Approximation of the vibration modes of a plate coupled with a fluid by low-order isoparametric finite elements
Departamento de Matemática,
Universidad Técnica Federico Santa María, Casilla 110-V,
Valparaiso, Chile. firstname.lastname@example.org.
Revised: 22 September 2004
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.
Mathematics Subject Classification: 65N15 / 65N30 / 74F10 / 74H25
Key words: Reissner-Mindlin / MITC methods / fluid-structure interaction.
© EDP Sciences, SMAI, 2004