Hygro-thermal bending behavior of porous FG nano-beams via local/nonlocal strain and stress gradient theories of elasticity

This work studies the bending response of porous functionally graded Bernoulli-Euler nano-beams under hygro-thermo-mechanical loadings. The governing equations of the elastostatic problems associated with both local/nonlocal stress- and strain-driven gradient models of elasticity were derived by using the virtual work principle. A Wolfram language code in Mathematica was then written to carry out a numerical investigation for different boundary conditions including cantilever and simply-simply conditions. The effects of the different parameters, such as porosity volume fraction, gradient index, nonlocal parameter, gradient length parameter and mixture parameter are presented. It is shown how the proposed approach is able to capture the structural behavior of porous functionally graded Bernoulli–Euler nano-beams under a hygro-thermal environment.