This paper aims to investigate, in large displacement and torsion context, the nonlinear dynamic behavior of thin-walled beams with open cross section subjected to various loadings by high-order implicit solvers. These homotopy transformations consist to modify the nonlinear discretized dynamic problem by introducing an arbitrary invertible pre-conditioner [K ] and an arbitrary path following parameter. The nonlinear strongly coupled equations of these structures are derived by using a 3D nonlinear dynamic model which accounts for large displacements and large torsion without any assumption on torsion angle amplitude. Coupling complex structural phenomena such that warping, bending-bending, and flexural-torsion are taken into account. Two examples of great practical interest of nonlinear dynamic problems of various thin-walled beams with open section are presented to validate the Key words and phrases. Thin-walled beam, open cross section, large displacement, large torsion, forced nonlinear dynamic, finite element, homotopy, power series expansion, Asymptotic Numerical Method (ANM).
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