Postbuckling analysis of cross-ply laminated cylindrical shell panels under parabolic mechanical edge loading

Postbuckling equilibrium paths of simply supported cross-ply laminated cylindrical shell panels subjected to non-uniform (parabolic) inplane loads are traced in this paper. Love's shell theory with higher order shear deformation theory and von Kármán nonlinear strain–displacement relations are used in the mathematical formulation of the problem. In the first step, the plate membrane problem is solved to evaluate the stress distribution within the prebuckling range as the applied inplane edge load is non-uniform. The governing shell panel postbuckling equations are derived from the principle of minimum total potential energy using the above stress distributions. Adopting multi-term Galerkin's approximation, the governing equations are reduced into a set of non-linear algebraic equations. Newton–Raphson method in conjunction with Riks approach is employed to plot the postbuckling paths through limit points. Numerical results are presented for symmetric (0/90/0) crossply laminated cylindrical shell panels under parabolic inplane load, lateral distributed load and initial imperfections. Limit loads and snap-through behavior of shell panels are studied.     

Stability analysis of cross-ply laminated shells of revolution using a curved axisymmetric shell finite element

A curved axisymmetric shell finite element based on a consistent first-order shear deformable shell theory is developed for the linear stability analysis of cross-ply laminated shells of revolution under compressive loads. Finite element analysis results are presented for isotropic, orthotropic and cross-ply laminated shells of revolution in comparison with the analytical and numerical results found in the literature. These comparisons demonstrate the applicability and the high performance of the element in stability analysis of thin and moderately thick cross-ply laminated composite shells of revolution under compressive loads.     

Postbuckling analysis of circular cylindrical shells under external pressure

The postbuckling behavior of circular cylindrical shells of finite length under uniform external pressure is analysed using the spline finite strip method. A Total Lagrangian formulation on the displacement dependent pressure load in the orthogonal curvilinear reference frame is derived. An improvement for the arc-length iteration method is presented. The postbuckling equilibrium path and the contour map of equal radial deflection computed are in good agreement with the experimental and analytical results reported in Esslinger, M. and Geier, B., Postbuckling Behaviour of Structures, Springer-Verlag, Wien, New York, 1975.     

Elasticity solution for static analysis of laminated cylindrical panel using differential quadrature method

The three-dimensional (3D) solution for static analysis of cross-ply cylindrical panel is presented using differential quadrature method (DQM) and Fourier series approach. The panel is assumed to be simply-supported at one pair of opposite edges and arbitrary conditions at the other pair. Applying the DQM to the governing differential equations and to the boundary conditions along the axial or circumferential directions, new state equations about state variables at discrete points are derived. Displacement and stress fields according to the various kinds of edges conditions are obtained by solving these state equations. The method is validated by comparing numerical results for the simply-supported edges with that available in the literature.     

Delamination buckling for composite laminated cylindrical shells in Hamilton system

In this article, a semi-analytical three-dimensional model based on the modified Hellinger–Reissner (H–R) variational principle and a nonlinear spring-layer model are presented for the buckling analysis of composite laminated cylindrical shells with a delamination. The method allows the effect of transverse shear deformation in the control equations of the composite laminated structures. In addition, it uses a two-dimensional mesh and can ensure that the number of variables is independent of the layer number. The nonlinear spring-layer model between the exterior and interior sub-laminates ensures the continuity of transverse stresses and displacements in the undelaminated region by specifying infinite values of springs and therefore avoids the possibility of material penetration phenomenon in the delaminated region. As an application of the present method, the influence of the delamination length on the critical buckling loads of delaminated composite laminated stiffened cylindrical shells is investigated.     

Simple solution for buckling of orthotropic circular cylindrical shells

Most papers dealing with the analysis of the buckling behaviour of orthotropic circular cylindrical shells provide solutions which are complex in nature and difficult to use. In this paper the theory has been developed to the point that relatively simple solutions of a general nature have been formulated. Based on Flugge's linear theory for isotropic cylindrical shells, a general buckling solution under combined axial compression and external pressure was derived. For moderate-length orthotropic cylindrical shells loaded by either external pressure or axial compression, buckling loads are formulated in a simple form.     

