A total Lagrangian Timoshenko beam formulation for geometrically nonlinear isogeometric analysis of planar curved beams

This paper presents a new total Lagrangian Timoshenko beam formulation with the isogeometric analysis approach for a geometrically nonlinear analysis of planar curved beams. The proposed formulation is derived from the two-dimensional continuum theory, and a beam configuration is characterized by the beam axis and the director vectors of cross sections. Non-uniform rational B-spline (NURBS) curves are used for the geometric representation of the beam axis and the discretization of the unknown kinematics, i.e., the translational displacements of the beam axis and the cross-sectional rotation angle. Several well-established examples covering the analysis of many types of beam, i.e., straight, curved, and free-form beams with varying curvature, are considered. The obtained results by the proposed formulation are compared with those in the literature, and the accuracy and efficiency of the proposed formulation are assessed. The prominent properties of using NURBS curves in analysis, i.e., effective reduction in locking effects, higher accuracy per degree-of-freedom, and better geometric representations, are also verified for the proposed beam formulation.