The computation of nonlinear instability for multilayer composite cylindrical shells

In this paper,energy method and finite difference method are used to Compute theinstability behavior of multilayered fiber composite cylindrical shells under axialcompression,hydrostatic pressure and torsion.The influences of initial imperfections,geometrical nonlinearities of shells and physical nonlinearities of the materials to thebuckling and postbuckling behavior of the shells are considered.The effect of transverseshear is also discussed.The computational results of this paper are well agreed with theexperimental data.     

A boundary layer theory for the buckling of thin cylindrical shells under external pressure

Based on the boundary layer theory for the buckling of thin elastic shells suggested in ref. [14]. the buckling and postbuckling behavior of clamped circular cylindrical shells under lateral or hydrostatic pressure is studied applying singular perturbation method by taking deflection as perturbation parameter. The effects of initial geometric imperfection are also considered. Some numerical results for perfect and imperfect cylindrical shells are given. The analytical results obtained are compared with some experimental data in detail, which shows that both are rather coincident.     

Limit Analysis of Circular Cylindrical Shells under Hydrostatic Pressure*

The problem of limit analysis of circular cylindrical shells under hydrostatic pressure is dealt with. On the basis of Hodge plastic yield condition, solutions are achieved by solving systems of simultaneous algebraic nonlinear equations. Several cases of different boundary conditions are considered.     

Compound strip analysis of ring-stiffened cylindrical shells under hydrostatic pressure

The efficient compound strip method is used to analyse the buckling of ring-stiffened cylindrical shells under hydrostatic pressure. The eccentricity of stiffeners is taken into account. Numerical examples are given to illustrate the efficiency and accuracy of this method.     

环壳屈曲的渐近解

本文提出分析圆环壳屈曲的一种渐近解析方法,由Sanders非线性平衡方程和壳中面变形协调方程推导出静水外压下环壳的稳定方程,求出了方程的渐近解,理论计算的临界压力值与Fishlowitz的实验结果符合良好,并研究了屈曲前非线性变形对临界载荷的影响。     

The initial postbuckling behavior of ring stiffened shells under hydrostatic pressure

In this article the initial postbuckling behavior of ring stiffened cylindrical shells under hydrostatic pressure is analyzed by Koiter's theory. The nonlinear bending equations consistent with boundary conditions have been used in prebuckling state. The eigenvalue problem is solved by Galerkin's method. The obtained buckling loads are compared with the results which are based on classical stability theory. As calculating examples, three typical outside-stiffened cylinders with different ring stiffener parameters are chosen. The results show that the strength of stiffener not only influences buckling load obviously, but also changes the imperfection-sensitivity of cylindrical shells.     

Experimental investigation of the buckling instability of monocoque shells

Buckling of a series of thin-metal, shallow spherical shells under a uniform hydrostatic pressure has been investigated. Stress and deformation histories, as well as the critical buckling pressure and the post-buckling behavior, have been determined. Comparisons with theoretical analyses for buckling of spherical caps are given. Results are presented for an initial phase of a stability study of truncated conical sections which have been subjected to combinations of axial load and lateral pressure. A series of roll-formed and butt-welded, truncated aluminum conical shells with a 75-deg base angle have been tested. Buckle modes for axial-load condition alone, laterial-pressure load alone and combinations of these loading conditions are described. Interaction curves for the conditions investigated are given.     

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.     

Equilibrium and buckling of combined shells under uniform external pressure

Nonlinear strain is used to formulate the energy functional of combined structure with several kind of shells. The nonlinear finite element method (N.F.E.M.) is proposed for calculating bending and buckling of the structure subjected to external hydrostatic pressure. The numerical results are found to be in good agreement with experimental ones.     

Experiments on the postbuckling behavior of circular cylindrical shells under hydrostatic pressure

Detailed experimental studies are performed on the postbuckling behavior of circular cylindrical shells under hydrostatic pressure, by using lap-jointed polyester test cylinders with radius 100 mm, thickness 0.25 mm and lengths ranging from 23 to 165 mm. Connections of the edge shortening and radial displacement with applied pressures as well as wave forms for typical postbuckling configurations are determined for various values of the shell curvature parameterZ ranging from 20 to 1000. It is found that the buckling pressure and the corresponding wave number for each cylinder compare favorably with those theoretically predicted, and that the minimum pressure after buckling decreases with the increase inZ, until it becomes about 70 percent of the theoretical buckling pressure for long shells withZ greater than 200.     

