Dynamic analysis of a thin-walled beam with open cross section subjected to dynamic loads using a high-order implicit algorithm

In this paper, the forced nonlinear dynamic behavior of thin-walled beams with open cross section under external dynamic loads is analyzed by means of a high order implicit algorithm. This algorithm is developed using a 3 D nonlinear model that takes into account the large torsion without any assumption on the torsion angle amplitude neither in the constitutive law nor in the derivation for governing dynamic equations. This algorithm is built by employing the following four steps: 1 – the space and time discretization procedures, 2 – a change of variable, 3 – a homotopy transformation, 4 – techniques used in the Asymptotic Numerical Method (ANM) (Cochelin et al., 2007; Mottaqui et al., 2010) [1,2]. The originality of this work reside in the fact that we use, for the first time, this algorithm for nonlinear analysis of thin-walled beams with open cross section under an arbitrary load. The space and time discretizations are performed respectively by the finite elements method and by the classical implicit Newmark scheme. The performance of the high order implicit algorithm is tested on four examples of nonlinear dynamic: a mono-symmetrical beam with a T cross section under external dynamic load, a mono-symmetrical beam with U cross-section under external dynamic load, a bi-symmetrical clamped-free beam IPE 300 under harmonic loads and a bi-symmetrical simply supported beam with cruciform section under harmonic loads. A comparison of the obtained results with those computed by the Abaqus industrial code is given. This comparison confirms the robustness, accuracy and efficiency of this high order implicit algorithm.