Asymmetric Buckling of Imperfect Spherical Shells

A study is presented concerning the buckling characteristics of spherical shells with small initial symmetric and asymmetric imperfections in the geometry. The governing nonlinear partial differential equations are formulated using general relations with no restriction on shallowness. The effect of initial geometric imperfections is included in the equations. The shell material is assumed to be linearly elastic. The solution of the differential equations is carried out numerically using the method of L.V. Kantorovich in combination with finite differences. Numerical results are obtained by means of a digital computer, for spherical shells clamped at the boundary and subjected to uniform external pressure. Buckling pressures are determined from the load deflection relationship. The cases of asymmetric imperfections, and symmetric imperfections are studied. A wide range of shell geometries and imperfections is covered. Comparison with earlier experimental results shows good agreement.