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Mathematics > Analysis of PDEs

arXiv:2206.08047 (math)
[Submitted on 16 Jun 2022]

Title:Unrestricted deformations of thin elastic structures interacting with fluids

Authors:Malte Kampschulte, Sebastian Schwarzacher, Gianmarco Sperone
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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.
Comments: 43 pages
Subjects: Analysis of PDEs (math.AP)
MSC classes: 74F10 (Primary), 76D05, 35Q30, 35Q35, 35Q74, 35R35, 76D03 (Secondary)
Cite as: arXiv:2206.08047 [math.AP]
  (or arXiv:2206.08047v1 [math.AP] for this version)
  https://doi.org/10.48550/arXiv.2206.08047

Submission history

From: Malte Kampschulte [view email]
[v1] Thu, 16 Jun 2022 10:03:59 UTC (52 KB)
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