Analytical method for the construction of solutions to the Foppl-von Karman equations governing deflections of a thin flat plate

    Authors

    R. A. Van Gorder

    Comments

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    Abbreviated Journal Title

    Int. J. Non-Linear Mech.

    Keywords

    Foppl-von Karman equations; Deflections of thin flat plates; Non-linear; PDEs; Perturbation methods; Homotopy analysis; Discrete residual error; analysis; HOMOTOPY ANALYSIS METHOD; NONLINEAR DIFFERENTIAL-EQUATIONS; VISCOUS-FLOW; PROBLEMS; NON-NEWTONIAN FLUIDS; EMDEN-FOWLER TYPE; COMPLIANT SUBSTRATE; SERIES SOLUTIONS; GENERAL-APPROACH; PATTERNS; MODEL; Mechanics

    Abstract

    We discuss the method of linearization and construction of perturbation solutions for the Foppl-von Karman equations, a set of non-linear partial differential equations describing the large deflections of thin flat plates. In particular, we present a linearization method for the Foppl-von Karman equations which preserves much of the structure of the original equations, which in turn enables us to construct qualitatively meaningful perturbation solutions in relatively few terms. Interestingly, the perturbation solutions do not rely on any small parameters, as an auxiliary parameter is introduced and later taken to unity. The obtained solutions are given recursively, and a method of error analysis is provided to ensure convergence of the solutions. Hence, with appropriate general boundary data, we show that one may construct solutions to a desired accuracy over the finite bounded domain. We show that our solutions agree with the exact solutions in the limit as the thickness of the plate is made arbitrarily small. (C) 2012 Elsevier Ltd. All rights reserved.

    Journal Title

    International Journal of Non-Linear Mechanics

    Volume

    47

    Issue/Number

    3

    Publication Date

    1-1-2012

    Document Type

    Article

    Language

    English

    First Page

    1

    Last Page

    6

    WOS Identifier

    WOS:000304689300001

    ISSN

    0020-7462

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