ABSTRACT
A closed-form analytical solution is presented for the complete determination of the stress state and deformations within parabolic ogival toroidal vessels under internal pressure. Linear theory-equations for the vessels are formulated on the basis of the theory of thin-shells of revolution. The equations are simplified and systematically solved using the general strategy of Zingoni (2018), in which the Geckeler approximations are adopted, and the membrane solution is superimposed with an approximate bending solution of the bending-theory equations. The accuracy of the developed solution algorithm is demonstrated through a numerical example by comparing results with those from finite element analysis. Excellent agreement is achieved throughout the vessel. The accuracy of the developed method demonstrates the validity of Geckeler approximations even in the anticlastic surfaces of shells of revolution.
