Geometrically nonlinear multi-patch isogeometric analysis of planar curved Euler–Bernoulli beams

• Published in: Computer methods in applied mechanics and engineering 2020-07, Vol.366, p.113078, Article 113078
• Main Authors: Vo, Duy, Nanakorn, Pruettha
• Format: Article
• Language: English
• Subjects: Basis functions; Beam theory (structures); Beamforming; Boundary conditions; Curved beams; Degrees of freedom; Euler-Bernoulli beams; Isogeometric analysis (IGA) of beams; Kinematics; Large displacement analysis; Multi-patch beam structures; Non-Uniform Rational B-Spline (NURBS); Nonlinear analysis; Rigid connections; Rotational degrees of freedom
• ISSN: 0045-7825; 1879-2138
• DOI: 10.1016/j.cma.2020.113078

This study proposes a novel isogeometric beam formulation for thin, elastic, planar curved beams subjected to large displacements. The Euler–Bernoulli beam theory is employed. In the formulation, a two-dimensional continuum beam is entirely described by its axis and a convective frame rigidly attached to the beam axis. Rational B-spline basis functions are used to construct the geometrical approximation of the beam axis, and the translational displacements of the beam axis are considered as the unknown kinematics. A property of NURBS curves is used to introduce rotational degrees of freedom at both ends of the beam. With the end rotational degrees of freedom, applying rotational boundary conditions and concentrated moments are straightforward. In addition, rigid connections between beams can be easily simulated. The accuracy and efficiency of the proposed beam formulation are verified by several well-established problems.