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

A new two-noded shear flexible curved beam element which is impervious to m embrane and sheer locking is proposed herein. The element with three degree s of freedom at each node is based on curvilinear deep shell theory. Starti ng with a cubic polynomial representation for radial displacement (w), the displacement field for tangential displacement (u) and section rotation (th eta) 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 p roperties of the element. The procedure facilitates quartic polynomial repr esentation for both u and theta for curved element configurations, which re duces to linear and quadratic polynomials for u and theta, respectively, fo r 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 c lassical thin beam solutions. This simple C-0 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 (C) 1999 John Wiley & Sons, Ltd .