A Model for Shear Deformable Curved Beam Made of Functionally Graded Materials

Abstract

In this paper the Heillinger-Reissner principle is employed to derive a new model for a curved beam made of functionally graded materials. The model is developed on the assumptions that the shear deformability is not negligible. The Hellinger-Reissner principle can be handled in order to derive the motion equations together with a consistent description of the constitutive equations. This leads to obtain the shear coefficients of the beam theory as an inherent part of the model deduction, thus avoiding the imposition of shear coefficients arbitrarily taken from other approaches, as one can see in many papers of the open literature.
Despite the technological importance of new materials, it is interesting to remark that curved beam models for the aforementioned graded materials are not available under the conception of a one-dimensional beam theory. On the other hand, this model contains the curved model for isotropic materials and particular cases for laminated composite beams.
A finite element procedure is employed in order to solve the motions equations for free vibrations problems with or without the presence of initial stresses. Different types of laws of graded properties are tested. Parametric studies and comparisons with analytical solutions are performed as well.