Coiflets solutions for Föppl-von Kármán equations governing large deflection of a thin flat plate by a novel wavelet-homotopy approach
- 47 Downloads
In this paper, a novel technique incorporated the homotopy analysis method (HAM) with Coiflets is developed to obtain highly accurate solutions of the Föppl-von Kármán 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 Föppl-von Kármán 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.
KeywordsCoiflets Galerkin method Wavelet Foppl-von Karman equations
Unable to display preview. Download preview PDF.
This work is partially supported by the National Natural Science Foundation of China (Approval No. 11272209 and 11432009).
- 1.Föppl, A.: Vorlesungen über technische mechanik Bd. 3,B.G. Teubner, Leipzig (1907)Google Scholar
- 2.von Karman, T.: Festigkeitsproblem im maschinenbau. Encyk. D. Math. Wiss. 4, 311–385 (1910)Google Scholar
- 3.Sokolnikoff, I.S.: Mathematical Theory of Elasticity. McGraw-Hill (1956)Google Scholar
- 4.Landau, L.D., Lifshit’S, E.M.: Theory of Elasticity. World Book Publishing Company (1999)Google Scholar
- 20.Liao, S.J.: The proposed homotopy analysis technique for the solution of nonlinear problems. Shanghai Jiao Tong University, Ph.d thesis (1992)Google Scholar
- 28.Stein, E.M., Weiss, G.: Introduction to fourier analysis on euclidean spaces. Princeton Math. Ser. 212(2), 484–503 (2009)Google Scholar
- 29.Wang, J.Z.: Generalized theory and arithmetic of orthogonal wavelets and applications to researches of mechanics including piezoelectric smart structures. Lanzhou University, Ph.d thesis (2001)Google Scholar
- 32.Xing, R.: Wavelet-based homotopy analysis method for nonlinear matrix system and its application in burgers equation. Math. Problems Eng. 2013,(2013-6-25) 2013 (5), 14–26 (2013)Google Scholar
- 33.Muskhelishvili, N.I.: Some Basic Problems of the Mathematical Theory of Elasticity. P.Noordhoff Ltd (1953)Google Scholar
- 34.Tian, J.: The Mathematical Theory and Applications of Biorthogonal Coifman Wavelet Systems. Rice University, Ph.D. thesis (1996)Google Scholar
- 35.Liu, X.J.: A Wavelet Method for Uniformly Solving Nonlinear Problems and Its Application to Quantitative Research on Flexible Structures with Large Deformation. Lanzhou University, Ph.d thesis (2014)Google Scholar