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We analyze an isoparametric finite element method to compute the vibration modes of a plate, modeled by Reissner-Mindlin equations, in contact with a compressible fluid, described in terms of displacement variables. To avoid locking in the plate, we consider a low-order method of the so called MITC (Mixed Interpolation of Tensorial Component) family on quadrilateral meshes. To avoid spurious modes in the fluid, we use a low-order hexahedral Raviart-Thomas elements and a non conforming coupling is used on the fluid-structure interface. Applying a general approximation theory for spectral problems, under mild assumptions, we obtain optimal order error estimates for the computed eigenfunctions, as well as a double order for the eigenvalues. These estimates are valid with constants independent of the plate thickness. Finally, we report several numerical experiments showing the behavior of the methods.
@article{M2AN_2004__38_6_1055_0,
author = {Hern\'andez, Erwin},
title = {Approximation of the vibration modes of a plate coupled with a fluid by low-order isoparametric finite elements},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {1055--1070},
publisher = {EDP-Sciences},
volume = {38},
number = {6},
year = {2004},
doi = {10.1051/m2an:2004050},
mrnumber = {2108944},
zbl = {1130.74453},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/m2an:2004050/}
}
TY - JOUR AU - Hernández, Erwin TI - Approximation of the vibration modes of a plate coupled with a fluid by low-order isoparametric finite elements JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2004 SP - 1055 EP - 1070 VL - 38 IS - 6 PB - EDP-Sciences UR - http://geodesic.mathdoc.fr/articles/10.1051/m2an:2004050/ DO - 10.1051/m2an:2004050 LA - en ID - M2AN_2004__38_6_1055_0 ER -
%0 Journal Article %A Hernández, Erwin %T Approximation of the vibration modes of a plate coupled with a fluid by low-order isoparametric finite elements %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2004 %P 1055-1070 %V 38 %N 6 %I EDP-Sciences %U http://geodesic.mathdoc.fr/articles/10.1051/m2an:2004050/ %R 10.1051/m2an:2004050 %G en %F M2AN_2004__38_6_1055_0
Hernández, Erwin. Approximation of the vibration modes of a plate coupled with a fluid by low-order isoparametric finite elements. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 38 (2004) no. 6, pp. 1055-1070. doi: 10.1051/m2an:2004050
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