Modified decomposition method applied to laminated thick plates in nonlinear bending

•A new approach to solve nonlinear bending in laminate thick plates.•Incremental approach on the Adomian decomposition method for multivariable problem.•Linear solution enhancement to obtain nonlinear solutions.•Nonlinear system of equations solved without perturbations or linearisation.•Linear term...

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Bibliographic Details
Published in:Communications in nonlinear science & numerical simulation 2020-02, Vol.81, p.105015, Article 105015
Main Authors: Lisbôa, Tales V., Marczak, Rogério J.
Format: Article
Language:English
Subjects:
Adomian’s polynomials
Approximation
Bending
Decomposition
Laminated thick plates
Large displacement
Mathematical analysis
Mindlin plates
Modified adomian’s decomposition method
Nonlinear systems
Nonlinearity
Plate theory
Polynomials
Rayleigh-Ritz method
Taylor series
Thick plates
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Summary:•A new approach to solve nonlinear bending in laminate thick plates.•Incremental approach on the Adomian decomposition method for multivariable problem.•Linear solution enhancement to obtain nonlinear solutions.•Nonlinear system of equations solved without perturbations or linearisation.•Linear term updating to achieve global convergence. The paper aims at the application of a modified version of the Adomian Decomposition Method (ADM) to nonlinear bending of laminated thick plates. The Mindlin plate theory along with the equivalent single layer concept is used in this study. The nonlinearity is taken into account through the von Kármán equations. The governing equations of the problem are decomposed into linear and nonlinear terms while the solution is expanded in series, as a requirement for constructing the ADM recursive system. The first approximation (first term of the series) corresponds to the linear response of the problem. The subsequent ones are incorporations of the problem’s nonlinearity, obtained with the aid of the Adomian’s polynomials: generalised Taylor series around the linear solution particularly tailored for the specific nonlinearity. pb-2 Rayleigh-Ritz method is employed to determine the problem’s stationary point. An incremental procedure is also introduced in order to increase the convergence radius. Numerical results are shown and compared with those found in the literature. Good agreement was found in all evaluated cases.
ISSN:1007-5704
1878-7274
DOI:10.1016/j.cnsns.2019.105015