Reduction of the Sanders-Koiter equations for fully anisotropic circular cylindrical shells to two coupled equations for a stress and a curvature function

With the aid of the static-geometric duality of Goldenveizer (1961), Cartes ian tensor notation, and nondimensionalization, it is shown that the equati ons of linear shell theory of Sanders (1959) and Koiter (1959), when specia lized to a circular cylindrical shell with stress-strain relations exhibiti ng full anisotropy (21 elastic-geometric constants), can be reduced, with n o essential loss of accuracy, to two coupled fourth-order partial different ial equations for a stress function F and a curvature function G. Auxiliary formulas for the midsurface displacement components are also given. For is otropic shells with uncoupled stress-strain relations, the equations reduce to a form given by Danielson and Simmonds (1969). The reduction is achieve d by adding certain negligibly small terms to the given stress-strain relat ions. For orthotropic shells of mean radius R and thickness h with uncouple d stress-strain relations. it is shown that the very short decay length of O(root hR) and the very long decay length of O(R root R/h) (associated with separable solutions of the form e(-Rz) sin n theta), depend, respectively, to within a relative error of O(h/R), only on the products of different pa irs of rite eight possible elastic constants.