Coupled polynomial field approach for elimination of flexure and torsion locking phenomena in the Timoshenko and Euler–Bernoulli curved beam elements

The curvature related locking phenomena in the out-of-plane deformation of Timoshenko and Euler–Bernoulli curved beam elements are demonstrated and a novel approach is proposed to circumvent them. Both flexure and Torsion locking phenomena are noticed in Timoshenko beam and torsion locking phenomenon alone in Euler–Bernoulli beam. Two locking-free curved beam finite element models are developed using coupled polynomial displacement field interpolations to eliminate these locking effects. The coupled polynomial interpolation fields are derived independently for Timoshenko and Euler–Bernoulli beam elements using the governing equations. The presence of penalty terms in the coupled displacement fields incorporates the flexure–torsion coupling and flexure–shear coupling effects in an approximate manner and produce no spurious constraints in the extreme geometric limits of flexure, torsion and shear stiffnesses. The proposed coupled polynomial finite element models, as special cases, reduce to the conventional Timoshenko beam element and Euler–Bernoulli beam element, respectively. These models are shown to perform consistently over a wide range of flexure-to-shear (EI/GA) and flexure-to-torsion (EI/GJ) stiffness ratios and are inherently devoid of flexure, torsion and shear locking phenomena. The efficacy, accuracy and reliability of the proposed models to straight and curved beam applications are demonstrated through numerical examples.