A comprehensive analysis of in-plane functionally graded plates using improved first-order mixed finite element model

In this study, the mechanical behaviors of the in-plane functionally graded plate (IFG) are comprehensively explored via a finite element (FE) model. The current FE model is developed base on improved first-order shear deformation theory (FSDT) in conjunction with the mixed FE formulation. The volume fraction as well as the material properties change smoothly along the width and length of the plates for six different patterns. A simple improved transverse shear stress is applied to modify its distribution across the thickness of the IFG plates. Hence, the transverse shear stress equals zeros on the lower and upper surfaces of the IFG plates. Besides, no shear correction factor is needed for calculation of shear strain energy. A four-node mixed plate element, IMQ4, is established via mixed FE formulation for mechanical analysis of the IFG plates. The accuracy and fast convergence rate are validated via some examples. A comprehensive parametric analysis is provided to demonstrate the roles of several parameters including the material gradient index, the side-to-thickness ratio, aspect ratio, and boundary conditions on the mechanical behaviors of the IFG plates.