Decomposition of the initial stability problem for a cylindrical shell under non‐symmetric loads

Abstract

Numerical aspects of initial stability analysis of a cylindrical shell of non‐constant parameters along the generator and under non‐symmetrical loads are considered. A variational approach based on Sanders' and Donnell's non‐linear equations of thin, elastic shells is applied. The problem is decomposed to determine: the stability vectors in the axial direction in the first step, and the critical load and the stability vector in the circumferential direction in the second step. The discretization is based on finite Fourier representations and the finite difference method. To find the approximate stability vector in the axial direction an auxiliary problem for axisymmetric loads is solved. The error of the method is defined and the effectiveness of the method is estimated. The decomposition leads to small and fast algorithms suitable for personal computers. Shells with constant and stepped thicknesses under wind loads are calculated as examples. Tested algorithms show considerable effectiveness and good accuracy of results.