Axisymmetrical buckling behavior of truncated shallow spherical shells subjected to line moment loads

Abstract

This paper is concerned with the nonlinear stability of simply supported shallow spherical shells with a center hole under the action of a uniformly distributed line moment along a circle concentric with the shell boundary. A set of truncated monomials have been used in representing various discontinuous distributions in order to simplify formulations. We have computed the load-deflection curves, buckling loads, radial membrane forces and the critical geometrical parameter Kc for shells with various center-hole radii. Our numerical results show that (1) both the initial shell stiffness and the buckling load are decreased due to the presence of a center hole with a free boundary. If the hole edge is reinforced with a rigid ring, the truncation not only raises the initial shell stiffness and the buckling load of the shell but also its critical geometrical parameter Kc. The effects of the truncation increase upon increasing the radius of the center hole; (2) for shells with large geometrical parameter K, the radial membrane forces at critical buckling become partly tensional and the buckling load will be almost unaffected by the truncation if the center hole is situated inside the tensile region.