000015643 001__ 15643
000015643 005__ 20161115135325.0
000015643 04107 $$aeng
000015643 046__ $$k2013-06-12
000015643 100__ $$aIdesman, A.
000015643 24500 $$aFinite Element Modeling of Linear Elastodynamics Problems With Explicit Time-Integration Methods and Linear Elements With Reduced Dispersion. Comparative Study of Different Finite Element Techniques Used for Elastodynamics.

000015643 24630 $$n34.$$pComputational Methods in Structural Dynamics and Earhquake Engineering
000015643 260__ $$bNational Technical University of Athens, 2013
000015643 506__ $$arestricted
000015643 520__ $$2eng$$aWe have developed two finite element techniques with reduced dispersion for linear elastodynamics that are used with explicit time-integration methods. These techniques are based on the modified integration rule for the mass and stiffness matrices and on the averaged mass matrix approaches that lead to the numerical dispersion reduction for linear finite elements. The analytical study of numerical dispersion for the new techniques is carried out in the 1-D, 2-D and 3-D cases. The numerical study of the effectiveness of the dispersion reduction techniques includes two-stage time-integration approach with the filtering stage (developed in our previous papers) that quantifies and removes spurious high-frequency oscillations from numerical results. We have found that in contrast to the standard linear elements with explicit time-integration methods and the lumped mass matrix, the finite element techniques with reduced dispersion yield more accurate results at small time increments (smaller than the stability limit) in the 2D and 3-D cases. The advantages of the new technique are illustrated by the solution of the 1-D and 2-D impact problems. The new approaches with reduced dispersion can be easily implemented into existing finite element codes and lead to significant reduction in computation time at the same accuracy compared with the standard finite element formulations. Finally, we compare the accuracy of the linear elements with reduced dispersion, the spectral low- and high-order elements as well as the isogeometric elements by the solution of the 1-D impact problem. For all these solutions we use two-stage time integration technique with the filtering stage that removes spurious oscillations and allows an accurate comparison of different space discretization techniques used for elastodynamics. It is also interesting to mention that the amount of numerical dissipation at the filtering stage can be used as a quantitative measure for the comparison of accuracy of the different numerical formulations used for elastodynamics.

000015643 540__ $$aText je chráněný podle autorského zákona č. 121/2000 Sb.
000015643 653__ $$aelastic waves, numerical dispersion, explicit time integration, finite elements.

000015643 7112_ $$aCOMPDYN 2013 - 4th International Thematic Conference$$cIsland of Kos (GR)$$d2013-06-12 / 2013-06-14$$gCOMPDYN2013
000015643 720__ $$aIdesman, A.
000015643 8560_ $$ffischerc@itam.cas.cz
000015643 8564_ $$s3429531$$uhttps://invenio.itam.cas.cz/record/15643/files/1189.pdf$$yOriginal version of the author's contribution as presented on CD, section: CD-MS 12 ADVANCES IN NUMERICAL METHODS FOR LINEAR AND NON-LINEAR DYNAMICS
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000015643 962__ $$r15525
000015643 980__ $$aPAPER