Thin Plates and Shells

Abstract

In the preceding chapter, several cases of thin elastic plates loaded in the plane of the plate were analyzed using plane stress or plane strain equations. The resulting deformations are confined to the plane of the plate in accordance with the plane strain assumption. If such a plate is loaded transverse to the plane, the plate bends and the deflection of the surface in the normal direction is predominant, similar to a gridwork of beams. Correspondingly a distributed transverse loading can be efficiently resisted by an initially curved thin surface structure such as a cylindrical or spherical tank. The initial curvature mobilizes in-plane or membrane resistance that can be far more efficient than the bending resistance provided by flat plates. Several classical problems for the bending of rectangular and circular plates and for the membrane behavior of thin shells of revolution are presented as an introduction to this extensive topic.