Buckling of cylindrical shells with random imperfections

Abstract

The buckling stability analysis of long cylindrical shells with random imperfections subjected to axial load is treated using two different approaches. The first study is based on a Lyapunov method which enables one to establish sufficient conditions for buckling stability of a long cylindrical shell with axisymmetric random imperfections. A perturbed system of equations in the neighborhood of the prebuckling solution is investigated. By reducing the problem to a system of integral equations, it is observed that the stability boundary value problem of a long shell is similar to that of a dynamical system with random parametric excitations. Initial imperfections were assumed to have Gaussian distribution and an exponential cosine correlation function. The critical load was obtained as a function of the root mean square of the imperfections. Results obtained are qualitatively similar to those of Koiter for a periodic imperfection (Ref. 1). The second part is based on the approximate method of truncated hierarchy. The prebuckling state of equilibrium for asymmetric imperfections is found by a successive substitution technique. A homogeneous variational system of equations is set up in order to examine the existence of bifurcation in the neighborhood of the equilibrium state. These last equations involve random parametric terms. The truncated hierarchy method is applied and characteristic equations are obtained. Various exponential cosine correlation functions associated with asymmetric imperfections are examined numerically. Qualitatively the results obtained are as anticipated.