An improved hybrid-stress element approach to torsion of shafts

A four-noded torsional element with only four stress parameters is develope d based on the Hellinger-Reissner principle by optimizing element trial str esses through the introduction of incompatible displacements. Two boundary hybrid-stress elements with six stress parameters are also developed to mee t the traction-free condition on one or two adjacent sides of a four-noded element, respectively. Numerical results show that these elements give accu rate results for the warping displacement, the angle of twist per unit leng th, as well as the shear stresses for shafts with a polygonal cross-section . Comparison with alternative displacement and stress elements shows that t he 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. (C) 1999 Elsevier Science Ltd. All rig hts reserved.