Nonlinear multiple-scale solution of a cylindrical shell

Abstract

A multiple-scale perturbation technique is used with a two-parameter expansion to study the asymptotic solution of Reissner’s axisymmetric finite-deformation equations for a circular cylindrical shell with an edge-bending moment load. Beyond the assumptions of Reissner’s differential equations, it is assumed that (1) the rotations of a shell element are finite but not excessively large, (2) thickness variations in the differential equations are of order one and (3) the boundary-layer behavior is of the linear bending type to a first approximation. An asymptotic solution is then found which is uniformly valid in that it contains boundary-layer effects and corrections for extending the analysis into the shell’s interior. Upon considering certain limits, it is observed that the solution contains well-established linear and nonlinear approximations to the solution.