Green’s Function for a Closed, Infinite, Circular Cylindrical Elastic Shell

An acceptable variant of the Koiter–Morley equations for an elastically isotropic circular cylindrical shell is replaced by a constant coefficient fourth-order partial differential equation for a complex-valued displacement-stress function. An approximate formal solution for the associated “free-space” Green’s function (i.e., the Green’s function for a closed, infinite shell) is derived using an inner and outer expansion. The point wise error in this solution is shown rigorously to be of relative order $(h∕a)(1+h∕a∣x∣)$⁠, where $h$ is the constant thickness of the shell, $a$ is the radius of the mid surface, and $ax$ is distance along a generator of the mid surface.