Refined beam elements with arbitrary cross-section geometries

This paper presents hierarchical beam elements on the basis of the Carrera Unified Formulation. The displacement components are expanded in terms of the section coordinates, (x, y), using a set of 1-D generalized displacement variables. N-Order Taylor type expansions are employed. N is a free parameter of the formulation. Linear, quadratic and cubic approximations along the beam axis, (z), are introduced to develop finite element matrices. These are obtained in terms of a few fundamental nuclei whose form is independent of both N and the number of element nodes. Convergence and assessment with available results is first made. Additional analyses consider different beam sections (square and airfoil-shaped) as well as loading conditions (bending and torsion). It has mainly been concluded that the proposed model is capable of furnishing 3-D stress states in the considered beams with conventional (rectangular) and unconventional (thin-walled airfoil) sections.