Spherical Shells

Abstract

The cylindrical and conical shells considered in Chaps. 5 and 6 are special cases of shells of revolution. Spherical shells are another special case of shells of revolution. A spherical shell is a doubly-curved shell characterized by a middle surface generated by the rotation of a circular cure line segment (generator) about a fixed axis. If the axis of rotation along the diameter of the circle of the line segment, a spherical shell with constant curvature in the meridional and circumferential directions will be resulted and the two radii of curvature are equal. It is noticeable that the spherical shells are very stiff for both in-plane and bending loads due to the curvature of the middle surface, which is also a reason for the analysis difficulties of the shells, especially the exact three-dimensional elasticity (3-D) analysis. The spherical shells can be closed and open. If the generator rotates less than one full revolution about the axis, the spherical shell is open and has four boundaries. If further, the generator rotates one full revolution about the axis and the proper continuity conditions are satisfied along the junction line, a closed spherical shell results, which has only two edges.