A gradient elasticity model of Bernoulli-Euler nanobeams in non-isothermal environments

The Bernoulli Euler beam formulation is extended by means of the nonlocal strain gradient theory in the nonhomogenous temperature field setting. Starting from the nonlocal continuum mechanics, a thermodynamically consistent model is obtained. The governing higher order system of differential equations for axial and transverse displacements is presented. Utilization of boundary conditions is demonstrated on four examples. It can be concluded that the nonhomogenous temperature field has a profound influence on the nanobeam mechanics. Some conclusions are drawn at the end of the paper. (C) 2015 Elsevier Masson SAS. All rights reserved.