, September–October, 1974.     

Stability and vibration of empty and fluid-filled circular cylindrical shells under static and periodic axial loads

In the present study, the dynamic stability of simply supported, circular cylindrical shells subjected to dynamic axial loads is analysed. Geometric nonlinearities due to finite-amplitude shell motion are considered by using the Donnell’s nonlinear shallow-shell theory. The effect of structural damping is taken into account. A discretization method based on a series expansion involving a relatively large number of linear modes, including axisymmetric and asymmetric modes, and on the Galerkin procedure is developed. Axisymmetric modes are included; indeed, they are essential in simulating the inward deflection of the mean oscillation with respect to the equilibrium position and in describing the axisymmetric deflection due to axial loads. A finite length, simply supported shell is considered; the boundary conditions are satisfied, including the contribution of external axial loads acting at the shell edges. The effect of a contained liquid is investigated. The linear dynamic stability and nonlinear response are analysed by using continuation techniques and direct simulations.     

Geometrically nonlinear vibration of laminated composite cylindrical thin shells with non-continuous elastic boundary conditions

The geometrically nonlinear forced vibration response of non-continuous elastic-supported laminated composite thin cylindrical shells is investigated in this paper. Two kinds of non-continuous elastic supports are simulated by using artificial springs, which are point and arc constraints, respectively. By using a set of Chebyshev polynomials as the admissible displacement function, the nonlinear differential equation of motion of the shell subjected to periodic radial point loading is obtained through the Lagrange equations, in which the geometric nonlinearity is considered by using Donnell’s nonlinear shell theory. Then, these equations are solved by using the numerical method to obtain nonlinear amplitude–frequency response curves. The numerical results illustrate the effects of spring stiffness and constraint range on the nonlinear forced vibration of points-supported and arcs-supported laminated composite cylindrical shells. The results reveal that the geometric nonlinearity of the shell can be changed by adjusting the values of support stiffness and distribution areas of support, and the values of circumferential and radial stiffness have a more significant influence on amplitude–frequency response than the axial and torsional stiffness.

     

圆柱壳稳定性问题的研究进展

圆柱壳是工程实际中广泛应用的结构,其主要破坏形式是屈曲失稳．作为力学领域的经典问题,圆柱壳稳定性问题的研究非常之多．其中,受均匀轴向压力的圆柱壳由于临界屈曲载荷的理论预测值与早期试验结果之间的巨大差异,更是推动了壳体稳定性理论的不断发展．本文简要回顾了壳体稳定性理论的发展和分类,并对轴压圆柱壳体试验结果分散且远低于理论预测值的原因及含缺陷圆柱壳体的稳定性研究方法进行了总结,然后综述了地下空间顶管、储油罐、加筋圆柱壳及脱层圆柱壳等实际工程中广泛应用的圆柱壳结构稳定性研究的现状和趋势,最后展望了将来对工程应用中圆柱壳结构的稳定性研究的难点和方向．     

Nonlinear deformation and stability of noncircular cylindrical shells under internal pressure and axial compression

Stability analysis of noncircular shells is performed with allowance for nonlinear subcritical deformation. Explicit expressions for the rigid displacements of elements of noncircular cylindrical shells are obtained and used to construct shape functions of an effective quadrilateral finite element of natural curvature. A finiteelement algorithm for solving problems of nonlinear deformation and stability of shells is developed. Stability problem of an elliptic cylindrical shell is considered. The effect of the ellipticity and subcritical nonlinear deformation of the shell on the critical load is studied. Results obtained are compared with available experimental data.     

A rigorous solution for the axisymmetrical buckling of simply supported cylindrical sandwich shells under axial load

In this paper,based on ref[1],the axisymmetrical buckling of simply supportedcylindrical sandwich shells under the action of uniform axial load is solved by a rigorousmethod.The classical theory of shells is used for the two face sheets and the core isconsidered as a three-dimensional elastic body.A series of transcendental equations areobtained,from which the critical loads can be calculated by numerical methods.Numericalexamples are given to compare with the solutions of sandwich shell theories.     

A new displacement-type stability equation and general stability analysis of laminated composite circular conical shells with triangular grid stiffeners

In this paper,based on the theory of Donnell-type shallow shell,a new displacement-type stability equations is first developed for laminated composite circular conical shellswith triangular grid stiffeners by using the variational calculus and generalized smeared-stiffener theory.The most general bending stretching couplings,the effect of eccentricity ofstiffeners are considered.Then,for general stability of composite triangular grid stiffenedconical shells without twist coupling terms,the approximate formulas are obtained forcritical external pressure by using Galerkin‘s procedure.Numerical examples for a certainC/E composite conical shells with inside triangular grid stiffeners are calculated and theresults are in good agreement with the experimental data.Finally,the influence of someparameters on critical external pressure is studied.The stability equations developed andthe formulas for critical external pressure obtained in this paper should be very useful in theastronautical engineering design.     

