Plastic analysis of torsion of a prismatic beam

Abstract Finite element formulation for stress analysis of a twisting beam is developed. The formulation is effective for a prismatic beam with solid section as well as a thin‐walled beam, and can be applied both to a pure‐torsion problem and a warping‐torsion problem. The formulation is of a great advantage to an elastic‐plastic torsion problem. The formulation does not stand on the assumption of a thin‐walled structure, and therefore torsional rigidity of the section can be evaluated exactly without using the so‐called Saint‐Venant's torsional constant. Torsional rigidity is, in this paper, evaluated directly by a warping function of the section. Warping function is evaluated numerically due to shape of the section, due to progress of plastic region and due to effect of finite displacement (finite rotation, small strain). Pure‐torsion and warping‐torsion of a rectangular beam and an H‐beam, which have an elastic‐plastic material property, are analysed, and the extension to the finite displacement problem is discussed. Many numerical examples are provided in order to check the accuracy of the formulation.