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

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.