Accuracy Enhancement of Hybrid/Mixed Models for Thin-Walled Beam Assemblages

Abstract

Aiming to increase the accuracy and computational efficiency of shear, flexible, thin-walled beam assemblages with arbitrary cross-section, two C⁰-finite element models for three-dimensional analysis are developed based on the hybrid/mixed variational principle. To eliminate the shear/warping locking in these C⁰elements, the Hellinger-Reissner-variational principle is adopted. In this, both displacement and stress fields are approximated independently. To enhance the accuracy and performance of these models, the stress parameters are chosen to satisfy the equilibrium within the element level in addition to the conventional requirements; i.e., avoid all kinematic deformation modes and enable the resulting element to handle applications with constrained problems. Such stress parameters are of the interelement-independent type and, therefore, can be eliminated on the element level by applying the relevant stationary conditions, thus leading to the standard form of the stiffness equations for implementation. Further, the underlying generalized beam theory employed accounts for all coupled significant modes of deformations including stretching, bending, shear, torsion, as well as warping. The formulation is also valid for both open- and closed-type, thin-walled sections; this is accomplished by using kinematic descriptions accounting for both flexural and warping torsional effects. Despite the effort in selecting the stress field to satisfy equilibrium within the element level, the present models achieved better accuracy, robustness, and fast convergence.

Keywords:

• C⁰-finite elements, Warping effect, Independent displacement/Stress functions, Equilibrium within element domain