An efficient mixed interpolated curved beam element for geometrically nonlinear analysis

•Proposing a curved beam element having three nodes.•To alleviate locking phenomena and consider finite rotation are the aims.•Special tying points are found and utilized.•Performing geometrically nonlinear analysis of tapered and planar structures.•This scheme is based on the mixed interpolation of the strain fields. In this study, a curved beam element is developed for geometrically nonlinear analysis of planar structures. The main contribution of this research is to use high-performance formulation to alleviate locking phenomena and consider finite rotation. This scheme is based on the mixed interpolation of the strain fields. In this study, special tying points are found and utilized. One of the interesting advantages of the proposed element is the ability to model tapered structures. Moreover, the First-order Shear Deformation Theory (FSDT) and the Green-Lagrange strain are included. Several complicated and applicable nonlinear problems are solved to depict the efficiency and high accuracy of the proposed element, especially by fewer numbers of elements.