Intrinsically Selective Mass Scaling with Hierarchic Structural Element Formulations

Hierarchic shear deformable Reissner-Mindlin shell formulations possess the advantage of being intrinsically free from transverse shear locking [1], [2]. Transverse shear locking is avoided a priori through reparametrization of the kinematic variables. This reparametrization yields beam, plate and shell formulations with distinct transverse shear degrees of freedom.The efficiency of explicit dynamic analyses of thin-walled structures is limited by the critical time step size, which depends on the highest frequency of the discretized system. If Reissner-Mindlin type shell elements are used for discretization of a thin structure, the highest transverse shear frequencies limit the critical time step in explicit dynamic analyses, while being relatively unimportant for the structural response of the system. The basic idea of selective mass scaling is to scale down the highest frequencies in order to increase the critical time step size, while keeping the low frequency modes unaffected, see for instance [3]. In most concepts, this comes at the cost of non-diagonal mass matrices.In this contribution, we present recent investigations on selective mass scaling with hierarchic formulations. Since hierarchic formulations possess distinct transverse shear degrees of freedom, they offer the intrinsic ability for selective mass scaling of the shear frequency modes, while keeping the bending dominated modes mostly unaffected and retaining the diagonal structure of a lumped mass matrix. We discuss the effects of transverse shear parametrization, locking and mass lumping on the accuracy of results and a feasible time step.REFERENCES[1] R. Echter, B. Oesterle and M. Bischoff, A hierarchic family of isogeometric shell finite elements. Computer Methods in Applied Mechanics and Engineering, Vol. 254. pp. 170-180, 2013.[2] B. Oesterle, E. Ramm and M. Bischoff, A shear deformable, rotation-free isogeometric shell formulation. Computer Methods in Applied Mechanics and Engineering, Vol. 307, pp. 235-255, 2016.[3] G. Cocchetti, M. Pagani and U. Perego, Selective mass scaling and critical time-step estimate for explicit dynamics analyses with solid-shell elements. Computers and Structures, Vol. 27, pp. 39-52, 2013.