Buckling of circular plates with shell-stiffening on the boundary

Abstract

The present paper is concerned with the stability problems of a thin solid circular plate and some annular plates, each stiffened by a cylindrical shell on the external boundary. Assuming an axisymmetric dead load and non-axisymmetric deformations we determine the critical load in order to clarify what effect the stiffening shell has on the critical load. Using Kirchhoff's theory of thin shells and plates the paper presents the governing equations both for the circular plate and for the cylindrical shell, where the displacement field of the shell is obtained from a Galerkin function. The deflection of the plate and the Galerkin function are expanded into Fourier series and consequently all physical quantities in the structural elements as well. The boundary-and continuity conditions and last but not least numerical results are also presented.Mathematical Subject Classification: 74K20, 65L15