A two-noded locking-free shear flexible curved beam element

TLDR

The paper proposes a new two‑noded shear‑flexible curved beam element that eliminates membrane and shear locking. The element uses a three‑degree‑of‑freedom node formulation derived from curvilinear deep‑shell theory, employing cubic and quartic polynomial displacement fields for radial, tangential, and rotational components, and is validated for straight and curved beams across a wide range of slenderness ratios. The element shows no spurious constraints in thin regimes, converges to classical thin‑beam solutions, and outperforms comparable elements. © 1999 John Wiley & Sons, Ltd.

Abstract

A new two-noded shear flexible curved beam element which is impervious to membrane and shear locking is proposed herein. The element with three degrees of freedom at each node is based on curvilinear deep shell theory. Starting with a cubic polynomial representation for radial displacement (w), the displacement field for tangential displacement (u) and section rotation (θ) are determined by employing force-moment and moment-shear equilibrium equations. This results in polynomial displacement field whose coefficients are coupled by generalized degrees of freedom and material and geometric properties of the element. The procedure facilitates quartic polynomial representation for both u and θ for curved element configurations, which reduces to linear and quadratic polynomials for u and θ, respectively, for straight element configuration. These coupled polynomial coefficients do not give rise to any spurious constraints even in the extreme thin regimes, in which case, the present element exhibits excellent convergence to the classical thin beam solutions. This simple C0 element is validated for beam having straight/curved geometries over a wide range of slenderness ratios. The results indicates that performance of the element is much superior to other elements of the same class. Copyright © 1999 John Wiley & Sons, Ltd.