The Axisymmetric Buckling of Initially Imperfect Complete Spherical Shells

A theoretical investigation of the axisymmetric buckling of complete thin-walled spherical shells under uniform external pressure is undertaken to determine the effect of axisymmetric initial imperfections. In the analysis, the complete spherical shell is divided into two parts; the shallow cap in which the initial imperfection exists, and the remaining portion of the shell most of which deforms in simple contraction. The rotation of the meridian of the cap is assumed in the form of a polynomial function. Four matching conditions are enforced at the juncture of the cap and remainder. The total potential energy of the complete spherical shell is minimized in accordance with the Rayleigh-Ritz approximation method. Two types of initial imperfections are studied; one is an axisymmetric dimple, and the other is a spherical region whose radius of curvature is greater than that of the perfect spherical shell. The maximal values of the pressure parameter rho in the equilibrium state before snap-through were calculated for various values of the geometric parameter lambda, which is proportional to the angular extent of the imperfection for a given radius-to-thickness ratio, and the imperfection amplitude parameter delta, which is the ratio of the initial deviation of the shell mid-surface at the axis of rotation to the wall-thickness. The results of numerical computations show that for all values of delta the lowest buckling pressure is reached when lambda is about 4. (Author).