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Modeling elastic shells immersed in fluid
Author(s) -
Givelberg Edward
Publication year - 2004
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/cpa.20000
Subject(s) - shell (structure) , immersed boundary method , compressibility , mechanics , numerical analysis , planar , basilar membrane , vibration , bending , boundary value problem , convergence (economics) , fluid–structure interaction , hydroelasticity , classical mechanics , spherical shell , mathematics , cochlea , boundary (topology) , physics , acoustics , mathematical analysis , finite element method , computer science , engineering , mechanical engineering , computer graphics (images) , economic growth , thermodynamics , medicine , economics , anatomy
We describe a numerical method to simulate an elastic shell immersed in a viscous incompressible fluid. The method is developed as an extension of the immersed boundary method using shell equations based on the Kirchhoff‐Love and the planar stress hypotheses. A detailed derivation of the shell equations used in the numerical method is presented. This derivation, as well as the numerical method, uses techniques of differential geometry. Our main motivation for developing this method is its use in constructing a comprehensive, three‐dimensional computational model of the cochlea (the inner ear). The central object of study within the cochlea is the basilar membrane, which is immersed in fluid and whose elastic properties rather resemble those of a shell. We apply the method to a specific example, which is a prototype of a piece of the basilar membrane, and study the convergence of the method in this case. Some typical features of cochlear mechanics are already captured in this simple model. In particular, numerical experiments have shown a traveling wave propagating from the base to the apex of the model shell in response to external excitation in the fluid. © 2004 Wiley Periodicals, Inc.