Finite element analysis of Saint–Venant torsion problem with exact integration of the elastic–plastic constitutive equations Original Research Article

In this paper torsion of prismatic bars considering elastic–plastic material behaviour is studied. Based on the presented variational formulation associated isoparametric finite elements are developed. The unknown warping function is approximated using an isoparametric concept. The elastic–plastic stresses are obtained by an exact integration of the rate equations. Thus the ultimate torque can be calculated in one single load step. This quantity describes the plastic reserve of a bar subjected to torsion. Furthermore, for linear isotropic hardening no local iterations are necessary to compute the stresses at the integration points. The numerical results are in very good agreement with available analytical solutions for simple geometric shapes. The arbitrary shaped domains may be simply or multiple connected.