This paper proposes several normalized and non-normalized displacement fields based on hybrid and trigonometric hyperbolic shear strain shape functions in order to solve the analytical thermoelastic problem of simply-supported laminated composite and sandwich plates using the Carrera unified formulation (CUF) as strategy. The equivalent single layer (ESL) governing equations for laminated composite plate are obtained by employing the principle of virtual displacement (PVD) and are solved using Navier's method solution. Linear and nonlinear temperature distributions through the plate thickness are taken into account. A hybrid and trigonometric hyperbolic shear strain shape functions are introduced in normalized and non-normalized form in the mathematical model. The obtained results are compared with the classical polynomial ones for several order of expansion. Interesting approximations with 3D solution are shown for low and high order of expansion.