Isogeometric methods in structural dynamics and wave propagation

Abstract eng:
We review the discretization properties of classical finite element and NURBS-based isogeometric approximations on problems of structural vibrations and wave propagation. We find that, on the basis of equal numbers of degrees-of-freedom and bandwidth, NURBS have superior approximation properties. In fact, we observe that the high-mode behavior of classical finite elements is divergent with the order of approximation, a surprisingly negative result. On the other hand, NURBS offer almost spectral approximation properties, and all modes converge with increasing order of approximation. We also initiate the study of collocation methods for NURBS-based isogeometric analysis. The goal is to combine the accuracy of isogeometric analysis with the low computational cost of collocation to develop accurate and efficient procedures for large-scale structural dynamics and wave propagation problems. To this end, we present results for some simple one-dimensional model problems. We consider the cases of boundary-value and eigenvalue problems on periodic and finite domains, employing the so-called Greville abscissae as collocation points. The numerical results obtained are encouraging and motivate more extensive evaluation.

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