An analytical solution to the bending problem of micro-plate using a new displacement potential function

In this paper, to include small-scale effect, the augmented Love Displacement Potential Functions (DPF) are developed for isotropic micro or nano-scale mediums based on couple stress theory. By substituting the new DPF into the equilibrium equations, the governing equations were simplied to two linear partial differential equations of sixth and fourth orders. Then, the governing differential equations were solved for simply supported rectangular plate using the separation of variable method by satisfying exact boundary conditions without any simplication assumptions. Displacements, bending and torsional moments of rectangular plate were obtained for different length-scale parameters and aspect and Poisson's ratios. The obtained results were compared with other studies, which showed excellent agreement.