Abstract
The need of lightweight design in structural engineering is steadily growing due to economic and ecological reasons. This usually causes the structure to exhibit moderate to large displacements and rotations, resulting in a distributed nonlinear behavior. However, the characterization of geometrical nonlinearities is challenging and sensitive to structural boundaries and loading. It is commonly performed with numerical simulations, utilizing particularly finite element formulations. This study comprises simulations of a clamped-clamped beam with moderate to large amplitude oscillations. Four different (commercial and noncommercial) numerical approaches are considered: three finite element representations and one assumed-modes approach. A first comparison is conducted when the system is under a sine sweep excitation over one single mode. Subsequently, a modified model featuring nonlinear internal resonance is considered, to disclose differences in the modeling of the nonlinearity when coupling between modes occurs. The results show some expected features for geometrical nonlinearities in all methods, but also some important differences, especially when the modal interaction is activated.
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References
Di Maio, D., delli Carri, A., Magi, F., Sever, I.A.: Detection of nonlinear behaviour of composite components before and after endurance trials. Conf. Proc. Soc. Exp. Mech. Ser. (2014). https://doi.org/10.1007/978-3-319-04522-1_8
Dassault Systems. Simulia, May 2018
ANSYS Mechanical APDL. Version Release 15
Sonneville, V., Cardona, A., Brüls, O.: Geometrically exact beam finite element formulated on the special Euclidean group SE(3). Comput. Methods Appl. Mech. Eng. 268, 451–474 (2014). https://doi.org/10.1016/j.cma.2013.10.008
Anastasio, D., Marchesiello, S., Noël, J.P., Kerschen, G.: Subspace-based identification of a distributed nonlinearity in time and frequency domains. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-74280-9_30
Detroux, T., Renson, L., Masset, L., Kerschen, G.: The harmonic balance method for bifurcation analysis of large-scale nonlinear mechanical systems. Comput. Methods Appl. Mech. Eng. 296, 18–38 (2015). https://doi.org/10.1016/j.cma.2015.07.017
Hilber, H.M., Hughes, T.J.R., Taylor, R.L.: Improved numerical dissipation for time integration algorithms in structural dynamics. Earthq. Eng. Struct. Dyn. 5, 283–292 (1977). https://doi.org/10.1002/eqe.4290050306
Newmark, N.M.: A method of computation for structural dynamics. J. Eng. Mech. 85, 67–94 (1959). https://doi.org/10.1016/j.compgeo.2015.08.008
Chung, J., Hulbert, G.M.: A time integration algorithm for structural dynamics with improved numerical dissipation: the generalized-α method. J. Appl. Mech. 60, 371–375 (1993). https://doi.org/10.1115/1.2900803
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Anastasio, D. et al. (2020). Dynamics of Geometrically-Nonlinear Beam Structures, Part 1: Numerical Modeling. In: Kerschen, G., Brake, M., Renson, L. (eds) Nonlinear Structures and Systems, Volume 1. Conference Proceedings of the Society for Experimental Mechanics Series. Springer, Cham. https://doi.org/10.1007/978-3-030-12391-8_28
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DOI: https://doi.org/10.1007/978-3-030-12391-8_28
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