Mixed variational formulations of finite element analysis of elastoacoustic/slosh fluid-structure interaction

CARLOS A. FELIPPADepartment o/Aerospace Engineering andCenter/or Space Structures and ControlsUniversity of Colorado, Boulder, CO 80509-0_9, USAROGER OHAYONOffice National D't_tudes et de Recherehes A6rospatialcsBP 7P., 9_3P.2 Chatillon, FranceABSTRACTA general three-field variational principle is obtained for the motion of an acoustic fluid enclosed ina rigid or flexible container by the method of canonical decomposition applied to a modified formof the wave equation in the displacement potential. The general principle is specialized to a mixedtwo-field principle that contains the fluid displacement potential and pressure as independent fields.Thls principle contains a free parameter a. Semldlscrete finite-element equations of motion based onthis principle are displayed and applied to the transient response and free-vibrations of the coupledfluld-structure problem. It is shown that a particular setting of a yields a rich set of formulationsthat can be customized to fit physical and computational requirements. TiLe variational principle isthen extended to handle slosh motions in a uniform gravity field, and used to derived semidlscreteequations of motion that account for such effects.1. INTRODUCTIONAn elastic container (the structure) is totally or partly filled with a compressible liquid or gas (thefluid). The fluid structure system is initially in static equilibrium in a steady body force field suchas gravity or centrifugal forces. We consider small departures from equilibrium that result in forcedor free vibratory motions. To analyze these motions the fluid is treated _ a linear acoustic fluid,i.e., compressible but irrotational and inviscid. The purpose of tile present work is1. To derive variational equations of motion based on a mixed variational principle for the fluidsubsystem.2. To obtain semldlscrete equations of motion following spatial discretization of the coupled prob-lem by the finite element method.The derivation of the mixed variational principle for the fluid is based on the method of canoni-cal equations advocated by Oden and Reddy