Exact solutions for elastic response in micro- and nano-beams considering strain gradient elasticity

This paper presents the exact solutions derived for the static bending response of simply supported isotropic micro- and nano-beams. The governing differential equations of equilibrium and the associated boundary conditions for the beam are derived by applying the variational principle over the internal energy functional involving strain and strain gradient terms. The Mindlin’s Form II model for higher order metrics of energy involving strain...