The purpose of this paper is to illustrate the application of a new superposition method for the title problem and to explain its advantages with respect to the traditional superposition method. It is shown that the analytical manipulations are significantly less in the new approach, and this is achieved without any loss of rigour or accuracy. Further, the new method is also shown to facilitate incorporation of complicating effects like material orthotropy, in-plane forces or an elastic foundation without any change in the analytical methodology or the nature of the final equations. © 2008 Elsevier Ltd. All rights reserved.