A three-noded shear-flexible curved beam element based on coupled displacement field interpolations

Abstract

An efficient shear-flexible three-noded curved beam element is proposed herein. The shear flexibility is based on Timoshenko beam theory and the element has three degrees of freedom, viz., tangential displacement (u), radial displacement (w) and the section-rotation (θ). A quartic polynomial interpolation for flexural rotation ψ is assumed a priori. Making use of the physical composition of θ in terms of ψ and u, a novel way of deriving the polynomial interpolations for u and w is presented, by solving force-moment and moment-shear equilibrium equations simultaneously. The field interpolation for θ is then constructed from that of ψ and u. The procedure leads to high-order polynomial field interpolations which share some of the generalized degrees of freedom, by means of coefficients involving material and geometric properties of the element. When applied to a straight Euler-Bernoulli beam, all the coupled coefficients vanish and the formulation reduces to classical quintic-in-w and quadratic-in-u element, with u, w, and ∂w/∂x as degrees of freedom. The element is totally devoid of membrane and shear locking phenomena. The formulation presents an efficient utilization of the nine generalized degrees of freedom available for the polynomial interpolation of field variables for a three-noded curved beam element. Numerical examples on static and free vibration analyses demonstrate the efficacy and locking-free property of the element.