Boundary-Level-Constrained Refinement for suppressing trimming-induced high-frequency outliers in explicit isogeometric analysis

In explicit dynamics, the critical time step is governed by the maximum eigenfrequency of the semi-discrete system. In Isogeometric Analysis (IGA), open knot vectors introduce a characteristic spectral boundary effect that can lead to high-frequency outliers and restrict the admissible time step. In the row-sum-lumped setting considered here, extending the computational patch and trimming away the exterior boundary functions mitigates this time-step penalty, but does not necessarily prevent boundary-adjacent basis functions from governing the maximum eigenfrequency. We show that reduced-support basis functions adjacent to the trimming boundary can remain governing contributors to the maximum eigenfrequency even for knot-exact trimming, i.e., in the absence of small cut cells. Hence, small cut cells are not required for trimming-induced time-step penalties. Knot-exact and arbitrary trimming represent different degrees of support reduction within the same underlying mechanism. To control this effect, we propose the Boundary-Level-Constrained Refinement (BLCR) strategy, a local refinement constraint for LR- and THB-splines. BLCR constrains the refinement level of basis functions whose support intersects the trimming boundary relative to that of the refined interior. In all configurations investigated in this work, this constraint ensures that the maximum eigenfrequency is governed by untrimmed interior basis functions rather than by trimmed functions at the boundary. Consequently, the trimming-induced high-frequency outliers governing the critical time step are suppressed, yielding a larger admissible time step than globally refined trimmed B-splines with the same interior resolution. BLCR preserves the diagonal row-sum-lumped mass formulation and requires no additional stabilization. The method specifically targets the upper spectral limit governing the critical time step and is not intended to resolve general spectral-accuracy limitations of mass lumping. The underlying mechanism is analyzed using mathematical bounds on the maximum system eigenfrequency and validated in an industrial sheet metal forming simulation with LS-DYNA, where substantially increased stable time steps are obtained while the investigated response quantities remain in close agreement.