Large torsion analysis of thin-walled open sections beams by the Asymptotic Numerical Method

This paper presents a continuation algorithm based on the Asymptotic Numerical Method (ANM) to study instability phenomena of large torsion of thin-walled open sections beams under various external loadings. The proposed algorithm connects perturbation techniques with a discretization principle and a continuation method without the use of a correction process. In the model, the equilibrium and material constitutive equations are established without any assumption on torsion angle amplitude. In presence of eccentric loads and large torsion context, the right hand side of the equilibrium equations is highly nonlinear and contributes to the tangent stiffness matrix. A 3D beam element having two nodes with seven degrees of freedom is considered in mesh process. Several numerical examples from buckling of thin-walled open sections beams are analyzed to assess the efficiency and the reliability of the method. Comparisons are made with known commercial software. The proposed ANM algorithm is more reliable and less time consuming than other iterative classical methods.