Influence of Severe Non-linear Thermal Gradients on the Vibration and Buckling of Porosity-Dependent Five-Layered FG-GPLRC Sandwich Plates using Unconstrained TSDT

This study presents a closed-form analytical solution for the thermo-mechanical buckling and free vibration of simply supported (SSSS) five-layered functionally graded graphene platelet-reinforced composite (FG-GPLRC) porous sandwich plates under non-linear thermal gradients. Reddy's unconstrained third-order shear deformation theory (TSDT) is adopted, and the governing equations are solved via the Navier double Fourier series method. Effective material properties are evaluated through the Halpin-Tsai micromechanics model, and the non-linear temperature field is determined from the steady-state one-dimensional Fourier heat conduction equation. Numerical results show that the GPL-X dispersion pattern yields higher fundamental frequencies and critical thermal buckling thresholds than the GPL-U and GPL-O patterns, consistent with the parallel-axis theorem applied to the bending stiffness integrals. The five-layered configuration eliminates bending-stretching coupling and reduces interlaminar thermal stress discontinuities compared to conventional three-layered designs. Under the present material system, the non-linear (NLD) and linear (LD) temperature distributions produce equivalent thermal force resultants N T , attributable to the moderate spatial variation of the effective thermal conductivity K(z). The derived solutions serve as benchmark results for the analysis of multilayered FG-GPLRC plates in thermal environments.