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Related papers: Solution of the Kirchhoff-Plateau problem

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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…

Analysis of PDEs · Mathematics 2026-01-30 Vincenzo Bianca , Edoardo Bocchi , Filippo Gazzola

A circular von Karman plate is considered bonded at its boundary to a circular Kirchhoff rod via a hinge like junction. There is a mismatch of dimension between the rod and the plate boundary in their respective stress free configurations.…

Classical Physics · Physics 2025-01-22 Deepankar Das , Basant Lal Sharma

We rigorously derive a Blake-Zisserman-Kirchhoff theory for thin plates with material voids, starting from a three-dimensional model with elastic bulk and interfacial energy featuring a Willmore-type curvature penalization. The effective…

Analysis of PDEs · Mathematics 2025-04-09 Manuel Friedrich , Leonard Kreutz , Konstantinos Zemas

We propose a model based on a Ginzburg-Landau approach to study a strain relief mechanism at a free interface of a non-hydrostatically stressed solid, commonly observed in thin-film growth. The evolving instability, known as the Grinfeld…

Materials Science · Physics 2009-10-31 Judith Mueller , Martin Grant

We consider a conservative system consisting of an elastic plate interacting with a gas filling a semi-infinite tube. The plate is placed on the bottom of the tube. The dynamics of the gas velocity potential is governed by the linear wave…

Analysis of PDEs · Mathematics 2016-01-19 Igor Chueshov

We consider a fluid-structure interaction model for an incompressible fluid where the elastic response of the free boundary is given by a damped Kirchhoff plate model. Utilizing the Newton polygon approach, we first prove maximal regularity…

Analysis of PDEs · Mathematics 2022-02-23 Robert Denk , Jürgen Saal

In this paper we consider the inverse problem of determining a rigid inclusion inside a thin plate by applying a couple field at the boundary and by measuring the induced transversal displacement and its normal derivative at the boundary of…

Analysis of PDEs · Mathematics 2018-06-25 Antonino Morassi , Edi Rosset , Sergio Vessella

In this paper, we present an analytical study, in the one space dimensional case, of the fluid dynamics system proposed in [4] to model the formation of biofilms. After showing the hyperbolicity of the system, we show that, in a open…

Analysis of PDEs · Mathematics 2015-06-05 Roberta Bianchini , Roberto Natalini

Solving the Plateau problem means to find the surface with minimal area among all surfaces with a given boundary. Part of the problem actually consists of giving a suitable definition to the notions of 'surface', 'area' and 'boundary'. In…

Classical Analysis and ODEs · Mathematics 2018-07-17 Edoardo Cavallotto

The problem of determining equilibrium configurations of the free surface of a conducting liquid is considered with allowance for a finite interelectrode distance. The analogy is established between this electrostatic problem and that of…

Fluid Dynamics · Physics 2009-11-10 N. M. Zubarev , O. V. Zubareva

Soap films at equilibrium are modeled, rather than as surfaces, as regions of small total volume through the introduction of a capillarity problem with a homotopic spanning condition. This point of view introduces a length scale in the…

Analysis of PDEs · Mathematics 2022-03-28 Darren King , Francesco Maggi , Salvatore Stuvard

We report an experimental study on the dynamics of a thin film of polymer solution coating a vertical fiber. The liquid film has first a constant thickness and then undergoes the Rayleigh-Plateau instability which leads to the formation of…

Fluid Dynamics · Physics 2013-05-21 François Boulogne , Ludovic Pauchard , Frédérique Giorgiutti-Dauphiné

A pinned or free-floating rigid plate lying on the free surface of a thin film of viscous fluid, which itself lies on top of a horizontal substrate that is moving to the right at a constant speed is considered. The focus of the present work…

Classical Physics · Physics 2022-09-07 Philippe H. Trinh , Stephen K. Wilson , Howard A. Stone

We are interested in studying an unsteady fluid-structure interaction problem in a three-dimensional space. We consider a homogeneous Newtonian fluid which is modeled by the Navier-Stokes equations. Whereas the motion of the structure is…

Analysis of PDEs · Mathematics 2019-10-14 Fatima Abbas , Ayman Mourad

Slender bodies capable of spontaneous motion in the absence of external actuation in an otherwise quiescent fluid are common in biological, physical and technological contexts. The interplay between the spontaneous fluid flow, Brownian…

Soft Condensed Matter · Physics 2015-08-13 Abhrajit Laskar , R. Adhikari

A plate is rigid if its admissible displacement fields inducing vanishing two-dimensional strain tensors must vanish. We prove that the nonlinear model of Kirchhoff-Love for such a plate has a solution for any applied forces and boundary…

Analysis of PDEs · Mathematics 2025-11-19 Trung Hieu Giang , Cristinel Mardare

We present a new composite mesh finite element method for fluid--structure interaction problems. The method is based on surrounding the structure by a boundary-fitted fluid mesh which is embedded into a fixed background fluid mesh. The…

Numerical Analysis · Mathematics 2016-01-20 Andre Massing , Mats G. Larson , Anders Logg , Marie E. Rognes

Starting from a nonlinear 2D/1D fluid-structure interaction problem between a thin layer of a viscous fluid and a thin elastic structure, on the vanishing limit of the relative fluid thickness, we rigorously derive a sixth-order thin-film…

Analysis of PDEs · Mathematics 2022-07-27 Mario Bukal , Boris Muha

The shape assumed by a slender elastic structure is a function both of the geometry of the space in which it exists and the forces it experiences. We explore by experiments and theoretical analysis, the morphological phase-space of a…

Soft Condensed Matter · Physics 2023-12-11 S Ganga Prasath , Joel Marthelot , Rama Govindarajan , Narayanan Menon

We analyze a linear 3D/3D fluid-structure interaction problem between a thin layer of a viscous fluid and a thin elastic plate-like structure with the aim of deriving a simplified reduced model. Based on suitable energy dissipation…

Analysis of PDEs · Mathematics 2020-08-07 Mario Bukal , Boris Muha