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

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.