UNIVERSITY OF COLORADO AT DENVER

PLACE: Mathematics Conference Room 626 UCD Building, 1250 14th St., Denver

TIME: NOON (Refreshments served at 11:45 am)

DATE: Sept. 18, 2000

Title:
      Formulation and Analysis of Finite Element Methods for Hydroelastic Eigenvalue Problems

Speaker:
      Pat Ryan
       Senior Staff Engineer, Lockheed Martin Space Systems


Abstract:
The formulation, consistency and accuracy of finite element methods for the
calculation of vibration response of fluid-structure systems is discussed.
This talk largely follows the analysis in [1]. We prove the existence of a
discrete sequence of real eigenpairs of an incompressible fluid contained in
a linear elastic solid via a variational formulation which identifies a
compact operator in an appropriate Hilbert space setting. A nonconforming
finite element approximation of this variational problem is presented, and
it is proved that as the mesh is refined, all finite element eigenpairs
converge to those of the variational problem. An extension of nonconforming
approximation theory presented in [2] is discussed, and a priori error
estimates for both eigenvalues and eigenfunctions are proved for arbitrary
three dimensional polyhedral domains encountered in engineering practice.
These estimates are verified by numerical experiments performed in both
NASTRAN and research-based codes.

The talk will also place this work in context with recent papers ([3], [4]),
and will conclude with a discussion of directions for future study.


References

[1] Pat Ryan, Eigenvalue and Eigenfunction Error Estimates for Finite
Element Formulations of Linear Hydroelasticity, to be published in
Mathematics of Computation.

[2] B. Mercier, J. Osborn, J. Rappaz, and P. A. Raviart, Eigenvalue
Approximation by Mixed and Hybrid Methods, Math. Comp.,36 (1981) 427-453.

[3] Rodolfo Rodriguez and Jorge Solomin, The Order of Convergence of
Eigenfrequencies in Finite Element Approximations of Fluid-Structure
Interaction Problems, Math. Comp., 65, (1996), 1463-1475

[4] Daniele Boffi, Franco Brezzi, and Luca Gastaldi, On the Problem of
Spurious Eigenvalues in the Approximation of Linear Elliptic Problems in
Mixed Form, Math. Comp., S 0025-5718(99)01072-8, Article electronically
published on February 19, 1999