Nonlocal three-dimensional theory of elasticity for buckling behavior of functionally graded porous nanoplates using volume integrals

In this paper, the buckling of rectangular functionally graded (FG) porous nanoplates based on three-dimensional elasticity is investigated. Since, similar researches have been done in two-dimensional analyses in which only large deflections with constant thickness were studied by using various plate theories; therefore, discussion of large deformations and change in thickness of plates after deflection in this study is examined. Moreover, porosity is assumed in two situations, even and uneven distributions considered in several conditions. Using nonlocal elasticity theory, nonlocal three-dimensional equations are obtained. Regarding difficulties in solving three-dimensional differential equations, simple analytical methods are assumed and proposed. The most important results show that even porosity makes the plate softer and results of uneven porosity are so close to the prefect material which leads to this considerable conclusion that porosity as an uneven distribution cannot be an important factor in static stability analyses of FG nanoplates.