Nonlocal third-order shear deformation plate theory with application to bending and vibration of plates

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. Finally, the relations between nonlocal third-order, first-order and classical theories are discussed by numerical results.