Approximation of the vibration modes of a plate coupled with a fluid by low-order isoparametric finite elements

Erwin Hernández

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

  • Volume: 38, Issue: 6, page 1055-1070
  • ISSN: 0764-583X

Abstract

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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.

How to cite

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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: Mathematical Modelling and Numerical Analysis 38.6 (2010): 1055-1070. <http://eudml.org/doc/194247>.

@article{Hernández2010,
abstract = { 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. },
author = {Hernández, Erwin},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Reissner-Mindlin; MITC methods; fluid-structure interaction.},
language = {eng},
month = {3},
number = {6},
pages = {1055-1070},
publisher = {EDP Sciences},
title = {Approximation of the vibration modes of a plate coupled with a fluid by low-order isoparametric finite elements},
url = {http://eudml.org/doc/194247},
volume = {38},
year = {2010},
}

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
DA - 2010/3//
PB - EDP Sciences
VL - 38
IS - 6
SP - 1055
EP - 1070
AB - 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.
LA - eng
KW - Reissner-Mindlin; MITC methods; fluid-structure interaction.
UR - http://eudml.org/doc/194247
ER -

References

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