Approximation of the vibration modes of a plate coupled with a fluid by low-order isoparametric finite elements
ESAIM: Modélisation mathématique et analyse numérique, Tome 38 (2004) no. 6, pp. 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 : 10.1051/m2an:2004050
Classification : 65N15, 65N30, 74F10, 74H25
Mots-clés : Reissner-Mindlin, MITC methods, fluid-structure interaction
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Hernández, Erwin. Approximation of the vibration modes of a plate coupled with a fluid by low-order isoparametric finite elements. ESAIM: Modélisation mathématique et analyse numérique, Tome 38 (2004) no. 6, pp. 1055-1070. doi : 10.1051/m2an:2004050. http://archive.numdam.org/articles/10.1051/m2an:2004050/

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