free vibration analysis of fg nanoplates using quasi-3d hyperbolic refined plate theory and the isogeometric approach

in this paper, quasi three-dimensional (quasi-3d) hyperbolic shear deformation theory is used for the free vibration analysis of functionally graded nanoplates by using the isogeometric analysis (iga) approach and nonlocal elasticity theory. the quasi-3d theory using five independent unknowns satisfies the free transverse shear stress conditions on the top and bottom surfaces of plate and so a shear correction factor is not needed. the displacement field takes into account both shear deformation and thickness stretching effect and the equations are derived based on physical neutral surface position. the iga approach can easily formulate c¹ continuous elements by using non-uniform rational b-spline (nurbs) functions. numerical results are compared with other solutions.