Advances on kinematically exact rod models for thin-walled open-section members: Consistent warping function and nonlinear constitutive equation

Abstract

This work proposes two advances on kinematically exact rod models for thin-walled open section members: (i) an explicit analytical expression for the cross-section warping function, including both primary and secondary warping for arbitrary section geometries, and (ii) a nonlinear elastic constitutive equation with all higher-order strain terms included, suitable for truly finite strains. By not neglecting any of the strain terms at the constitutive level, full bending, compression and torsional strain couplings are enabled. This improves the model performance in capturing buckling phenomena and describing the developed post-critical configurations. Since the stress-resultants end up with elaborate expressions, numerical rather than analytical integration over the cross-section is preferred for their computation, which explains the need for knowing a priori the warping function (and its directional derivatives) in the entire cross-section, including in the thickness direction. The advances are implemented in a 7-DOF (3 displacements, 3 rotations and one warping intensity) rod model available in an in-house finite element program. Validation is performed using existing results from the literature as well as solutions obtained with shell models from a commercial software. The proposed advances proved to fix pathological behavior of previous rod models in both torsional and lateral–torsional buckling problems, as well as numerical convergence issues in developed post-critical configurations.