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

An e cient shear- exible three-noded curved beam element is proposed herein. The shear exibility is based on Timoshenko beam theory and the element has three degrees of freedom, viz., tangential dis- placement (u), radial displacement (w) and the section-rotation ( ). A quartic polynomial interpolation for exural rotation is assumed a priori. Making use of the physical composition of in terms of 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 eld interpolation for is then constructed from that of and u. The procedure leads to high-order polynomial eld interpo- lations which share some of the generalized degrees of freedom, by means of coe cients involving material and geometric properties of the element. When applied to a straight Euler{Bernoulli beam, all the coupled coe cients 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 e cient utilization of the nine generalized de- grees of freedom available for the polynomial interpolation of eld variables for a three-noded curved beam element. Numerical examples on static and free vibration analyses demonstrate the e cacy and locking-free property of the element