Coiflets solutions for Föppl-von Kármán equations governing large deflection of a thin flat plate by a novel wavelet-homotopy approach

Abstract

In this paper, a novel technique incorporated the homotopy analysis method (HAM) with Coiflets is developed to obtain highly accurate solutions of the Foppl-von Karman equations for large bending deflection. The characteristic scale transformation is introduced to nondimensionalize the governing equations. The results are obtained for the transformed nondimensional equations, which are in very excellent agreement with analytical ones or numerical benchmarks performing good efficiency and validity. Besides, we notice the nonlinearity of the Foppl-von Karman equations is closely connected with the load and length-width ratio of the plate. For the case of the plate suffering tremendous loads, the traditional linear theory does not work, while our Coiflets solutions are still very accurate. It is expected that our proposed approach not only keeps the outstanding merits of the HAM technique for handling strong nonlinearity, but also improves on the computational efficiency to a great extent.