Accurate Fourth Order Equation for Circular Cylindrical Shells

Abstract

A pair of complex conjugate fourth-order partial differential equations which govern the deformation of circular cylindrical shells is presented. This pair of equations has at least the same accuracy as the Flugge equation and is as accurate as an equation can be within the scope of the Kirchhoff assumptions. Because they are complex conjugates, only one of the equations need be considered. The advantage in using the present pair of equations, besides their accuracy, is that the solutions of these equations can be readily found in simple closed forms as shown in the paper. This simplifies the calculations considerably in solving problems of cylindrical shells. Unlike the accurate Flugge equation and other equally accurate equations for cylindrical shells, their solutions can only be found approximately by trial and error.