Title: Simulation of large deflections of a flexible cantilever beam fabricated from functionally graded materials by the Adomian decomposition method

Authors: Randolph Rach; Jun-Sheng Duan; Abdul-Majid Wazwaz

Addresses: The George Adomian Center for Applied Mathematics, 316 South Maple Street, Hartford, MI 49057-1225, USA ' School of Sciences, Shanghai Institute of Technology, Shanghai 201418, China ' Department of Mathematics, Saint Xavier University, Chicago, IL 60655, USA

Abstract: In this work, we use the Adomian decomposition method to study large deflections of a flexible cantilever beam fabricated from functionally graded materials with a sinusoidal nonlinearity. We convert the specified nonlinear boundary value problem with Dirichlet and Neumann boundary conditions, that governs the large deflections, to an equivalent nonlinear Fredholm-Volterra integral equation. We illustrate the obtained approximations by appropriate graphs and examine the resulting possible errors. Finally, we discuss the relationship of the deflection and the model parameters.

Keywords: large deflection; boundary value problem; flexible cantilever beam; functionally graded material; Adomian decomposition method; Adomian polynomials.

DOI: 10.1504/IJDSDE.2020.109104

International Journal of Dynamical Systems and Differential Equations, 2020 Vol.10 No.4, pp.287 - 298

Received: 22 Sep 2018
Accepted: 01 Dec 2018
Published online: 20 Aug 2020 *

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