A new structural model of warping torsion. II: Evaluation for a model problem - Armero, F. (International journal of solids and structures, 2022)
This paper presents an evaluation of the mixed formulation of warping torsion developed in the first part of this work. Specifically, we present a comparative study with two widely-used existing formulations, namely, the TWKV formulation of Timoshenko–Wagner–Kappus–Vlasov involving only the twist rotation (thus constraining the twist to the warping) and the RBV formulation of Reissner–Benscoter–Vlasov incorporating an additional warping field, as the newly proposed mixed formulation. However, in big contrast to those two formulations, the new formulation involves an alternative kinematic relation between the twist and warping motivated by a full mixed treatment of the axial strain–stress response. The evaluations are based on the exact closed-form solution for a model problem of a prismatic elastic shaft, with the torsional constants appearing in the different formulations computed with plane finite element approximations of the relevant warping functions on the cross section. The structural models are also compared with full 3D finite element simulations of the elastic solids. The new mixed formulation is found to improve upon the over-stiff constrained TWKV formulation as well as the RBV formulation with its physically incorrect stresses.