Numerical solution for a fluid-active structure interaction

Modelling of multiphysics problems is essential in many engineering fields, such as aerospace, automotive, bio-medical, civil and naval engineering: current trends are to develop and solve physic models, more accurate and representative of real complex systems. In this paper we present a numerical solution for a fluid-active structure interaction and our procedure is tested on two simple problems in a bi-dimensional domain; procedure can be extended to three dimensional domains and used to study industrial applications. First problem examined is the mass adduction of an incompressible fluid flow in a rectangular bi-dimensional domain: the walls are fixed except for the top wall that is like a double clamped beam. Beam is bended under the fluid pressure and bending deformations are revealed from piezoelectric patches bounded on the beam surface. Beam is modelled with solid bi-dimensional element under plain-strain hypothesis. Second problem studied is the inflation of a rectangular section: injection of an incompressible flow, at low speed, is used to inflate a thin solid structure and piezoelectric patches are used as sensors to monitor the process. Fluid domain has all moving boundaries (interface with structure) except for the inlet zone that is fixed in space; during inflation the structure is deformed, stretched and wrinkled and piezoelectric patches transform these mechanical inputs in an electrical output (electric potential) that can be used as a structural health monitoring. A mixed finite element formulation is used to solve the non linear incompressible, viscous and time dependent two dimensional fluid flow and a classical finite element displacement formulation, for linear elasticity, is used to solve an active structure made of solid with piezoelectric material. To avoid ill-shaped elements and achieve a better solution, an updating mesh algorithm is used near the interface zone during time integration. Numerical results are then presented and discussed; a comparison with theoretical model or results available in literature is presented where possible.