Analysis of the stability of frames composed of thin-walled beams with open cross-section using a High Order Continuation Method

This study presents the numerical modeling of frames composed of thin-walled beams with open cross-section subjected to large torsions by a High Order Continuation Method (HOCM), based on Asymptotic Numerical Method (ANM) techniques. The theoretical model is developed using $3D$ beam kinematics, which accounts for flexion-torsion coupling and large rotations. The connection between beams is ensured by joints (stiffening plates) to avoid local deformations, mathematically modeled by compatibility conditions applied to the connection nodes. The equilibrium equations are established using the minimization of the Lagrangian. Discretization is performed with a two-node beam element having seven degrees of freedom per node. The transformation from local to global reference frames is done using Euler angles for the first six degrees of freedom, while the transformation of the seventh degree of freedom is related to the transmission of warping between elements. The equilibrium equations are solved using a HOCM. Tested examples of frames of thin-walled beams with open cross-section subjected to different loadings and boundary conditions are investigated. The obtained results are compared with those calculated by the commercial software ABAQUS and with those from the literature.