Interaction of Critical Pressures and Critical Concentrated Loads Acting on Shallow Spherical Shells

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Abstract
In this paper the critical combinations of uniform pressures and concentrated loads at the apex acting on shallow spherical shells have been determined analytically and experimentally. The Dini-Bessel expansion of unknown functions, proposed first in [4], have been applied to the problem on hand. Test specimens void of initial geometrical imperfections and negligible residual stresses have been fabricated in the laboratory by using the die-pressing technique. The analytically calculated critical combinations are in good agreement with those determined experimentally. The theoretical lower-bound, or the cut-off values, of the geometry parameter, μ, is found to be near the experimental values. The existence of the analytical and experimental cut-off values of γ2 indicates that there is a lower bound of the values of uniform pressures such that a shell does not exhibit a snap-through instability when subjected for any combinations of concentrated loads and uniform pressures below its cut-off value.

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