🤖 AI Summary
For immersed isogeometric analysis (IGA) of plate and shell problems in explicit dynamics, two key challenges arise: excessively small critical time steps—caused by high-order PDEs, structural slenderness, and ill-conditioned cut elements—and spurious oscillations induced by lumped mass matrices. This paper proposes a polynomial-expansion-based stabilization technique compatible with lumped mass matrices. The method simultaneously increases the critical time step by orders of magnitude and restores boundary-fitted discretization accuracy on physical boundaries. To the best of our knowledge, it is the first approach enabling stable, explicit immersed IGA for plate and shell structures. Numerical experiments demonstrate that the proposed method effectively suppresses spurious high-frequency modes, achieves dynamic response accuracy comparable to conventional boundary-fitted IGA, and significantly enhances the efficiency and robustness of explicit simulations for complex plate and shell geometries.
📝 Abstract
Finite element plate and shell formulations are ubiquitous in structural analysis for modeling all kinds of slender structures, both for static and dynamic analyses. The latter are particularly challenging as the high order nature of the underlying partial differential equations and the slenderness of the structures all impose a stringent constraint on the critical time step in explicit dynamics. Unfortunately, badly cut elements in immersed finite element discretizations further aggravate the issue. While lumping the mass matrix often increases the critical time step, it might also trigger spurious oscillations in the approximate solution thereby compromising the numerical solution. In this article, we extend our previous work in cite{voet2025stabilization} to allow stable immersogeometric analysis of plate and shell problems with lumped mass matrices. This technique is based on polynomial extensions and restores a level of accuracy comparable to boundary-fitted discretizations.