Bending Analysis of Bidirectional FGM Timoshenko Nanobeam Subjected to Mechanical and Magnetic Forces and Resting on Winkler–Pasternak Foundation

Abstract

Bending of bidirectional functionally graded nanobeams under mechanical loads and magnetic force was investigated. The nanobeam is assumed to be resting on the Winkler–Pasternak foundation. Eringen’s nonlocal elasticity theory and Timoshenko beam model are utilized to describe the mechanical behavior of the nanobeam. Material properties of the functionally graded beam are assumed to vary in the thickness and length of the nanobeam. Hamilton’s principle is employed to derive the governing equation and related boundary conditions. These equations are solved using the generalized differential quadrature method. The obtained results are compared with the results presented in other studies, to ensure the validity and versatility of this method. This comparison shows a good agreement between the results. Results are presented and discussed for different values of functionally graded materials indices, different aspect ratios, and different boundary conditions. The effect of the magnetic field and elastic foundation on buckling load has also been studied. The difference in nanobeam behavior for different values of the size-effect parameter is clearly shown.