A five unknowns high order shear deformation finite element model for functionally graded plates bending behavior analysis

Abstract

In the present study, a simple four-node high-order shear deformation plate bending element based on modified first-order shear deformation theory has been developed to analyze functionally graded plates subjected to both sinusoidal or uniformly distributed transversal loads. Unlike other high-order shear deformation theories, the number of unknowns has been reduced to five by using the condition of zero transverse shear stress at the free top and bottom surfaces of the FG plate and by the assumption that the transverse shear strains are quadratically distributed through the thickness. The concept of transverse shear stress-energy has been employed to improve the element performance. Furthermore, the assumed natural shear strain technique has been employed to avoid any potential locking phenomenon. Moreover, the principle of minimum total potential energy has been used to derive the elementary stiffness matrix and the loading vector. To avoid the membrane–bending coupling, the concept of the neutral plane has been introduced. The developed finite element has been validated through a set of tests available in the literature.