Abstract In this paper, a simple refined plate theory that can be used to analyze the bending and free vibration behavior of functionally graded plates is proposed. This theory requires only three unknowns for analyzing the bending of a functionally graded plate and only one for analyzing the free vibration of a functionally graded plate. Compared with the classical plate theory which contains three unknown quantities, the simple refined plate theory proposed in this paper takes into account the transversely shear effect and improves the accuracy of the calculation. Unlike the first-order shear deformation plate theory, this simple refined plate theory introduces a polynomial-type shear strain function that satisfies the boundary condition of zero shear stress on the upper and lower surfaces of the plate, so no shear correction is required. The accuracy and convenience of this simple refined plate theory were verified by comparing with existing literature, and the bending and free vibration mechanical behaviors of functionally graded plates were investigated based on this simple refined plate theory.
2023, Vol. 44 
