# Fluid-Structure Interaction - Elastic Beam

## Model Data

**Type:**
multiphysics
structural mechanics
fluid dynamics

**Physics Modes:**
fluid structure interaction

**Keywords:**
nonlinear elasticity
fluid structure

Fluid-structure interaction benchmark problem for stationary, laminar, and incompressible flow around a cylinder with an attached elastic beam. Although it is not possible to derive an analytical solution to these test cases, numerical solutions to benchmark reference quantities have been established for the beam deformation, drag, and lift forces [1].

The test configurations consider a solid cylinder centered at (0.2, 0.2) with
diameter *d = 0.1* in a *l = 2.2* by *h = 0.41* rectangular channel. The fluid
is assumed to have a constant density and viscosity, and a fully developed
parabolic velocity profile is prescribed at the inlet. A beam of length *0.4*
and width *0.02* is fixed to the end of the cylinder. First a static solution
with a Reynolds number *Re = 20* is considered, and then an instationary
solution with *Re = 100*.

This model is available as an automated tutorial by selecting **Model Examples and Tutorials…** >
**Multiphysics** > **Fluid-Structure Interaction - Elastic Beam**
from the **File** menu, and also as the MATLAB simulation m-script example ex_fluidstructure1.
Step-by-step tutorial instructions to set up and run this model are linked below.

## Reference

[1] Hron J. *A monolithic FEM/multigrid solver for ALE
formulation of fluid structure interaction with application in
biomechanics*. In H.-J. Bungartz and M. Schaefer, editors,
Fluid-Structure Interaction: Modelling, Simulation, Optimisation,
LLNCSE. Springer, 2006.