XXXI - Six Different Stress Functions for Membranes of Revolution

Abstract

In the membrane theory of shells there are one moment and three force equilibrium equations. For shells of revolution, force equilibrium in a meridional plane may be expressed in the radial and axial directions or in the tangential and normal directions. An observation by Reissner suggests six different ways of introducing a membrane stress function into the linear theory of shells of revolution, each stress function implying the identical satisfaction of all but one equilibrium equation. Three of the stress functions turn out to be special cases of results of Pucher, Finzi, and Vekua from general membrane theory; another is a stress function introduced by Nemenyi specifically for shells of revolution, and two appear to be new.