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The third-order shear deformation plate theory of Reddy [A simple higher-order theory for laminated composite plates, J. Appl. Mech. 51 (1984) 745–752] is reformulated using the nonlocal linear elasticity theory of Eringen. This theory has ability to capture the both small scale effects and quadratic variation of shear strain and consequently shear stress through the plate thickness. Analytical solutions of bending and free vibration of a simply supported rectangular plate are presented using this theory to illustrate the effect of nonlocal theory on deflection and natural frequency of the plates.
The primary objective of this paper is to present a general formulation for functionally graded plates (FGPs) using a new higher-order shear deformation plate theory with only four unknown functions. The present theory satisfies equilibrium conditions at the top and bottom faces of the plate without using shear correction factors. The hyperbolic function in terms of thickness coordinate is used in the displacement field to account for shear deformation.
The present plate theory contains kinematics of higher-order displacement field of plates, a system of higher-order differential equilibrium equations in terms of the three generalized displacements of bending plates, and a system of boundary conditions at each edge of plate boundaries. The present shear deformation theory of plates is validated by applying it to solve torsional plates and simply supported plates. The obtained solutions using the present theory are compared with the solutions of other shear-deformation theories. A good agreement is achieved through these comparisons and the advantages of the present theory are clearly verified. The shear deformation plate theory.