An updated Lagrangian Bezier finite element formulation for the analysis of slender beams

A G(1)-conforming finite element formulation based on the Kirchhoff beam model suitable for the analysis of structures composed by coupling of slender beams is presented. A new set of kinematic parameters is introduced in order to account for the continuity required by the rod model. This new set of kinematic parameters defines the G(1)-map that guarantees continuity of the rotations at the ends of the beam. The tangent stiffness matrix for the proposed Kirchhoff beam model is derived in a consistent way. It is shown that an additional geometric term, specific for the G(1)-conforming formulation, appears in the tangent stiffness matrix. In order to avoid the singularities arising with the introduction of the G(1)-map, an updated Lagrangian formulation is adopted. In this way, a G(1)-conforming Bezier finite element based on the Kirchhoff beam model able to model large deformations of space rod systems is obtained. Several numerical examples show the high accuracy and the robustness of the proposed conforming formulation.