A new solution for FGM thin rectangular plate bending with variable thickness

Abstract This study presents a novel analytical solution for the bending analysis of functionally graded material (FGM) thin rectangular plates with variable thickness. The Levy-type method is extended based on the classical thin-plate theory in order to provide a new exact and practical solution for solving this problem. It is assumed that the material properties varied through the thickness direction in a power-law distribution. Types of loading, thickness variation, plate’s boundary condition, and plate’s material combination were chosen as the state variables which affected on the non-dimensional plate’s deflection. By governing equations, some partial differential equations were appeared which were solved analytically by using generalized Fourier series. Finally, the non-dimensional thin rectangular FGM plate’s deflection under various loading types were calculated. The results demonstrate that the proposed method provides an accurate and computationally efficient tool for analyzing FGM plates with non-uniform thickness, offering significant advantages over conventional numerical approaches in terms of computational cost and solution precision. By increasing the power law index ( $$k$$ ), non-dimensional deflection values increased through all of the other variables such as plate’s boundary conditions.