Approximation of the vibration modes of a plate coupled with a fluid by low-order isoparametric finite elements
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 38 (2004) no. 6, p. 1055-1070

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.

DOI : https://doi.org/10.1051/m2an:2004050
Classification:  65N15,  65N30,  74F10,  74H25
Keywords: Reissner-Mindlin, MITC methods, fluid-structure interaction
@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 - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     publisher = {EDP-Sciences},
     volume = {38},
     number = {6},
     year = {2004},
     pages = {1055-1070},
     doi = {10.1051/m2an:2004050},
     zbl = {1130.74453},
     mrnumber = {2108944},
     language = {en},
     url = {http://www.numdam.org/item/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 - Modélisation Mathématique et Analyse Numérique, Volume 38 (2004) no. 6, pp. 1055-1070. doi : 10.1051/m2an:2004050. http://www.numdam.org/item/M2AN_2004__38_6_1055_0/

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