Buckling behaviour of ring-loaded shallow spherical shells with a centre hole

Abstract

Results are presented of theoretical investigations into the elastic symmetrical buckling of clamped shallow spherical shells with a centre hole under a ring load, which are obtained by using both successive iterative techniques and cubic B-spline approximations. To find out the effect of the centre hole on buckling behaviour, clamped shallow shells with different boundary conditions at the hole edge (the centre hole edge is free or may be reinforced with a rigid ring) have been studied. It is shown that the presence of the centre hole causes opposed effects on the buckling behaviour for two kinds of clamped shells studied. This paper also investigates the limiting case in which the radius of the centre hole approaches zero. The results obtained are qualitatively similar to those observed by Evan-Iwanowski and Loo [Syracuse University Report, pp. 834–835, 1962] and Mescall [ Proc. 4th South-eastern Conf. on Appl. Mech., pp. 183–197, 1968] for complete shallow spherical caps subjected to ring load. However, detailed investigations indicate that the buckling load for a ring-loaded shell is in accord with that for a concentrated loaded shell when the ratio of loaded radius to shell base radius is less than a critical value. Upon an increase of the radius ratio beyond this critical value, the buckling load drops discontinuously due to the appearance of a new bump on the initial part of the load-deflection curve. The new maximum (i.e. buckling load) rises rapidly with the increase of radius ratio while the original maximum seems almost unaffected. For still larger loaded radius, the centre deflection becomes negative at low load and there is a point at which the slope of the load-deflection curve becomes infinite. Thus the corresponding buckling load rises drastically.