Computation of Super-Convergent Nodal Stresses of Timoshenko Beam Elements by EEP Method

The newly proposed element energy projection(EEP) method has been applied to the computation of super-convergent nodal stresses of Timoshenko beam elements. General formulas based on element projection theorem were derived and illustrative numerical examples using two typical elements were given. Both the analysis and examples show that EEP method also works very well for the problems with vector function solutions. The EEP method gives super-convergent nodal stresses, which are well comparable to the nodal displacements in terms of both convergence rate and error magnitude. And in addition, it can overcome the "shear locking" difficulty for stresses even when the displacements are badly affected. This research paves the way for application of the EEP method to general one-dimensional systems of ordinary differential equations.