A Planar Beam Finite-Element Formulation With Individually Interpolated Shear Deformation

Abstract

This paper introduces a new planar gradient deficient beam element based on the absolute nodal coordinate formulation. In the proposed formulation, the centerline position is interpolated using cubic polynomials while shear deformation is taken into account via independently interpolated linear terms. The orientation of the cross section, which is defined by the axial slope of the element's centerline position combined with the independent shear terms, is coupled with the displacement field. A structural mechanics based formulation is used to describe the strain energy via generalized strains derived using a local element coordinate frame. The accuracy and the convergence properties of the proposed formulation are verified using numerical tests in both static and dynamics cases. The numerical results show good agreement with reference formulations in terms of accuracy and convergence.