A simplified version of Reissner's non-linear equations for a first-approximation theory of shells of revolution

Abstract

The static equations of the first-approximation theory of thin shells of revolution suffering small strains but arbitrarily large rotations are reduced, to within errors inherent in the assumption of a quadratic strain-energy density without transverse shear strains, to a coupled pair of equations for the meridional angle of rotation and a stress function. These equations are simpler than both Reissner's equations as well as a simpler version of Reissner's equations proposed by Koiter whose equations, like ours, are virtually free of Poisson's ratio.