Shock initiated instabilities in underwater cylindrical structures

An experimental investigation to understand the mechanisms of dynamic buckling instability in cylindrical structures due to underwater explosive loadings is conducted. In particular, the effects of initial hydrostatic pressure coupled with a dynamic pressure pulse on the stability of metallic cylindrical shells are evaluated. The experiments are conducted at varying initial hydrostatic pressures, below the critical buckling pressure, to estimate the threshold after which dynamic buckling will initiate. The transient underwater full-field deformations of the structures during shock wave loading are captured using high-speed stereo photography coupled with modified 3-D Digital Image Correlation (DIC) technique. Experimental results show that increasing initial hydrostatic pressure decreases the natural vibration frequency of the structure indicating loss in structural stiffness. DIC measurements reveal that the initial structural excitations primarily consist of axisymmetric vibrations due to symmetrical shock wave loading in the experiments. Following their decay after a few longitudinal reverberations, the primary mode of vibration evolves which continues throughout later in time. At the initial hydrostatic pressures below the threshold value, these vibrations are stable in nature. The analytical solutions for the vibration frequency and the transient response of cylindrical shell are discussed in the article by accounting for both (1) the added mass effect of the surrounding water and (2) the effect of initial stress on the shell imposed by the hydrostatic pressure. The analytical solutions match reasonably well with the experimental vibration frequencies. Later, the transient response of a cylindrical shell subjected to a general underwater pressure wave loading is derived which leads to the analytical prediction of dynamic stability.     

Imperfection sensitivity of an orthotropic spherical shell under external pressure

In the first part of this paper, rib-stiffened thin-walled spherical shells under external hydrostatic pressure are optimized using classical approximate methods and empirical knock-down-factors. In the second part of the paper, the influence of known imperfections is investigated.The thin-walled spherical shells under external pressure are very sensitive to geometrical imperfections. Hoff recognized that for entire isotropic spherical shells the more likely imperfection will be a local circular dent, which for such shells, can always be considered as an axisymmetric one. Hoff's idea has been further investigated by Koga–Hoff, Galletly et al. These results showed that for a given depth of an imperfection a critical size of the corresponding circular dent exists, giving the minimum for the actual load carrying capacity of the shell.This paper suggests to extend Hoff's theory to isogrid and waffle-grid stiffened spherical shells. The issue of these investigations is a set of knock-down-factors plotted versus imperfection amplitude related to the total thickness of the rib-stiffened (isogrid or waffle-grid) shell. These curves fit reasonably with those established for isotropic shells by Hoff et al. or by Koiter, and enable to estimate the jeopardy of measured actual dents.     

Buckling of cylindrical shells under combined torsion and hydrostatic pressure

Results are given for a series of tests conducted to determine the elastic buckling behavior of circular cylindrical shells under hydrostatic pressure and torsion, both for individual and for combined loads. Nondimensional interaction curves are presented in terms of the geometric parameters of the cylinders and, in general, follow the parabolaP+T ²=1, whereP andT are the nondimensional critical hydrostatic and torsional loads, respectively.     

Numerical modelling of the stability of loaded shells of revolution containing fluid flows

A mixed finite-element algorithm is proposed to study the dynamic behavior of loaded shells of revolution containing a stationary or moving compressible fluid. The behavior of the fluid is described by potential theory, whose equations are reduced to integral form using the Galerkin method. The dynamics of the shell is analyzed with the use of the variational principle of possible displacements, which includes the linearized Bernoulli equation for calculating the hydrodynamic pressure exerted on the shell by the fluid. The solution of the problem reduces to the calculation and analysis of the eigenvalues of the coupled system of equations. As an example, the effect of hydrostatic pressure on the dynamic behavior of shells of revolution containing a moving fluid is studied under various boundary conditions. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 2, pp. 185–195, March–April, 2008     

海底管道的弹塑性稳定性和屈曲传播

本文根据我国南海海底输油气铺管的要求系统分析了海底管道在弯曲与外水压力共同作用下的弹塑性稳定性和屈曲传播.研究了管道的极值型屈曲和分枝型屈曲.在考虑管道的初始非圆度和材料的物理非线性的情况下提出了临界屈曲载荷的计算方法.综述和评论了屈曲传播现象的本质和各种计算方法.介绍了我们所进行的全尺寸管道实验.在分析理论结果时与现行的有关设计规程进行了比较和评论.     

