Unrestricted deformations of thin elastic structures interacting with fluids

TL;DR

This paper studies the complex interaction between a freely moving elastic beam and surrounding fluids, allowing large deformations and analyzing the existence of solutions in dynamic fluid-structure interaction scenarios.

Contribution

It introduces a model for elastic beams with non-quadratic potential interacting with fluids, allowing unrestricted deformations and establishing weak-solution existence.

Findings

Existence of weak solutions up to potential collision

Model accommodates large deformations of elastic beams

Handles fluid-structure interaction with moving fluid domains

Abstract

In this paper we discuss the motion of a beam in interaction with fluids. We allow the beam to move freely in all coordinate directions. We consider the case of a beam situated in between two different fluids as well as the case where the beam is attached only to one fluid. In both cases the fluid-domain is time changing. The fluid is governed by the incompressible Navier-Stokes equations. The beam is elastic and governed by a hyperbolic partial differential equation. In order to allow for large deformations the elastic potential of the beam is non-quadratic and naturally possesses a non-convex state space. We derive the existence of weak-solutions up to the point of a potential collision.