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.     

Analysis of circular cylindrical shells under harmonic forces

A generalized thin shell theory for the stress-deformation analysis of thin-walled circular cylindrical shells is formulated based on the Hamilton's variational principle. The theory is applicable to multiple in-phase and out-of-phase harmonic forces and general boundary conditions. The stationary conditions of the Hamilton functional are then evoked to recover the equations of motion and boundary conditions of the problem. The unknown displacement fields are expanded as infinite complex Fourier series in the circumferential coordinate. The resulting field equations are observed to couple the radial, tangential and longitudinal displacement contributions within each mode, while uncoupling the contributions of a given Fourier mode from those of other Fourier modes. A general solution for the obtained field equations is developed for harmonic loading of general spatial distribution. The method developed is verified against well established solutions and its applicability to practical problems is illustrated through examples.     

Analysis and optimization of laminated composite circular cylindrical shell subjected to compressive axial and transverse transient dynamic loads

Optimization is one of the important stages in the design process. In this paper the genetic algorithms method is applied for weight and transient dynamic response and two constraints including critical buckling loads and principle strains optimization of laminated composite cylindrical shells. The multi-objective function seeks the minimum structural weight and transient dynamic response. Nine design variables including material properties (fibre and matrix), volume fraction of fibre, fibre orientation and thickness of each layer are considered. In analytical solution, vibration of composite circular cylindrical shells are investigated based on the first-order shear deformation shell theory. The boundary conditions are assumed to be fully simply support. The dynamic response of the composite shells is studied under transverse impulse and axial compressive 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. An example of simply supported laminated composite cylindrical shells is given to demonstrate the optimality of the solution obtained by the genetic algorithms technique. Results are shown that the weight coefficient of multi-objective function and the type of the constraints have considerable effect on the optimum weight and dynamic response.     

Stability of circular cylindrical steel shells under combined loading

Circular cylindrical shells made of steel are used in a large variety of civil engineering structures, e.g. in off-shore platforms, chimneys, silos, tanks, pipelines, bridge arches or wind turbine towers. They are often subjected to combined loading inducing membrane compressive and/or shear stress states which endanger the local structural stability (shell buckling). A comprehensive experimental and numerical investigation of cylindrical shells under combined loading has been performed which yielded a deeper insight into the real buckling behaviour under combined loading . Beyond that, it provided rules how to simulate numerically the realistic buckling behaviour by means of substitute geometric imperfections. A comparison with existing design codes for interactive shell buckling reveals significant shortcomings. A proposal for improved design rules is put forward.     

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.     

单层叉筒网壳结构的几何非线性静力稳定分析

通过跟踪网壳结构的非线性荷载一位移全过程响应，完整地了解了该结构在整个加载过程中的强度、稳定性以及刚度的变化历程，合理确定其稳定承载力，通过分析对单层网壳的静力稳定特性有了较全面的了解。     

Dynamic and static axial crushing of axially stiffened cylindrical shells

The axial impact of cylindrical tubes, which incorporate axial stiffeners, is examined in this paper. For comparison purposes, the effect of static loading is also studied. An examination is made into the influence of stiffener depth (T), number of stiffeners (N) and the effect of placing the stiffeners externally or internally.

The experimental results on mild steel specimens show that there are considerable differences between the static and dynamic modes of failure, and that an optimum T/D ratio may exist for a given value of N.     

Transient vibrations of laminated composite cylindrical shells exposed to underwater shock waves

The problem of the transient vibration of an elastic laminated composite cylindrical shell with infinite length exposed to an underwater shock wave is solved approximately. The linear acoustic plane wave assumption and Sanders thin shell theory are adopted. The reflected-afterflow virtual-source (RAVS) procedure is used to model the fluid–structure interaction involved during the underwater shock event. For the validity of the present analysis, the response of a laminated cylindrical shell under step plane wave is first analyzed and compared with the numerical solution available in the literature. Detailed numerical results for the transient responses of the shells under an exponentially decaying underwater shock wave are presented, and the influences of fiber angle, shell radius and thickness upon the dimensionless radial velocity, mid-surface strain, 0th mode radial displacement and 1st mode radial velocity of the shells, are investigated.     

