Equilibrium configurations of a 3D fluid-beam interaction problem

We study a fluid-structure interaction problem between a viscous incompressible fluid and an elastic beam with fixed endpoints in a static setting. The 3D fluid domain is bounded, nonsmooth and non simply connected, the fluid is modeled by the stationary Navier-Stokes equations subject to inflow/outflow conditions. The structure is modeled by a stationary 1D beam equation with a load density involving the force exerted by the fluid and, thereby, may vary its position. In a smallness regime, we prove the existence and uniqueness of the solution to the PDE-ODE coupled system.

💡 Research Summary

The paper addresses a static fluid–structure interaction (FSI) problem in which a viscous incompressible fluid occupies a three‑dimensional wind‑tunnel‑like domain and an elastic beam with fixed endpoints is placed inside the tunnel. The fluid domain Ωₕ is obtained by removing the beam Bₕ from a rectangular parallelepiped P = (−R,R)×(−1,1)²; the beam may move vertically by a displacement function h(y) defined on the interval y∈