Higher order shear deformation bending results of a magnetoelectrothermoelastic functionally graded nanobeam in thermal, mechanical, electrical, and magnetic environments

In this paper, nonlocal magnetoelectrothermoelastic analysis of a functionally graded nanobeam subjected to magnetoelectroelastic loads is investigated. Third-order shear deformation theory of beams is used to formulate the problem. The principle of virtual work as well as nonlocal magnetoelectrothermoelastic relations are used to derive the governing equations of equilibrium. The nanobeam is subjected to transverse loads and initial electric and magnetic potentials. The bending results of the nanobeam are derived for a simply supported nanobeam in terms of parameters of loadings, materials, and geometries. The obtained results in this paper are validated by comparison with corresponding reference. The influence of important parameters such as in-homogeneous parameter, initial electric and magnetic potentials, nonlocal parameter, and thermal loads is investigated on the mechanical and electrical results in detail. In addition, electric and magnetic potential distributions through the thickness direction is investigated in terms of parameters of the problem.