New refined higher-order shear deformation theories for functionally graded plates conforming to graded variations of material properties

Abstract

This paper proposes new refined higher-order shear deformation theories (RHSDTs) for functionally graded (FG) plates conforming to graded variations of material properties. The theoretical formulation starts with initial displacement descriptions based on general higher-order theories, determines in-plane stress fields using geometrical and constitutive relations, and further achieves transverse shear stress fields though equilibrium equations. By imposing tangential stress-free conditions and defining new variables, the transverse shear stress expressions without differential variables are obtained. Then, the uniform and quadratic distributions of the transverse displacement field are considered, respectively, and the final displacement expressions of the present 2D and quasi-3D RHSDTs are further formulated by integrating the associated shear strain expressions. This novel formulation approach first introduces gradient parameters of FG materials into the shear strain shape functions. Compared with traditional HSDTs, the present refined theories fully incorporate the influences of the graded variations of material properties and can better predict mechanical responses for FG plates. Moreover, the governing equations and associated analytical solutions are presented. Numerical examples demonstrate high accuracy of the present RHSDTs and reflect their obvious accuracy advantages over traditional HSDTs especially when predicting the transverse shear stresses for FG plates with arbitrary gradients. Furthermore, it is also validated that the present RHSDTs with more shear expansion terms have higher accuracy for the prediction of transverse shear stress fields.