Immersed IGA and mass lumping for explicit dynamics of structural elements
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Isogeometric analysis (IGA) is able to provide numerous advantages compared to 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 infinitesimal critical time steps to ensure stability, and thus simulation times become infeasible. Immersed IGA is an alternative that could provide stability and efficiency, leveraging the effect of higher-order inter-element continuity in conjunction with either a Lumped Mass Matrix or by introducing α-stabilization along with a Consistent Mass Matrix. In the first scenario the limiting of the largest eigenfrequency is massive and simulation times can be decreased significantly, while in the second case the restriction is smaller but still crucial. Studies on simple 1D bar problems in the immersed setting indicate that while the lumping of the mass is enhancing stability and efficiency, it significantly deteriorates the accuracy in comparison to an analogous case where consistent mass is employed. This work is investigating these effects on a similar setting (bar), as well as extending to the 2D domain (membrane) and 4th order partial differential equation problems (beam, plate).