| The formulation, consistency, and accuracy of finite element methods for calculation of structural dynamic response of unconstrained liquid-filled spacecraft and launch vehicle propellant tanks is investigated. The equations of motion of a fluid-structure system with a free surface are developed in a material description, with respect to an accelerating spatial reference frame. Several solution methods for these equations are discussed. For the special case of a completely enclosed fluid in an inertial reference frame, the existence of a countable sequence of real hydroelastic eigenvalues and associated eigenfunctions of an infinite dimensional variational problem, posed in an arbitrary three-dimensional polyhedral domain, is rigorously established. A nonconforming finite element approximation of this variational problem is presented, and a priori error estimates for eigenvalues and eigenfunctions are proved. Variational and finite element methods for the approximation of eigenvalues and eigenfunctions of an accelerating fluid-structure system with a free-surface are presented, and existence and error estimates are obtained for this case as well. Substructure modal synthesis techniques for slosh-structure interaction are similarly formulated and analyzed. The accuracy of the error estimates are verified in three dimensional numerical simulations using the NASTRAN finite element code. |
