Analysis of three-dimensional locking-free curved beam element

Most existing curved beam elements suffer from poor convergence difficulties and a heavy computational burden while limit themselves to 2D problems. In this paper, we address and overcome these difficulties by developing a new three-noded locking-free 3D curved beam element. The element formulations, which employ coupled consistent polynomial displacement fields, satisfy the membrane locking-free requirement of being able to recover the inextensible bending mode of the curved beam. Quintic transverse displacement interpolation functions are used to represent the bending deformation of the beam, while the axial and torsional displacement fields are derived by integration of the presumably linear membrane and torsional shear strain fields, which are coupled with the transverse displacement fields. Numerical results of two- and three-dimensional applications are presented to demonstrate the superior accuracy and high convergence rate of the newly developed curved beam element compared with existing ones.