Treatment of acoustic fluid–structure interaction by localized Lagrange multipliers: Formulation

Abstract

A new concept is presented for modeling the dynamic interaction between an acoustic fluid and an elastic structure. The coupling of this multiphysics system is done by inserting a kinematic interface frame between the fluid and the structure, and using node-collocated Lagrange multipliers to connect the frame to each subsystem. The time-domain response analysis is performed by a partitioned analysis procedure. The main advantages of this localized Lagrange multiplier (LLM) primal-dual coupling method are: complete localization of the structure and fluid subsystems, elimination of the conventional predictor in the partitioned time integration method, and the ability to accommodate non-matching meshes. The standard Newmark time integrator is used on both the fluid and structure models. It is shown that if the integrator is A-stable and second-order accurate for a monolithic treatment, it retains those properties for both Mortar and LLM partitioned solution procedures. Infinite and finite piston problems are used to explain and verify the methodology. A sequel paper under preparation presents and discusses a set of benchmark and application examples that involve the response of existing dams to seismic excitation.