APPLICATION OF BETA-SPLINE APPROXIMATION TO SYMMETRICAL BUCKLING PROBLEMS OF TRUNCATED SHALLOW SPHERICAL-SHELLS SUBJECTED TO LINE LOADS

By using cubic B-spline approximations, reasonably accurate solutions are obtained for line-loaded shallow spherical shells with a centre hole within a wide range of values of the geometrical parameter K (0 less-than-or-equal-to K less-than-or-equal-to 400, K = square-root 12(1 - v2)2f/h, f = shell rise, h = shell thickness). It was found that the buckling loads P(c) as well as the buckling threshold of the geometrical parameter K(c) increase monotonically as the radius of the centre hole beta increases if the hole edge is reinforced with a rigid ring and the outer edge of the shell is simply supported. However, the effect of the centre hole on P(c) decreases rapidly as K increases and becomes negligible for K greater-than-or-equal-to 45 and beta less-than-or-equal-to 0.4.