A FEM formulation for the analysis of laminated and functionally graded hyperelastic beams with continuous transverse shear stresses

In this study we present an alternative finite element formulation to solve two-dimensional laminated and functionally graded bar elements with continuum transverse stress distribution. The considered structural elements are long or short and the strain level can be large. Thus, it is necessary to consider a hyperelastic constitutive model capable of representing large strains. Enhancements - regularization of the Reissner-Mindlin kinematics and the zigzag effect - are developed to impose continuous transverse shear stress. The regularized Reissner-Mindlin kinematics is important for both laminated and functionally graded materials, while the zigzag enhancement is important only for laminates. The formulation is developed considering laminated bars; however, as the number of laminas is unlimited and keeps the number of degrees of freedom; functionally graded materials are directly represented. An additional degree of freedom is considered for large strains, improving the element volumetric performance. The formulation is validated comparing the proposed kinematics with literature results.