SUMMARYAn 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 displacement (u), radial displacement (w) and the section-rotation (Â). 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 ÿeld interpolation for  is then constructed from that of and u. The procedure leads to high-order polynomial ÿeld interpolations 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 degrees of freedom available for the polynomial interpolation of ÿeld 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.
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 ( ) 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 for curved element configurations, which reduces to linear and quadratic polynomials for u and , 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 C 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.
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