The axisymmetric postbuckling behaviour of shallow spherical domes

Abstract

On the assumption that the buckling of an elastic, shallow spherical dome, rigidly clamped along a contour and loaded by a uniform transverse pressure, is finite and axisymmetric, its postbuckling behaviour is investigated. A solution is constructed based on the Marguerre equations using the Rayleigh-Ritz method with the displacements approximated by finite sums over Bessel functions. The system of non-linear algebraic equations obtained in this case is solved by the method of prolongation (the arc-length method). The effect of the wall-thinness parameter of the dome on its deformation curve is analysed. The phenomena of the generation of limit points in the loading trajectory, their merging and subsequent disappearance, as well as the phenomena of the joining of isolated loops to the main branch of the loading trajectory and of their detachment from it are discovered. The high sensitivity of the dome to deviations from an ideal shape is demonstrated.