Selective mass scaling and critical time-step estimate for explicit dynamics analyses with solid-shell elements

Explicit integration is often used in highly nonlinear finite element structural dynamics simulations. However, explicit time integration is stable only if the used time-step is smaller than a critical threshold, which can be shown to depend on the smallest geometrical dimension of the finite elements in the mesh. This aspect is particularly critical when solid-shell elements are used for the analysis of thin walled structures, since the small thickness can lead to unacceptably small time-steps. A selective mass scaling technique, based on a linear transformation of the element degrees of freedom, is proposed in this paper to increase the size of the critical time-step without affecting the dynamic response. An analytical procedure is also developed for the computation of the element highest eigenfrequency and estimate of the critical time-step size. The computational effectiveness and accuracy of the proposed methodology is tested on the basis of numerical examples.