Load Of Cylindrical Shells Research Articles

Effect of Orthotropic Mechanical Property on the Limit Load of Cylindrical Shell under Internal Pressure

At present the orthotropic pressurized metal structure is generally used as the isotropic one, ignoring the anisotropic characteristics of material caused during rolling process. At the same time, the elastic stress analysis design method is commonly used in pressure vessel, and the load capacity coming from plasticity of material has not been utilized. Therefore, elastic-plastic analysis of orthotropic pressurized structure is of great theoretical significance and engineering value. In present paper the limit load of orthotropic titanium cylindrical shell under internal pressure was studied. By finite element method with twice elastic slope criterion the variations of limit load for orthotropic and isotropic titanium cylindrical shells under different diameter-thickness ratios were investigated. The effect of orthotropic mechanical property on limit load of titanium cylindrical shell was discussed. At the same time, the difference of limit loads between orthotropic and isotropic titanium cylindrical shells was compared. The calculation results show that the limit loads of orthotropic and isotropic titanium cylindrical shell increase with the diameter-thickness ratio, and the limit load of orthotropic titanium cylindrical shell increases more obviously. Additionally, if the yield strength of isotropic cylindrical shell is the same as or close to the yield strength of circumferential direction for orthotropic titanium cylindrical shell, the difference of limit load is smaller. While the yield strength of isotropic cylindrical shell is much different from the yield strength of circumferential direction for orthotropic titanium cylindrical shell, the difference of the limit load is higher.

Analytical study on the buckling of cylindrical shells with stepwise variable thickness subjected to uniform external pressure

ABSTRACTThis article focuses on the buckling of cylindrical shells with stepwise variable thickness subjected to uniform external pressure. First, combining the method of separation of variables, perturbation method, and Fourier series expansion, an analytical method for the buckling analysis of cylindrical shells with axisymmetric thickness variation subjected to external pressure is established. The method is verified by comparing with the previous results. Then, the stepwise variable thickness of cylindrical shells is described exactly by the arc tangent function. Finally, using the presented method, a general formula for the critical buckling load of cylindrical shells with stepwise variable thickness subjected to uniform external pressure is derived. This general formula is compared and discussed with some empirical formulae in the current design standards. This study lays a theoretical foundation for the calculation of the buckling load of cylindrical shells with stepwise variable thickness subjected to uniform external pressure. Moreover, it provides a reference and guidance for the further revision of related standards.

Buckling of axial compressed cylindrical shells with stepwise variable thickness

This paper focuses on an analytical research on the critical buckling load of cylindrical shells with stepwise variable wall thickness under axial compression. An arctan function is established to describe the thickness variation along the axial direction of this kind of cylindrical shells accurately. By using the methods of separation of variables, small parameter perturbation and Fourier series expansion, analytical formulas of the critical buckling load of cylindrical shells with arbitrary axisymmetric thickness variation under axial compression are derived. The analysis is based on the thin shell theory. Analytic results show that the critical buckling load of the uniform shell with constant thickness obtained from this paper is identical with the classical solution. Two important cases of thickness variation pattern are also investigated with these analytical formulas and the results coincide well with those obtained from other authors. The cylindrical shells with stepwise variable wall thickness, which are widely used in actual engineering, are studied by this method and the analytical formulas of critical buckling load under axial compression are obtained. Furthermore, an example is presented to illustrate the effects of each strake

Approximate formulation for bifurcation buckling loads of axially compressed cylindrical shells with an elastic core

This paper proposes an approximate formulation to estimate the bifurcation buckling loads of cylindrical shells with soft elastic cores under the conditions of axial compression. In general, thin-walled, axially compressed cylindrical shells buckle into a diamond pattern in the elastic range. However, buckling symmetrical with respect to the axis of the cylinder may occur when the cylindrical shell is supported by an elastic medium. By considering this characteristic, we introduce the simplified approximate formulation that can give sufficiently accurate results for the bifurcation buckling loads of cylindrical shells. Moreover the results are compared with the exact buckling loads in order to confirm the accuracy of the proposed approximate formulation.

