NUMERICAL METHODS FOR THE ANALYSIS OF FLUID-STRUCTURE INTERACTION PROBLEMS

Numerical methods for the solution of transient two-dimensional and axisymmetric three-dimensional fluid-solid interaction problems are developed and analyzed. The methods use an arbitrary moving reference frame for the kinematic description. Conservation laws for this kinematic description are developed in both differential and variational forms. The use of an arbitrary moving reference frame allows the interior of the fluid region to be modeled by a conventional Eulerian description while the solid region is modeled using a Lagrangian description. Since the arbitrary moving frame includes both Eulerian and Lagrangian descriptions as subsets, the interface condition between the fluid and solid can be determined from the kinematics and conservation laws instead of the special interface treatments used in previous methods.;The treatment of impact problems by discrete methods is also examined. Methods to mitigate the additional errors associated with impact problems are given.;Numerical solutions are presented for several problems in order to demonstrate the effectiveness of the method.;An implicit finite element approximation is constructed for the governing equations. The properties of the discrete formulation are studied by perturbation and spectral methods.