Advances on a kinematically exact rod model for thin-walled open section members: consistent warping function and nonlinear constitutive equation. - Kassab, Marcos Pires (2022)
Structural models accounting for exact kinematics are well-suited for the description of critical loads and post-critical behaviour. For thin-walled open-section members, the associated rod formulations must take cross-sectional non-uniform warping into account, since it becomes a relevant load-carrying mechanism due to the very small torsion stiffness of such members. For this work, advances on kinematically exact rod models for thin-walled open section members, taking into account both primary and secondary cross-sectional warpings and advanced constitutive equations, are proposed. For thin-walled open-section members with linear elastic constitutive equation, the warping effects are fully characterized by the well-known torsion inertia from the Saint-Venants uniform torsion theory and the warping constant from the Vlasovs theory. The former has a wellknown analytic expression, whilst the latter is obtained only considering the so-called primary warping, which is the warping in the direction of the cross-section´s walls lengths. The walls´ thickness warping, or secondary warping, is typically neglected. However, for more advanced constitutive equations, such as the ones of interest here, explicit knowledge of the warping and its directional derivatives are of utmost importance for the stress resultants integrations, justifying the need of a warping function that accounts for both primary and secondary cross-sectional components. This work incorporates two exact constitutive equations (i.e. retaining all the strain terms), in order to enable full bending, compression and torsional strain couplings in the finite strain regime: one based on the Saint-Venants material, which is generally unsuited to truly finite strains, and another based on the polyconvex neo-Hookean Simo-Ciarlets material. The model was implemented in PEFSYS, which is an in-house nonlinear finite element program. Validation is performed using existing results from the literature as well as solutions obtained with shell models in ANSYS commercial software.