AN ANALYTICAL STUDY OF ROTATIONALLY SYMMETRIC NON-LINEAR BUCKLING OF A COMPLETE SPHERICAL SHELL UNDER EXTERNAL PRESSURE

The non-linear post-buckling behaviour of a complete spherical shell is studied analytically in the vicinity of the buckling load. It is assumed that the shell buckles in a rotationally symmetric wave pattern and specific attention is given to deformation modes symmetric about the equator, in the longitudinal direction. The energy functional is reduced to approximate functions using the Rayleigh-Ritz method with which two types of assumed functions are considered, viz. Legendre polynomials and localized Rayleigh functions (finite elements). The algebraic equations of equilibrium are solved approximately using a series expansion technique, and it is shown that the use of Legendre polynomials gives exact values for the coefficients of the series, whilst use of the finite element method results in coefficients which converge monotonically to the exact values as the number of elements is increased. © 1968.