Efficient coupled polynomial interpolation scheme for out-of-plane free vibration analysis of curved beams

• We use coupled field interpolation approach to avoid torsion and flexure locking.
• We study out-of-plane vibration of Timoshenko & Euler–Bernoulli curved beam elements.
• Performance of coupled and independent curved beam elements is evaluated.
• The stiffness and consistent mass matrices do not produce any spurious constraints.
• These finite element models perform consistently over all stiffness ratio regime.

The performance of two curved beam finite element models based on coupled polynomial displacement fields is investigated for out-of-plane vibration of arches. These two-noded beam models employ curvilinear strain definitions and have three degrees of freedom per node namely, out-of-plane translation (v), out-of-plane bending rotation (θz) and torsion rotation (θs). The coupled polynomial interpolation fields are derived independently for Timoshenko and Euler–Bernoulli beam elements using the force-moment equilibrium equations. Numerical performance of these elements for constrained and unconstrained arches is compared with the conventional curved beam models which are based on independent polynomial fields. The formulation is shown to be free from any spurious constraints in the limit of ‘flexureless torsion’ and ‘torsionless flexure’ and hence devoid of flexure and torsion locking. The resulting stiffness and consistent mass matrices generated from the coupled displacement models show excellent convergence of natural frequencies in locking regimes. The accuracy of the shear flexibility added to the elements is also demonstrated. The coupled polynomial 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.