Selective mass scaling for Timoshenko beam and Mindlin plate elements based on the discrete strain gap method

The conditional stability of explicit time integration algorithms limits the critical time step size, which depends on the highest natural frequency of the discretized problem. For shear deformable structural finite element formulations, efficiency is typically limited by the highest transverse shear frequencies. Selective mass scaling (SMS) methods aim at selectively scaling the high frequencies while preserving the important low frequency content. In particular, recent SMS concepts, which are inspired by the discrete strain gap (DSG) method [1] and, thus, are denoted as DSGSMS concepts, result in effective and accurate methods, which naturally preserve both linear and angular momentum. In this contribution, we extend previous work on DSGSMS for shear deformable element formulations [2] with respect to several aspects. First, we perform a theoretical analysis of the DSGSMS method that provides new insight into spectral properties and analytical time step estimates. Second, we extend the DSGSMS method from Timoshenko beam elements to Mindlin plate elements. Third, we test the extended concept with respect to spectral accuracy and the transient behavior in explicit time integration.

Subjects

selective mass scaling

explicit dynamics

critical time step

Timoshenko beam elements

Mindlin plate elements

discrete strain gap method

DDC Class

690: Building, Construction

Funding(s)

Auf Finite-Elemente-Technologie basierende selektive Massenskalierung für explizite Dynamik dünnwandiger Strukturen

Options

Selective mass scaling for Timoshenko beam and Mindlin plate elements based on the discrete strain gap method