Hierarchic Formulations for Explicit Dynamic Analyses of Thin-walled Structures
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The hierarchic concept for structural element formulations has been developed within the group of the authors with a focus on shear deformable Reissner-Mindlin shell formulations [1, 2, 3]. Via reparametrization of the kinematic variables, these formulations possess distinct degrees of freedom for transverse shear. This directly results in element formulations that are intrinsically free from transverse shear locking. In addition, the hierarchic structure can be exploited towards an intrinsically selective mass scaling (ISMS) scheme [4]. That is, the high shear frequencies, which limit the critical time step in explicit analyses, are scaled while the low bending dominated branch of the frequency spectrum remains mostly unaffected. This stands in contrast to conventional rotational mass scaling for shear deformable elements, where the total rotational inertia is scaled and, therefore, also bending frequencies and linear momentum are manipulated. In this contribution, we present recent investigations on ISMS for hierarchic plate and shell formulations. We discuss the effects of transverse shear parametrization in several transient problems with respect to efficiency and accuracy. REFERENCES [1] R. Echter, B. Oesterle and M. Bischoff, A hierarchic family of isogeometric shell finite elements. Comput. Methods Appl. Mech. Engrg., Vol. 254. pp. 170–180, 2013. [2] B. Oesterle, E. Ramm and M. Bischoff, A shear deformable, rotation-free isogeometric shell formulation. Comput. Methods Appl. Mech. Engrg., Vol. 307, pp. 235–255, 2016. [3] B. Oesterle, R. Sachse and E. Ramm and M. Bischoff, Hierarchic isogeometric large rotation shell elements including linearized transverse shear parametrization. Comput. Methods Appl. Mech. Engrg., Vol. 321, pp. 383-405, 2017. [4] B. Oesterle, J. Trippmacher, A. Tkachuk, and M. Bischoff, Intrinsically selective mass scaling with hierarchic structural element formulations. Proceedings of the YIC 2021 - VI ECCOMAS Young Investigators Conference, pp. 99-108, 2021.