Size-dependent Hygrothermal Buckling of Porous Functionally Graded Nanoplates on Kerr Foundations via OVFSDT and NSGT

Abstract

Porous functionally graded (FG) nanoplates are candidate elements of thermal-protection, sensing and actuation systems in aerospace vehicles, where temperature and moisture act together. The hygrothermal and mechanical buckling of such nanoplates resting on a three-parameter Kerr elastic foundation is studied with a one-variable first-order shear deformation theory (OVFSDT) combined with the nonlocal strain gradient theory (NSGT). The kinematics are written about the physical neutral surface, which removes the stretching–bending coupling of the FG section and allows the problem to be reduced exactly to a single unknown, the bending deflection. It is shown that the relation between the shear and bending deflections survives the nonlocal strain gradient operators unchanged, so the size-dependent stability problem is governed by one fourth-order equation. Closed-form critical loads are obtained by the Navier procedure for simply-supported plates under uniaxial and biaxial compression, and critical temperature rises are obtained for uniform, linear and nonlinear (steady heat-conduction) hygrothermal distributions through the thickness. Even and uneven porosity distributions are considered. In the classical limit the present solution reproduces the published thermal-buckling results of Yaghoobi and Torabi to all reported digits, and is practically identical to the mechanical results of Thai and Kim for homogeneous plates. New benchmark tables and parametric figures show the competing softening (nonlocal) and hardening (strain-gradient) effects, the role of the upper-spring layer of the Kerr model, the influence of porosity, and the reduction of the critical temperature with moisture concentration.