A Method for Approximate Stability Analysis and Its Application to Circular Cylindrical Shells Under Circumferentially Varying Edge Loads

Abstract

A procedure is presented which relates the solution of the stability problem for an elastic structure subjected to a complex prebuckling stress distribution, to that of a solved stability problem for the same structure but with a “simple” stress distribution. The procedure reduces to obtaining the characteristic roots of a symmetric matrix. It is then applied to the buckling problem of a circular cylindrical shell subjected to a circumferentially varying compressive stress field and boundary conditions of the SS1-2 types. The main result is that for the boundary conditions and number of harmonic terms in the edge load taken, the buckling parameter approaches, as h/R → 0, that of a cylinder uniformly subjected to the maximum circumferential stress.