Effect of edge shears and diaphragms on buckling of thin laminated medium-length cylindrical shells with low effective shear modulus under external pressure

Abstract

Governing equations based on the generalized kinematic hypotheses of Timoshenko and including the effect of transverse shears are used to predict the buckling of a medium-length thin laminated cylindrical shell under action of the external normal pressure. It is assumed that some of layers are made of a “soft” material so that the effective shear modulus turns out to be too less than the effective Young’s modulus for the laminate. Of all possible variants of boundary conditions, the boundary conditions corresponding to the simple support of edges with and without diaphragms in their planes are considered. For the case of the simply supported edges with diaphragms, the critical buckling pressure as well as the modes of buckling are found in an explicit form. If one of the edges is free from the diaphragm, the boundary-value problem is solved by using the asymptotic approach, a solution being constructed in the form of the superposition of functions describing the main stress state and the edge effect integrals. It is shown that the absence of the edge diaphragm accounts for the appearance of the edge transverse shears (non-classical edge effect integrals) whose decay rate is lower than that of the classical simple edge effect integrals. The effect of edge shears and diaphragms as well on both the critical buckling pressure and eigenform is studied for a laminated cylindrical shell with any number of layers regardless of materials used for laminae. As an example, the buckling of a cylindrical sandwich assembled from the ABS-plastic and magnetorheological elastomer under different levels of an applied magnetic field is examined.