A rigorous method for the analysis of localization of axisymmetric buckling patterns in thick cylindrical shells (original) (raw)

A semi-analytical buckling analysis of imperfect cylindrical shells under axial compression

International Journal of Solids and Structures, 2003

In the framework of the cellular bifurcation theory, we investigate the effect of distributed and/or localized imperfections on the buckling of long cylindrical shells under axial compression. Using a double scale perturbative approach including modes interaction, we establish that the evolution of amplitudes of instability patterns is governed by a nonhomogeneous second order system of three non-linear complex equations. The localized imperfections are included by employing jump conditions for their amplitude and permitting discontinuous derivatives. By solving these amplitude equations, we show the influence of distributed and/or localized imperfections on the reduction of the critical load. To assess the validity of the present method, our results are compared to those given by two finite element codes.

Elastoplastic bifurcation and collapse of axially loaded cylindrical shells

International Journal of Solids and Structures, 2008

In this paper, a shell finite element is designed within the total Lagrangian formulation framework to deal with the plastic buckling and post-buckling of thin structures, such as cylindrical shells. First, the numerical formulation is validated using available analytical results. Then it is shown to be able to provide the bifurcation modes-possibly the secondary ones-and describe the complex advanced post-critical state of a cylinder under axial compression, where the theory is no longer operative.

Rigorous buckling of laminated cylindrical shells

Thin-walled Structures, 2009

The effect of pre-buckled nonlinearity on the bifurcation point of laminated cylindrical shells is examined on the basis of Donnell's shell theory. The eigenvalue problem is solved iteratively about the nonlinear equilibrium state up to the bifurcation point. An algorithm is presented for the real buckling behavior, dispensing with the need to cover the entire nonlinear pattern. This algorithm is very important for structures characterized by a softening process in which the pre-buckled nonlinearity depresses the buckling level relative to the classical one.

On dynamic buckling phenomena in axially loaded elastic-plastic cylindrical shells

International Journal of Non-Linear Mechanics, 2002

Some characteristic features of the dynamic inelastic buckling behaviour of cylindrical shells subjected to axial impact loads are discussed. It is shown that the material properties and their approximations in the plastic range in uence the initial instability pattern and the ÿnal buckling shape of a shell having a given geometry. The phenomena of dynamic plastic buckling (when the entire length of a cylindrical shell wrinkles before the development of large radial displacements) and dynamic progressive buckling (when the folds in a cylindrical shell form sequentially) are analysed from the viewpoint of stress wave propagation resulting from an axial impact. It is shown that a high velocity impact causes an instantaneously applied load, with a maximum value at t = 0 and whether or not this load causes an inelastic collapse depends on the magnitude of the initial kinetic energy. ?

Nonlinear behavior and buckling of cylindrical shells subjected to localized external pressure

Journal of Engineering Mathematics, 2013

Buckling loads and postbuckling behavior of cylindrical shells subjected to localized external pressure are considered. The modified extended Kantorovich method with path-tracing technique is applied to determine the buckling loads of the cylindrical shells. It is found that the load is dependent nonmonotonically on geometrical parameters of the area subjected to external pressure. Respective postbuckling shapes show correlation with the shapes corresponding to secondary bifurcation paths for the cases of a cylindrical shell under uniform external pressure and a cylindrical shell under uniform axial load.

Elastoplastic buckling of axially compressed circular cylindrical shells

International Journal of Mechanical Sciences, 1992

Buckling of axially compressed circular cylindrical shells is examined within the framework of small strain elastoplasticity. A linear bifurcation model is used along with the J2 flow and deformation theories. All four possibilities of simple supports (SS1-SS4) and clamped edges (CL1-CL4) are considered. A general solution is given with special emphasis on the axially symmetric modes. Numerical results show that the weakening effect of the relaxed simple supports (SSI-SS2) is considerably reduced in the plastic range. A detailed comparison with available experirriental data points in favour of the deformation theory.

On load interaction in the non linear buckling analysis of cylindrical shells

Advances in Engineering Software, 1991

The elastic stability of shells or shell-like structures under two independent load parameters is considered. One of the loads is associated to a limit point form of buckling, whereas the second is a bifurcation. A simple one degree of freedom mechanical system is first investigated, for which an analytical solution is possible. Next, a cylindrical shell under the combined action of axial load and localised lateral pressure is studied via a non linear, two-dimensional, finite ele ment discretization. It is shown that both problems display the same general behaviour, with a stability boundary in the load space which is convex towards the region of stability. The results show the need of performing a full non-linear analysis to evaluate the stability boundary for the class of interaction prob lems considered.