Three-dimensional modelling of functionally graded beams using Saint-Venant

In this paper, the mechanical behaviour of functionally graded material beams is studied using the 3D Saint-Venant\'s theory, in which the section is free to warp in and out of its plane (Poisson\'s effects and out-of-plane warpings). The material properties of the FGM beam are distributed continuously through the thickness by several distributions, such as power-law distribution, exponential distribution, Mori-Tanaka schema and sigmoid distribution. The proposed method has been applied to study a simply supported FGM beam. The numerical results obtained are compared to other models in the literature, which show a high performance of the 3D exact theory used to describe the stress and strain fields in FGM beams.