Coupling and simulation of acoustic fluid-structure interaction systems using localized Lagrange multipliers

This thesis presents a new coupling method for treating the interaction of an acoustic fluid with a flexible structure, with emphasis on handling spatially non-matching meshes. It is based on the Localized Lagrange Multiplier (LLM) method. A frame is introduced as a "mediator" or "information relay" device between the fluid and the structure at the interaction surface. The frame is discretized in terms of kinematic variables. A Lagrange multiplier field is introduced between the frame and the structure, and another one between the frame and the fluid. The function of the multiplier pair is weak enforcement of kinematic continuity. This configuration completely decouples the structure and fluid models, because each model communicates to the frame through node collocated multipliers and not directly to each other.; In order to assure proper communication, energy formulations of the fluid and structure models are in terms of displacements and associated time derivatives. A novel transformation of the fluid displacement model into a fluid displacement potential model enforces the irrotational condition of the acoustic fluid. This transformation reduces the number of degrees of freedom in two and three-dimensions and is suitable for both vibration and transient analyses.; The LLM method facilitates the construction of separate discretizations using different mesh generation programs, as well as use of customized time integration methods. To advance the solution in time, the LLM coupling method is combined with a partitioned solution procedure. The time-stepping computations are organized in a way that eliminates the traditional prediction step characteristic of staggered solution procedures. This is accomplished by solving for the interface variables: Lagrange multipliers and frame states, and then feeding this solution back to the coupled components. This sequence forestalls the well-known stability degradation caused by prediction, yet it retains the desirable localization features of a partitioned analysis procedure. One consequence of this method is that if two A-stable integration schemes, such as the trapezoidal rule, are chosen for the fluid and structure, then the coupled system retains unconditional stability. Other time integration schemes, such as central difference, for one or both components can be readily accommodated.