Buckling analysis of non‐uniform cylindrical shells of a four lobed cross section under uniform axial compressions

Abstract

AbstractIn this paper, the Flügge's shell theory is modeled and the transfer matrix approach is used to investigate the elastic buckling behaviour of a cylindrical shell with a four lobed cross section with reduced thickness over part of its circumference under axial compressive loads. Modal displacements of the shell can be described by trigonometric functions and Fourier's approach is used to separate the variables. The buckling equations of the shell are reduced to eight first‐order differential equations in the circumferential coordinate, and by using the transfer matrix of the shell, these equations can be written in a matrix differential equation. The transfer matrix is derived from the differential equations of the cylindrical shells by introducing the trigonometric functions in the longitudinal direction and applying a numerical integration in the circumferential direction. The method is used to get the critical buckling loads and the buckling deformations for symmetrical and antisymmetrical shells. Computed results indicate the sensitivity of the buckling loads and the corresponding buckling deformations to the geometry of the non‐uniformity of the shell, and also to the radius of curvature at the lobed corners.