Immersed IGA and Mass Lumping for Explicit Dynamics of Structural Elements
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Isogeometric analysis (IGA) is able to provide numerous advantages over conventional Finite Element Analysis (FEA). In particular, the effect of higher-order inter-element continuity due to the smoothness of its spline-based basis functions leads to improved spectral accuracy over classical FEA, establishing IGA as a strong alternative in the field of structural dynamics. The focus of the current work is placed on immersed IGA. In immersed methods the presence of small cut elements can produce very large maximum eigenfrequencies, requiring too small critical time steps to ensure stability for explicit methods, leading to infeasible simulation times. The issue can be alleviated by leveraging IGA’s higher continuity in conjunction with a Lumped Mass Matrix, or with approaches related to stabilization and mass scaling while maintaining a Consistent Mass Matrix. Although mass lumping enhances stability and efficiency significantly, recent studies highlighted possible negative effects in accuracy when combined with IGA. By constructing studies in the 1D/2D domain and employing 2nd /4th order partial differential equations, this work investigates immersion, mass lumping and other factors, in an attempt to isolate their effects and provide a structured analysis on the topic.
