Bending analysis of magneto-electro-thermo-elastic functionally graded nano-beam based on Timoshenko beam theory

In this research, analysis of nonlocal magneto-electro-thermo-elastic of a functionally graded nanobeam due to magneto-electro-elastic loads has been done. In order to formulate the problem the Timoshenko theory of beams is utilized. The principle of virtual work, Hamilton’s principle as well as nonlocal magneto-electro-thermo-elastic relations has been recruited to derive the governing equations of equilibrium. The small size effect is captured using Eringen’s nonlocal elasticity theory. The Electric, Magnetic and Thermal fields are assumed in around of nanobeam. The nanobeam is subjected to transverse loads and initial electric and magnetic potentials. The constitutive relations is used in order to calculate the bending results of the nano-beam for a simply-supported nano-beam in terms of parameters of loadings, materials and geometries. The obtained results in this paper are validated by comparison with existing results in corresponding reference. Remarkable effects such as in-homogeneous parameter, nonlocal parameter, initial electric and magnetic potentials and thermal loads are investigated on the mechanical and electrical results in detail for nanobeams made of METE-FG materials. The results show that with increasing the nonlocal parameter and initial magnetic potentials, deflection of METE-FG nanobeam increases.