Finite element analysis for functionally graded porous nano-platesresting on elastic foundation

This paper proposes an improved triangular element based on the strain approach and the Reissner-Mindlin theory to investigate the static, free vibration, and buckling response of functionally graded porous (FGP) nano-plates resting on the Parternak's two-parameter elastic medium foundation. The internal pores of nano-plates are described by two distribution laws, including uneven porosity distribution and logarithmic-uneven porosity distribution. Using Hamilton's principle, equilibrium equations of FGP nano-plates lying on a two-parameter foundation are obtained. The most remarkable feature of the improved triangular element is the degrees of freedom of elements approximated by Lagrange functions for the membrane strain and by the high-degree polynomial functions for the bending strain. The numerical results of the present work are compared with the available results in the literature to evaluate the performance of the proposed approach. Effects of geometrical and material properties such as the power-law index n, the porosity coefficient S, the nonlocal coefficient u, and the parameters of the elastic foundation on the static, free vibration, and buckling behavior of the FGP nano-plates are examined in detail.