Theory of Shells

Abstract

In the preceding chapter we studied the geometry of curved surfaces with the intention of applying the results to the theory of shells. By a shell we understand a piece of solid matter contained in the narrow space between two curved surfaces which are parallel or almost parallel to each other. Their distance is the shell thickness h,which is supposed to be small compared with other dimensions of the shell, in particular, with its radii of curvature. The surface which halves the shell thickness everywhere is called the middle surface and serves in the stress analysis the same purpose as the middle plane of a plate or the axis of a beam. The deformation of the shell is described in terms of the deformation of its middle surface, and the stress system is described by stress resultants like those in plates and slabs, referred to a unit length of section through the middle surface.