Analytical description of pre-buckling and buckling states of barrelled shells under radial pressure

The work is devoted to the strength and elastic stability analysis of a barrelled shell loaded with uniform radial pressure. The shell is assumed to be isotropic, homogeneous and of constant thickness. The geometry of the shell is described as well as the field of displacement for which Kirchhoff–Love hypothesis is applied. On the basis of the linear equilibrium equations the relations describing the membrane state of stress in the pre-buckling state are derived. The buckling problem of the barrelled shell is described analytically and solved approximately with the use of Bubnov–Galerkin method. As a result the formula for the critical pressure is obtained. The numerical examples are presented which were solved analytically and with the use of finite element method. The comparison of the results obtained in both ways shows very good agreement as to the values of membrane forces, buckling load and buckling shape. The formulae presented in the paper may help in the design of shell structures in the shape of barrel.

► Stability of thin barrelled shells is discussed.
► Formulae describing membrane state of stress are shown.
► Elastic buckling problem of barrelled shell is solved analytically and using FEM.