In this dissertation, of standard and hierarchical finite element methods are derived for the first-order shear deformation theory and the effect of shear locking is investigated by the change in thickness ratio of plate. Together with preventing shear locking, using hierarchical finite element method results in more accurate natural frequencies for plate as compared to standard finite element. In the following, two-variable refined plate theory is presented and the equations of motion and formulations of standard and hierarchical finite element methods are derived. In this theory, the fundamental and higher are obtained from exact solutions, standard and hierarchical finite element methods for symmetric and unsymmetric laminated orthotropic plates. With comparing the results, the superiority of hierarchical finite element method is shown with respect to standard finite element method. Then, changing different parameters of angle-ply and cross-ply laminated orthotropic plates, such as modulus ratio, thickness ratio, aspect ratio, and different boundary conditions of the plate, the solutions are obtained for standard and hierarchical finite element methods and they are compared with those of exact methods. Key words : Standard finite element method, Hierarchical finite element method .
