Nonlinear isogeometric spatial Bernoulli beam

Abstract

A new element formulation of a geometrically nonlinear spatial curved beam assuming Bernoulli theory including torsion without warping is proposed. The element formulation is derived directly from the 3D-continuum by means of nonlinear kinematics, thus accounting for large displacements. The geometric description of the proposed element is adapted from the spatial rod of Greco and Cuomo (2013) and extended to a nonlinear element formulation. The proposed formulation can handle arbitrary orientations of the cross section along the beam.In this publication, NURBS are used as basis functions for discretization, since they can easily provide the required C1-continuity between elements. The presented element formulation has four degrees of freedom, three for displacements and one for the rotation around the center line. In order to prove the accuracy of the developed spatial Bernoulli beam, several numerical examples are presented and compared to analytic solutions and other element formulations.