An improved hybrid-stress element approach to torsion of shafts

Abstract

A four-noded torsional element with only four stress parameters is developed based on the Hellinger–Reissner principle by optimizing element trial stresses through the introduction of incompatible displacements. Two boundary hybrid-stress elements with six stress parameters are also developed to meet the traction-free condition on one or two adjacent sides of a four-noded element, respectively. Numerical results show that these elements give accurate results for the warping displacement, the angle of twist per unit length, as well as the shear stresses for shafts with a polygonal cross-section. Comparison with alternative displacement and stress elements shows that the present elements give results of the same accuracy with a coarser mesh. The elements are shown to be insensitive to mesh distortion and to exhibit rapid convergence with h-refinement.