Nonlinear analysis of stability for functionally graded plates type Al₂O₃ Under thermal loads based on the modified couples stress theory using a new warping function

Purpose This study employs the four-variable refined plate theory to analytically investigate the buckling behavior of asymmetric functionally graded material (FGM) plates on an elastic foundation under thermal loads. Design/methodology/approach The theory assumes that in-plane and transverse displacements comprise both bending and shear components, where the bending components do not affect shear forces, and the shear components do not influence bending moments. This approach captures a parabolic distribution of transverse shear strains across the plate’s thickness while satisfying zero traction boundary conditions on both the top and bottom surfaces without shear correction factors. Using the accurate neutral surface position, the governing stability equations are derived based on the minimal total potential energy principle. Nonlinear strain–displacement relationships are also incorporated. A Navier-type closed-form solution is proposed to determine the critical buckling temperature for simply supported FG plates on elastic foundations. Findings The study introduces a new transverse section warping function to account for transverse shearing effects. The proposed shear strain theory with the new warping function is shown to be both efficient and accurate, providing superior results when compared to prior theories. Originality/value This work contributes a novel analytical solution for the critical buckling temperature of FG plates under thermal loading, highlighting the refined theory’s potential for more accurate predictions by incorporating an advanced representation of transverse shearing and warping effects in asymmetric FGM plates.