A parametric study of the free vibration analysis of rotating laminated cylindrical shells using the method of discrete singular convolution

This paper deals with the free vibration analysis of rotating laminated cylindrical shells. The analysis uses discrete singular convolution (DSC) technique to determine frequencies. Regularized Shannon's delta (RSD) kernel is selected as singular convolution to illustrate the present algorithm. The formulations are based on the Love's first approximation shell theory, and include the effects of initial hoop tension and centrifugal and coriolis accelerations due to rotation. The spatial derivatives in both the governing equations and the boundary conditions are discretized by the DSC method. Frequency parameters are obtained for different types of boundary conditions, rotating velocity and geometric parameters. The effect of the circumferential node number on the vibrational behaviour of the shell is also analysed. The analysis has been verified by comparing results with those in the literature and sufficient agreement is obtained.     

Buckling of circular cylindrical shells partially subjected to external liquid pressure

Theoretical analyses are presented for the buckling of circular cylindrical shells partially subjected to external liquid pressure. The shells are assumed to stand vertically with the lower end clamped, and the upper end clamped or free. In the analyses, the Donnell equations are used for the basic equation, and prebuckling deformation as well as the membrane state of stress of the shell are taken into account. The Galerkin method is used, and the critical pressures at various liquid heights as well as the wave numbers, are obtained for a wide range of the geometrical parameters of the shell Z. A convenient chart which indicates the buckling liquid height for a given shell and liquid are presented. Experimental studies are also conducted by using test cylinders made of polyester film, and water. The theoretical and experimental results for the buckling liquid height, are in excellent agreement.     

Dynamic elastic instability of long circular cylindrical shells under pure bending

The present paper studies the responses and instabilities of long circular cylindrical shells subjected to dynamic pure bending. The dynamic instability characteristics of the shells subjected to a sudden step bending load of infinite duration are explored. Analysis is performed using nonlinear finite element numerical methods. Critical dynamic moments are determined through the use of Budiansky and Routh's stability criterion. Numerical predictions for the dynamic instability are compared with those static results given earlier by Brazier. The effects of shell geometry on the dynamic stability of the shells are shown. It is found that the dominating factor to affect the shell stability is the ovalization of the shell cross-section in the centre of the shell.     

圆柱形网壳的塑性极限分析

本探讨了圆柱形网壳结构的塑性极限分析，在分析过程中，采用拟壳法将圆柱形网壳结构等效为连续的夹层壳，然后对等效夹层壳进行塑性极限分析，由于夹层壳结构的极限条件是线性的，因而在求解时问题得到了大的简化，鉴于有矩理论的复杂性，本在作极限分析时，采用了无矩理论和半无矩理论的平衡方程分别作为中短壳和长壳的平衡方程。     

新型索承叉筒网壳的构形、分类与受力特性研究

叉筒网壳是一种由若干组圆柱面网壳相贯得到的空间结构,具有独特的建筑造型与受力性能.由于其传力路径简捷,主要集中于脊线或谷线,对边界约束要求较高,一定程度限制了其应用和发展.本文提出了一种新型索承叉筒网壳结构,并给出了三种不同的分类方法,较全面地概括了索承叉筒网壳结构的形体和种类,并提出了将索承叉筒网壳作为结构单元进行组合,构建大面积结构的设想.最后,以十二边形谷线式弦支叉筒网壳为例与叉筒网壳对比,并进行了参数分析,结果表明索承叉筒网壳结构静力性能得到较大的改善.     

斜拉双层柱面网壳与双层柱面网壳的对比分析

斜拉结构是一种新型大跨空间结构体系,满足了人们对于建筑大跨度的追求,因其良好的受力性能和宏伟的建筑造型而广泛应用于实际工程中。本文利用有限元软件对斜拉双层柱面网壳结构进行建模和分析。应用有限元法,与相应的普通双层网壳结构进行对比分析,从而为设计人员提供一些有用的资料以供参考。