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Finite element analysis of sloshing and hydroelastic vibrations under gravity

Published online by Cambridge University Press:  15 August 2002

Alfredo Bermúdez
Affiliation:
Departamento de Matemática Aplicada, Universidade de Santiago de Compostela, 15706 Santiago de Compostela, Spain. Partially supported by Programa de Cooperación Científica con Iberoamérica, M.E.C. and Acción Integrada Hispano-Francesa HF 1997-0194, Spain.
Rodolfo Rodríguez
Affiliation:
Departamento de Ingeniería Matemática, Universidad de Concepción, Casilla 4009, Concepción, Chile. Partially supported by FONDECYT (Chile) through its grant No. 1.960.615 and Subprogram A on Numerical Analysis of FONDAP in Applied Mathematics (Chile).
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Abstract

This paper deals with a finite element method to solve fluid-structure interaction problems. More precisely it concerns the numerical computation of harmonic hydroelastic vibrations under gravity. It is based on a displacement formulation for both the fluid and the solid. Gravity effects are included on the free surface of the fluid as wellas on the liquid-solid interface. The pressure of the fluid is used as a variable for the theoretical analysis leading to a well posed mixed linear eigenvalue problem.Lowest order triangular Raviart-Thomas elements are used for the fluid and classical piecewise linear elements for the solid. Transmission conditions at the fluid-solid interface are taken into account in a weak sense yielding a non conforming discretization. The method does not present spurious or circulation modes for nonzero frequencies.Convergence is proved and optimal error estimates are given.Finally, numerical results are shown.

Type
Research Article
Copyright
© EDP Sciences, SMAI, 1999

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