Intrinsically selective mass scaling with hierarchic plate formulations

The critical time step in explicit time integration methods depends on the highest natural angular frequency of the discretized problem. For shear deformable beam, plate and shell formulations, efficiency is therefore typically limited by the highest transverse shear frequencies, which are mostly of minor importance for the structural response. Direct parametrization using transverse shear variables within hierarchic structural element formulations allows a selective scaling of transverse shear frequencies in a simple manner, while bending frequencies remain practically unaffected. In particular, the novel concept of intrinsically selective mass scaling (ISMS) results in an efficient method that features high accuracy and preserves both linear and angular momentum for both consistent and lumped mass matrices. In addition, ISMS preserves the diagonal structure of lumped mass matrices. Similar to the underlying intrinsically locking-free, hierarchic concept for shear deformable structural element formulations, ISMS retains its beneficial properties for any smooth discretization scheme. In this contribution, we extend recent research on ISMS for beam formulations to the case of shear deformable plate formulations. We test our novel concept with respect to accuracy and efficiency by means of selected numerical experiments. We study both frequency spectra and the transient behavior in explicit time integration. To demonstrate the generality of ISMS, exemplarily both isogeometric discretizations based on B-splines and meshfree discretizations using local maximum-entropy approximants are investigated. • Novel intrinsically selective mass scaling (ISMS) for hierarchic plate formulations. • ISMS features high efficiency while preserving the accuracy of unscaled solutions. • ISMS naturally preserves both linear and angular momentum. • ISMS works intrinsically on formulation level—independent of the discretization. • ISMS works with various mass matrices and preserves the diagonality of lumped mass.