Selective mass scaling for distorted solid-shell elements in explicit dynamics: optimal scaling factor and stable time step estimate

The use of solid-shell elements in explicit dynamics has been so far limited by the small critical time step resulting from the small thickness of these elements in comparison with the in-plane dimensions. To reduce the element highest eigenfrequency in inertia dominated problems, the selective mass scaling approach previously proposed in [G. Cocchetti, M. Pagani and U. Perego, Comp. \& Struct. 2013; 127:39-52.] for parallelepiped elements is here reformulated for distorted solid-shell elements. The two following objectives are achieved: the critical time step is governed by the smallest element in-plane dimension and not anymore by the thickness; the mass matrix remains diagonal after the selective mass scaling. The proposed approach makes reference to one Gauss point, trilinear brick element, for which the maximum eigenfrequency can be computed analytically. For this element, it is shown that the proposed mass scaling can be interpreted as a geometric thickness scaling, obtaining in this way a simple criterion for the definition of the optimal mass scaling factor. A strategy for the effective computation of the element maximum eigenfrequency is also proposed. The considered mass scaling preserves the element translational inertia, while it modifies the rotational one, leading to errors in the kinetic energy when the motion rotational component is dominant. The error has been rigorously assessed for an individual element, and a simple formula for its estimate has been derived. Numerical tests, both in small and large displacements and rotations, using a state-of-the-art solid-shell element taken from the literature, confirm the effectiveness and accuracy of the proposed approach. Copyright {\copyright} 2014 John Wiley \& Sons, Ltd.