Convergence properties and derivative extraction of the superconvergent Timoshenko beam finite element Original Research Article

The superconvergent Timoshenko beam element of Reddy [Comput. Methods Appl. Mech. Engrg. 149 (1997) 113–132] is derived here using an assumed strain approach. A method of reference field formulation is proposed from which pointwise higher-order derivatives (moments and shears) can be derived for this element and theoretical proofs of the existence of such points are presented. It is shown that the order of convergence may be at least two orders higher than the FE derivative field in the cases where uniform discretization is adopted. Finally, a smoothed derivative field is derived by using a least-square polynomial fit over these points. Several simple numerical examples are presented to demonstrate the ability of the method to extract exact derivative fields from the FE results.