000013241 001__ 13241
000013241 005__ 20161114160333.0
000013241 04107 $$aeng
000013241 046__ $$k2009-06-22
000013241 100__ $$aHughes T. J., R.
000013241 24500 $$aIsogeometric methods in structural dynamics and wave propagation

000013241 24630 $$n2.$$pComputational Methods in Structural Dynamics and Earhquake Engineering
000013241 260__ $$bNational Technical University of Athens, 2009
000013241 506__ $$arestricted
000013241 520__ $$2eng$$aWe 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.

000013241 540__ $$aText je chráněný podle autorského zákona č. 121/2000 Sb.
000013241 653__ $$aIsogeometric analysis, B-splines, NURBS, Frequency spectrum, Wave propagation, Duality principle, Collocation methods, Greville abscissae. Abstract. 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.

000013241 7112_ $$aCOMPDYN 2009 - 2nd International Thematic Conference$$cIsland of Rhodes (GR)$$d2009-06-22 / 2009-06-24$$gCOMPDYN2009
000013241 720__ $$aHughes T. J., R.$$iReali, A.$$iSangalli, G.
000013241 8560_ $$ffischerc@itam.cas.cz
000013241 8564_ $$s347106$$uhttps://invenio.itam.cas.cz/record/13241/files/CD358.pdf$$yOriginal version of the author's contribution as presented on CD, section: Plenary lectures - i.
000013241 962__ $$r13074
000013241 980__ $$aPAPER