Analytical Calculation of Momentless Conical Shell with Elliptical Base

Differential equilibrium equations of the momentless shell theory are very easily integrated in cases of cylindrical and right circular conical shells. Shells of zero Gaussian curvature defined in arbitrary curvilinear coordinates are more difficult to analyze, which was reaffirmed by the case of elliptical conical shells. For the first time, analytical expressions of normal and tangential internal forces in a momentless right elliptical conical shell defined in non-orthogonal conjugate system of curvilinear coordinates are obtained. The derived results can be used for approximation of the stress state of thin conical shells with elliptical base and also for the investigation of stability of these shells. Four internal tangential forces obtained by integration of the system of four equilibrium equations of a shell element contain two unknown integration functions, which are determined by satisfying given boundary conditions. The application of obtained analytical equations is demonstrated by an example of analysis of a truncated elliptical conical shell with free upper edge. A uniformly distributed surface load in the direction of the vertical axis of the shell was assumed as external load. The presented formulae are easily adapted for the analysis of a right circular conical shell.