Optimization concept in the context of shear deformation theories was born for the development of accurate models to study the bending problem of structures. The present study seeks to extend such an approach to the dynamic analysis of plates. A compact and unified formulation with non-polynomial shear strain shape functions (SSSFs) is employed to develop a static and free vibration analysis of simply supported functionally graded plates. In this context, three new non-polynomial displacement fields are proposed using trigonometric and hyperbolic SSSFs. Then, the non-polynomial SSSFs are optimized by varying the arguments of the trigonometric and hyperbolic functions. Additionally, the Mori-Tanaka approach is used to estimate the effective properties of the functionally graded plates. The Principle of Virtual Displacement (PVD) and the Hamilton's Principle along with the Navier closed-form solution technique are used to obtain exact results. The obtained numerical results are in a good agreement with 3D and 2D higher order shear deformation theory solutions available in the literature.