变角度纤维复合材料圆柱壳的轴压屈曲

变角度纤维复合材料的纤维方向角可沿铺层面内连续变化,因此相应结构的性能具有更高的设计灵活性和更大的优化空间．本文假设纤维方向角沿圆柱壳的轴向呈正弦函数变化,对变角度纤维复合材料圆柱壳在两端简支边界条件下的轴压屈曲问题进行研究．基于Donnell经典壳体理论,推导变角度纤维复合材料圆柱壳的前屈曲控制方程并运用伽辽金法进行求解,然后采用瑞利里兹法求解屈曲问题．通过和现有文献及有限元数值结果的对比,验证了本文模型的收敛性和正确性,通过数值算例分析了纤维起始角和终止角的变化对圆柱壳的屈曲临界荷载的影响．本文的研究结果可为变角度纤维复合材料圆柱壳的分析和设计提供一定的参考．     

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通过对拱顶储罐罐壁承受轴向载荷、初始几何缺陷及轴压失稳状况研究,指 出在固定顶罐设计、建造和运行各阶段都应进行罐壁轴压稳定性校核. 根据圆柱薄壳稳定性 理论和轴压失稳临界应力数值分析计算结果,提出固定顶罐罐壁轴压稳定性校核方法和数学 模型,并运用回归分析方法建立罐壁轴压失稳临界应力计算公式. 对几种常用规格的拱顶罐 有初始挠度缺陷罐壁轴压稳定性分析表明：随储罐容积和罐壁初始挠度增大,罐壁轴压稳定 性呈减弱趋势.     

Buckling and Postbuckling of Laminated Thin Cylindrical Shells under Hygrothermal Environments

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Study of nonlinear deformation and stability of discretely reinforced elliptic cylindrical shells in transverse bending

A finite-element method for solving problems of nonlinear deformation and stability of nonuniformly discretely reinforced noncircular cylindrical shells is considered. An effective computer algorithm for the study of shells is developed. Stability of stringer cylindrical shells with an elliptical cross section in transverse bending is examined. The effect of ellipticity, nonlinearity of shell deformation at the subcritical stage, reinforcement discreteness, and heterogeneity on shell stability is determined.     

Stability of Cylindrical Shells with Local Imperfections

We propose a nonlinear approach to the stability analysis of imperfect cylindrical shells under axial compression. The approach takes into account the initial deflections (imperfections) of the shell shape from cylindrical. A series of typical initial deflections is analyzed: local and longitudinal bulges (dents) and unilateral annular corrugations. A nonlinear stability problem is solved. The results are represented as plots of the nondimensional stress versus the nondimensional amplitude of initial deflections. It is shown that the capabilities of the nonlinear theory for estimating the critical stresses for thin shells have not been exhausted yet and that it could be used in future to explain some phenomena experimentally observed in shells     

VIBRATIONS OF CIRCULAR CYLINDRICAL SHELLS WITH NONUNIFORM CONSTRAINTS,ELASTIC BED AND ADDED MASS. PART II: SHELLS CONTAINING OR IMMERSED IN AXIAL FLOW

The model introduced in Part I of the present study is extended to take into account a flowing fluid, a mean radial pressure and initial pre-stress in circular cylindrical shells. The axial flow can be external, internal or annular and is described by the potential theory for inviscid and incompressible fluid. The computer program DIVA has been developed. It takes into account all the following complicating effects on the vibrations of circular cylindrical shells: (i) nonuniform boundary conditions around the shell edges including elastic boundary conditions; (ii) fluid–structure interaction including both flowing and quiescent fluids; (iii) internal, external and annular fluids; (iv) effect of a mean radial pressure and initial pre-stress; (v) elastic bed of partial extension in circumferential and longitudinal directions; (vi) intermediate constraints; (vii) added masses. It can be considered the most complete computer program specifically dedicated to dynamics of circular cylindrical shells. The Flügge theory of shells is used to describe the shell deformations. The system has been proved to be conservative for any combination of boundary conditions with restrained displacement at the shell ends. Numerical results show that shells clamped at the upstream end and simply supported at the downstream end have a larger critical velocity than simply supported shells, solving the paradox of Horáček and Zolotarev.     

Effect of multiple localized geometric imperfections on stability of thin axisymmetric cylindrical shells under axial compression

Stability of imperfect elastic cylindrical shells which are subjected to uniform axial compression is analyzed by using the finite element method. Multiple interacting localized axisymmetric initial geometric imperfections, having either triangular or wavelet shapes, were considered. The effect of a single localized geometric imperfection was analyzed in order to assess the most adverse configuration in terms of shell aspect ratios. Then two or three geometric imperfections of a given shape and which were uniformly distributed along the shell length were introduced to quantify their global effect on the shell buckling strength. It was shown that with two or three interacting geometric imperfections further reduction of the buckling load is obtained. In the ranges of parameters that were investigated, the imperfection wavelength was found to be the major factor influencing shell stability; it is followed by the imperfection amplitude, then by the interval distance separating the localized imperfections. In a wide range of parameters this last factor was recognized to have almost no effect on buckling stresses.     

Stability of shells of revolution with curvilinear generators in axial compression

Summary Curvilinearity of the generators forces the structure to behave in a qualitatively different way under the action of axial forces. Firstly, up to loss of stability the individual generators of the system are in a state of longitudinal-transverse bending. Secondly for a shell with negative Gaussian curvature there may be a sharp drop in the critical axial compressive loads even in structures that deviate only slightly from the cylindrical.All this means that shells of revolution with curvilinear generators in axial compression cannot be designed for stability using the formulas derived for cylindrical systems.Prikladnaya Mekhanika, Vol. 2, No. 1, pp. 59–68, 1966