An analysis of shallow spheroidal shells by a semi-inverse contour method

This paper presents a linear analysis of a shallow prolate spheroidal shell with a planar elliptical boundary. The shell is subjected to a uniform load, q, and clamped along the boundary. The theory used in this paper is characterized by the well known Mushtari-Donnell-Vlasov equations which consist of a compatibility equation and an equilibrium equation where the normal displacement, w, and a stress function, φ, are the dependent variables.The method employed for the solution of this problem is developed in three major stages. The first stage involves the determination of w, under the assumption that the contours of w be ellipses concentric to the boundary. The second stage is devoted to the determination of a stress function φ, which, together with w, satisfies the MDV compatibility equation exactly. The third stage of the development is concerned with the computation of a loading, q^*, which, together with w and φ, satisfies the equilibrium equation exactly and which is nearly equal to the desired uniform loading q.