Analytical Buckling Solutions of Functionally Graded Plates With Complex Boundary Conditions Using the Finite Integral Transform Method

ABSTRACT This study derives analytical solutions for the biaxial buckling of functionally graded material (FGM) rectangular thin plates subjected to complex boundary conditions (BCs), particularly focusing on rotationally‐restrained BCs, employing the finite integral transform (FIT) approach. Obtaining these solutions analytically through traditional semi‐inverse methods is challenging, primarily due to the complex BCs and graded material properties of FGM plates, which significantly complicate the application of such methods. In the solution procedure, utilizing the FIT method, the fundamental high‐order partial differential equations (PDEs) for FGM rectangular thin plates' buckling analysis are converted to four sets of linear algebraic equations. This transformation facilitates the derivation of analytical solutions without pre‐determined deflection functions, thereby enhancing the efficiency of the solving process. To validate the results, this study systematically compares them with ABAQUS simulations and existing analytical solutions. The comparison demonstrates strong agreement, confirming the precision of the proposed technique. The approach is straightforward and versatile, applicable to both thick and moderately thick plates, and suitable for analyzing bending and vibration under diverse BCs. Furthermore, the effects of aspect ratio, rotational constraint coefficient, FGM distribution models, porosity distributions, and biaxial load ratio of the FGM plates are systematically investigated. The results establish reliable benchmarks for validating the accuracy of other analytical and numerical methods.