Large deflection and buckling behaviour of a spherical shell with inward point load and uniform external pressure

Abstract

The large deflection of a spherical shell loaded with an inward radial point load and a uniform external pressure is investigated by supposing that the shell suffers small deflections from two known exact solutions to the equations for large deflection. These two exact solutions being of a segment whose curvature is completely reversed, for the region in the neighbourhood of the point of application of the point load, and of an unstressed sphere for the remainder of the shell.In the first part of the paper load-deflection curves are obtained for constant external pressures with varying inward point loads. It is found that for certain combinations of the values of pressure and point load, the shell becomes unstable. This is believed to be the first time that the stability of spherical shells under combinations of independently varying load system has been discussed.The results obtained in the first part of the paper are used in the second part to investigate the post-buckling behaviour of perfect and imperfect spherical shells under uniform external pressure acting alone. The behaviour predicted for a perfect shell agrees satisfactorily with the work of previous authors; the behaviour of shells with geometrical imperfection has received no previous satisfactory treatment. It is found that a geometrical imperfection of half the thickness can reduce the buckling pressure to about one-fifth of the classical value for perfect shells.Experiments are described on copper shells having regions thinned by acid etching. Their results are in good agreement with the theoretical predictions.