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

An efficient shear-flexible three-noded curved beam element is proposed her ein. The shear flexibility is based on Timoshenko beam theory and the eleme nt has three degrees of freedom, viz., tangential displacement (u), radial displacement (w) and the section-rotation (theta). A quartic polynomial int erpolation for flexural rotation psi is assumed a priori. Making use of the physical composition of theta in terms of psi and u, a novel way of derivi ng the polynomial interpolations for a and w is presented, by solving force -moment and moment-shear equilibrium equations simultaneously. The field in terpolation for theta is then constructed from that of psi, and u. The proc edure leads to high-order polynomial field interpolations which share some of the generalized degrees of freedom, by means of coefficients involving m aterial and geometric properties of the element. When applied to a straight Euler-Bernoulli beam, all the coupled coefficients vanish and the formulat ion reduces to classical quintic-in-w and quadratic-in-u element, with u,w, and partial derivativew/partial derivativex as degrees of freedom. The ele ment is totally devoid of membrane and shear locking phenomena. The formula tion presents an efficient utilization of the nine generalized degrees of f reedom available for the polynomial interpolation of field variables for a three-noded curved beam element. Numerical examples on static and free vibr ation analyses demonstrate the efficacy and Locking-free property of the el ement. Copyright (C) 2001 John Wiley & Sons, Ltd.