Theoretical, experimental and numerical investigation on the behaviour of tubular shells under internal blast loading

Explosive loading of closed cylindrical structures is one of the most complicated types of high rate loadings that can be applied on fully closed structure. Considering the complexities and unknown factors that affect the dynamic-plastic behaviour of a fully closed tubular shell under internal blast loading, the main objective of this article is to achieve a better understanding of the deformation of such a structure through different theoretical, empirical and also numerical approaches. Based on some simplifying assumptions, a new pressure–time profile for the internal explosive loading of cylindrical shells whose length is shorter than its diameter would be introduced in this manuscript. Afterwards, the fundamental equations of motion would be solved by the use of the aforementioned profile so that a practical formula for the calculation of maximum radial deformation of shell would be obtained. Comparison between the theoretical values and the results of the experimental tests conducted on several pieces of aluminium shells shows that the accuracy of the new theory is approximately 82%. Furthermore, this problem will be also modelled by the use of LS-DYNA module. Considering three separate meshing zones on the explosive charge, conveying medium and also the shell body which were connected to each other on overlapping surfaces, the numerical results for the maximum transverse displacement of the shell would be obtained from the software. Comparison between the finite element method and experimental results shows an average error of around 24%.

Effect of methods for fixing and loading of cylindrical shells on their stability and supercritical behavior

The effect of the methods of fixing and external-pressure loading of an elastic isotropic cylindrical shell on its sub- and supercritical deformation is investigated. A geometrically nonlinear statement of the edge problem in the form of the technical theory of finite deflection hollow shells is applied. The edge problem is digitized with the Rayleigh-Ritz method. The solution to the set of nonlinear algebraic equations is sought using the methods of continuation by the parameter close to the optimal one. The versions of shell sealing and supporting as well as uniform lateral pressure and uniform compression are considered. The trajectories of shell loading are plotted and the shapes of their supercritical equilibrium states are found. The axial compressing load is found to exert a larger effect on the upper and lower critical pressure as compared to the conditions of shell end fixing. Moreover, axial loading of short shells yields an increase in the critical pressure rather than its decrease, as is customary in the theory of shell stability.

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

Limit Loads of Cylindrical Shells under Hydrostatic Pressure

The limit analysis of circular cylindrical shells under hydrostatic pressure is formulated as a mathematical programming problem using the static theorem of plasticity. The governing differential equilibrium equations and force boundary conditions are linearized through a finite difference scheme. This discretization is combined with a piecewise linearization of the nonlinear yield curve to convert the formulation into a conventional linear programming exercise. This approach is shown to be superior to the more commonly used analytical techniques. In particular, it is general, systematic, and does not require prior knowledge of the stress field or collapse mechanism. In spite of the fact that a lower-bound solution is not guaranteed due to possible yield violation at unchecked points in the structure, very accurate solutions can be obtained by suitably refining the finite difference mesh and, if necessary, the yield polygon. Examples of reported cases are solved to illustrate ease of application of the method, its flexibility, and accuracy.

Follower Force Effects on Stability of Shells under Hydrostatic Loads

The paper first classifies various kinds of pressure loads, then linear and nonlinear finite element buckling analyses of cylindrical shells under uniform and non-uniform loads are presented. In particular the influence of displacement dependent loads on the buckling load of cylindrical shells under water and wind loading is discussed. Finally, the paper summarizes the design rules for wind loaded cylindrical tanks recently developed in Austria and Germany. The study has three goals: to clarify the problem and the effect of follower loads, to demonstrate the capability of nonlinear finite element analyses, and to discuss some results for design practice.

Investigation of the effect of reinforcement on the size of the critical load for cylindrical shells of constant weight with holes

Investigation of the effect of reinforcement on the size of the critical load for cylindrical shells of constant weight with holes

Determination of the upper critical loads for cylindrical shells by nonlinear theory

Determination of the upper critical loads for cylindrical shells by nonlinear theory