Nonlinear inelastic uniform torsion of bars by BEM

Abstract

In this paper the elastic–plastic uniform torsion analysis of simply or multiply connected cylindrical bars of arbitrary cross-section taking into account the effect of geometric nonlinearity is presented employing the boundary element method. The stress–strain relationship for the material is assumed to be elastic–plastic–strain hardening. The incremental torque–rotation relationship is computed based on the finite displacement (finite rotation) theory, that is the transverse displacement components are expressed so as to be valid for large rotations and the longitudinal normal strain includes the second-order geometric nonlinear term often described as the “Wagner strain”. The proposed formulation does not stand on the assumption of a thin-walled structure and therefore the cross-section’s torsional rigidity is evaluated exactly without using the so-called Saint-Venant’s torsional constant. The torsional rigidity of the cross-section is evaluated directly employing the primary warping function of the cross-section depending on both its shape and the progress of the plastic region. A boundary value problem with respect to the aforementioned function is formulated and solved employing a BEM approach. The influence of the second Piola–Kirchhoff normal stress component to the plastic/elastic moment ratio in uniform inelastic torsion is demonstrated. The developed procedure retains most of the advantages of a BEM solution over a pure domain discretization method, although it requires domain discretization, which is used only to evaluate integrals.