Buckling of elastic-plastic shells of revolution with discrete elastic-plastic ring stiffeners

The theory is summarized for axisymmetric prebuckling and nonsymmetric bifurcation buckling of ring-stiffened shells of revolution. The analysis is based on finite difference energy minimization in which moderately large meridional rotations, elastic-plastic effects, and primary or secondary creep are included. This theory is implemented in a computer program called BOSOR5, for the analysis of segmented and branched ring-stiffened shells of revolution of multi-material construction.Comparisons between test and theory are given for axisymmetric collapse and nonsymmetric bifurcation buckling of 69 machined ring-stiffened aluminum cylinders submitted to external hydrostatic pressure. Because most of the cylinders fail at an average stress which corresponds to the knee of the stress-strain curve, the analytical predictions are not very sensitive to modeling particulars such as nodal point density or boundary conditions. Agreement between test and theory is improved if the analytical model reflects the fact that the shell and rings intersect over finite axial lenths.     

Membrane analysis and optimization of submerged domes with allowance for selfweight and skin cover load

This paper is concerned with membrane analysis and optimal design of submerged domes. In addition to hydrostatic pressure, domes are also subjected to selfweight and skin cover load, which are invariably present in these types of structures. Using the membrane theory for thin shells and by adopting a fully stressed design, equations governing the meridional curve of submerged domes are derived with allowance for selfweight and skin cover load. A set of nonlinear differential equations, which correspond to a two-point boundary problem, is solved by the shooting-optimization method. Based on a family of fully stressed designs associated with a given water depth and dome height, the optimal dome shape for minimum weight is determined.     

Static and dynamic buckling modes of a cylindrical shell under external pressure

We consider the problem of static and dynamic buckling modes of thin shells under external hydrostatic pressure. If the statement of the problem uses the linearized equations of motion obtained in the moderately large bending theory of shells according to the classical or refined model, then part of terms related to the external load in these equations are assumed to be conservative, and the other terms are assumed to be nonconservative. In this connection, we study four statements of the elastic stability problem for a cylindrical shell with hinged faces. The first of them is the statement of the static boundary value problem in the sense of Euler, where the action of external pressure is assumed to be conservative. The second statement is used to study small vibrations near the static equilibrium by a dynamic method for the same conservative load. The third and fourth statements of the problem correspond to the action of a nonconservative load and are similar to the first and second statements, respectively. They use the linearized equations of equilibrium and motion constructed earlier in a consistent version on the basis of a Timoshenko type model and allowing one to reveal all classical and nonclassical shell buckling modes.     

The vibration and buckling of laminated non-homogeneous orthotropic conical shells subjected to external pressure

In this paper, the free vibration and buckling of laminated homogeneous and non-homogeneous orthotropic truncated conical shells under lateral and hydrostatic pressures are studied. At first, the basic relations, the modified Donnell type dynamic stability and compatibility equations have been obtained for laminated orthotropic truncated conical shells, the Young's moduli and density of which vary piecewise continuously in the thickness direction. Applying superposition and Galerkin methods to the foregoing equations, the buckling pressures and dimensionless frequency parameter of laminated homogeneous and non-homogeneous orthotropic conical shells are obtained. The appropriate formulas for single-layer and laminated cylindrical shells made of homogeneous and non-homogeneous, orthotropic and isotropic materials are found as a special case. Finally, the effects of the number and ordering of layers, the variations of conical shell characteristics, together and separately variations of the Young's moduli and densities of the materials of layers on the critical lateral and hydrostatic pressures, and frequency parameter are found for different mode numbers. The results are compared with other works.     

A Review of External Pressure Testing Techniques for Shells including a Novel Volume-Control Method

A review of conventional testing methods for applying external hydrostatic pressure to buckling-critical shells is presented. A new “volume-control” pressure testing method, aimed at preventing catastrophic specimen failures and improving control of specimen deformation near the critical load, is also introduced. The implementation of conventional and volume-control systems in an experimental program involving the destructive pressure testing of ring-stiffened cylinders is described. The volume control method was found to improve control of the specimen deformations, especially near the critical load, and catastrophic failures observed while using a conventional setup were avoided. The quasi-static tracking of post-collapse load-deformation relationships for snap-through buckling behaviour was possible while using a volume-control system, but precise control of dynamic shell deformations during buckling was not achieved for specimens failing with large buckling lobes. Expressions for estimating the available control over specimen deformations for pressure testing systems are presented.