Modeling the non-trivial behavior of anisotropic beams: A simple Timoshenko beam with enhanced stress recovery and constitutive relations

In this work we analyze the non-trivial influence of material anisotropy on the structural behavior of a multi-layer planar beam. Indeed, analytical results available in literature are limited to homogeneous beams and several aspects have not been addressed yet, preventing a deep understanding of the mechanical response of anisotropic structural elements. This paper proposes an effective recovery of stress distributions and an energetically consistent evaluation of constitutive relations to be used within a planar Timoshenko beam model. The resulting structural analysis tool highlights the following peculiarities of anisotropic beams: (i) the transversal internal force affects the maximum axial stress up to 30%, and (ii) the anisotropy influences the beam displacements more than the standard shear deformation, even for extremely slender beams. A rigorous comparison with analytical and accurate 2D Finite Element solutions confirms the accuracy of the proposed approach, which leads to errors usually below 2%.