Thermal Buckling Analysis of Bimodular Functionally Graded Rectangular Thin Plates

This paper investigates the thermal buckling behavior of a four-edge simply supported bimodular functionally graded rectangular thin plate subjected to thermal loads. Unlike existing studies, this work introduces the bimodular effect into the thermal buckling analysis of functionally graded thin plates for the first time, accounting for the influence of tension–compression modulus on the critical temperature difference. The problem is challenging due to the complexity of materials and the nonlinearity of structural thermal buckling. For the theoretical analysis, we propose a simplified mechanical model which contains the four important assumptions: there exists a neutral plane in bending; the influence of shear stresses may be neglected; the membrane effect and bending effect are considered separately; and there are two different buckling regimes: a compression-dominated pre-buckling state and a bending-dominated post-buckling state. Three types of thermal loading cases are considered, including uniform temperature rise, linear temperature gradient through the thickness, and nonlinear temperature distribution satisfying Fourier’s law of heat conduction. Within the framework of the simplified mechanical model, the pre-buckling membrane forces, equilibrium equations, and stability equations are derived, thus obtaining a closed-form analytical expression for the critical buckling temperature difference under three different temperature rise modes. The reliability of the present analytical model is validated through comparison with finite element results. Furthermore, a detailed parametric study is conducted to reveal the influences of aspect ratio, width-to-thickness ratio of plate, bimodular indices, and gradient parameters of materials on the critical temperature difference. The results provide a theoretical basis for the thermal stability design of bimodular functionally graded plates operating in high-temperature environments.