Advanced mixed theories for bending analysis of functionally graded plates

In this paper functionally graded material (FGM) plates subjected to a transverse mechanical load are investigated. The unified formulation (UF) and the Reissner’s mixed variational theorem (RMVT) are extended to FGMs. RMVT permits to consider both displacements and transverse shear/normal stresses as primary variables. Significant improvements are obtained with respect to the classical models (based on the principle of virtual displacements (PVD)) where only the displacements are assumed. The proposed models consider various order of expansion for the primary variables through the thickness, and the description of the unknown variables can be equivalent single layer or layer wise. The material properties, that in a FGM layer change continuously in the thickness direction, are described via thickness functions that are a combination of Legendre’s polynomials. Results are related to bending problems and restricted to closed form cases. The proposed models are very general for the material properties, because they do not depend on the use of transition function in the thickness direction. The results are compared with 3D solutions and with PVD models. It is shown both the effectiveness of mixed theories to trace the 3D response as well as their superiority with respect to classical PVD applications.