000013445 001__ 13445
000013445 005__ 20161114165554.0
000013445 04107 $$aeng
000013445 046__ $$k2011-05-25
000013445 100__ $$aKolman, R.
000013445 24500 $$aDispersion Errors of B-Spline Based Finite Element Method  in One-Dimensional Elastic Wave Propagation

000013445 24630 $$n3.$$pComputational Methods in Structural Dynamics and Earhquake Engineering
000013445 260__ $$bNational Technical University of Athens, 2011
000013445 506__ $$arestricted
000013445 520__ $$2eng$$aThe spatial discretization of elastic continuum by finite element method (FEM) introduces dispersion errors to numerical solutions of wave propagation tasks. For higher order Lagrangian as well as Hermitian elements there are optical modes in their frequency spectra leading to spurious oscillations of shock induced responses in a vicinity of propagating wavefronts. Furthermore, the behavior of classical higher order elements accounts for discontinuities in their spectra as well as for false representation of maximum frequency, the error of which increases with element order. For brevity this property is called the divergent behavior in the text. The recent innovations in finite element analysis rely on spline-based shape functions, taking inspiration in CAD (Computer Aided Design) approaches where the B-splines and mainly NURBS (non-uniform rational B-spline) representations are regularly employed. B-spline as well as NURBS curves are piecewise polynomial curves that are differentiable up to a prescribed order. The B-splines functions, employed as finite element shape functions, are examined in this paper, using the 1D stress wave modeling as a testing vehicle. It is shown that the employed approach leads to substantial minimization of dispersion errors; furthermore the errors decrease with increasing order of B-spline elements. It is believed that the B-spline based FE technology represents a promising tool allowing to increase reliability of numerical solutions of wave propagation problems.

000013445 540__ $$aText je chráněný podle autorského zákona č. 121/2000 Sb.
000013445 653__ $$aWave Propagation, Dispersion Analysis, B-spline based finite element method.

000013445 7112_ $$aCOMPDYN 2011 - 3rd International Thematic Conference$$cIsland of Corfu (GR)$$d2011-05-25 / 2011-05-28$$gCOMPDYN2011
000013445 720__ $$aKolman, R.$$iPlesek, J.$$iOkrouhlik, M.$$iGabriel, D.
000013445 8560_ $$ffischerc@itam.cas.cz
000013445 8564_ $$s995351$$uhttp://invenio.itam.cas.cz/record/13445/files/117.pdf$$yOriginal version of the author's contribution as presented on CD, section: MS 04 Advances in Numerical Methods for Linear and Nonlinear Dynamics.
000013445 962__ $$r13401
000013445 980__ $$aPAPER