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

Author:

Greco Leopoldo1ORCID,Cuomo Massimo1,Castello Domenico1,Scrofani Angelo2

Affiliation:

1. Department of Civil Engineering and Architecture (DICAr), University of Catania, Catania, Italy

2. Department of Information Engineering, Computer Science and Mathematics (DISIM), University of L’Aquila, L’Aquila, Italy

Abstract

A G1-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 G1-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 G1-conforming formulation, appears in the tangent stiffness matrix. In order to avoid the singularities arising with the introduction of the G1-map, an updated Lagrangian formulation is adopted. In this way, a G1-conforming Bézier 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.

Publisher

SAGE Publications

Subject

Mechanics of Materials,General Materials Science,General Mathematics

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