Low‐Order Interpolation Functions for Curved Beams

Polynomial interpolation functions for finite element analysis of three‐dimensional (3‐D) curved beams are derived using small deformation theory. The performance of low‐order polynomials combined with selectively reduced integration is evaluated under torsional and membrane “locking” conditions. Low‐order polynomials are also used in a three‐field mixed formulation; in this approach, the constraint equations of the problems that result from the nonlinear geometry of the curved beam are enforced using collocation. It is shown that the proposed technique eliminates “locking” from the formulation. The resulting interpolation functions are coupled in pairs, reflecting the dependence that occurs between in‐plane flexural translation and axial deformation, and between out‐of‐plane flexural translation and torsional rotation in beams that are curved in plan. Consistent element stiffness and mass matrices obtained using the proposed functions represent properties of slender curved beams, and converge to those of a 3‐D straight‐frame element when the geometric curvature of the member becomes infinitely small.