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Approximation Technics for an Unsteady Dynamic Koiter Shell

Saloua Mani Aouadi
2007 Journal of Applied Mathematics  
We propose a mixed formulation in dynamical elasticity of shells which allows a locking-free finite element approximation in particular cases of Koiter shells.  ...  They establish an optimal error estimation as long as h 2 ε −1 is bounded. In the present paper, we introduce a mixed formulation for a bending-dominated dynamic Koiter shell.  ...  Our formulation is valid for Koiter shells. It includes dynamic effects and is valid for shells whose midsurface can have charts with discontinuous second derivatives.  ... 
doi:10.1155/2007/24238 fatcat:bn24sd6b3jellb6tbbng4yycyy

Page 114 of Aerospace Engineering Vol. 10, Issue 11 [page]

1951 Aerospace Engineering  
Proce dure for applying Southwell’s relaxation methods to the unsteady heat transfer through a uniform plain slab or a spherical shell Availability and Irreversibility in Thermodynamics. Joseph H.  ...  Heat-transfer coefficients were obtained by an iterative method that uses the results of Martinelli as a first approximation Simulated Altitude Investigation of Stewart-Warner Model 906-B Combustion Heater  ... 

Existence of a weak solution to a nonlinear fluid-structure interaction problem modeling the flow of an incompressible, viscous fluid in a cylinder with deformable walls [article]

Boris Muha, Suncica Canic
2012 arXiv   pre-print
Two cases are considered: the linearly viscoelastic and the linearly elastic Koiter shell.  ...  shell model.  ...  We consider the dynamics of a clamped Koiter shell with the boundary conditions η(0) = ∂ z η(0) = η(L) = ∂ z η(L) = 0.  ... 
arXiv:1207.5125v1 fatcat:rwxqeherjjbfrlvddedjgmcvzy

Existence and regularity of weak solutions for a fluid interacting with a non-linear shell in 3D [article]

Boris Muha, Sebastian Schwarzacher
2021 arXiv   pre-print
We study the unsteady incompressible Navier-Stokes equations in three dimensions interacting with a non-linear flexible shell of Koiter type.  ...  The known existence theory for weak solutions is extended to non-linear Koiter shell models.  ...  This is a phenomenon purely due to the non-linearity of the Koiter shell equations.  ... 
arXiv:1906.01962v3 fatcat:cy5ubnzqcvflzltakxj2qaux5u

Analysis of a 3D nonlinear moving boundary problem describing fluid-mesh-shell interaction

Sunčica Čanić, Marija Galić, Boris Muha
2020 Transactions of the American Mathematical Society  
Two-way coupling based on kinematic and dynamic coupling conditions is assumed between the fluid and composite structure, and between the mesh of curved rods and Koiter shell.  ...  We consider a nonlinear, moving boundary, fluid-structure interaction problem between a time-dependent incompressible, viscous fluid flow, and an elastic structure composed of a cylindrical shell supported  ...  The dynamic coupling condition describes the balance of forces. The force exerted by the Koiter shell onto the mesh is balanced by the force exerted by the mesh onto the Koiter shell.  ... 
doi:10.1090/tran/8125 fatcat:tgs5i5ohn5hmza5qhcwf6oubsa

Existence of a solution to a fluid-multi-layered-structure interaction problem [article]

Boris Muha, Suncica Canic
2013 arXiv   pre-print
The fluid flow, which is driven by the time-dependent dynamic pressure data, is governed by the 2D Navier-Stokes equations for an incompressible, viscous fluid, defined on a 2D cylinder.  ...  We study a nonlinear, unsteady, moving boundary, fluid-structure (FSI) problem in which the structure is composed of two layers: a thin layer which is in contact with the fluid, and a thick layer which  ...  Enrique Zuazua for pointing out the references [32, 33, 49, 55] . Furthermore, the authors would like to thank the following research support: Muha  ... 
arXiv:1305.5310v1 fatcat:eoaggskoazcpjkwyyei3l56jfi

Weak-strong uniqueness for an elastic plate interacting with the Navier Stokes equation [article]

Sebastian Schwarzacher, Matthias Sroczinski
2020 arXiv   pre-print
We show weak-strong uniqueness and stability results for the motion of a two or three dimensional fluid governed by the Navier-Stokes equation interacting with a flexible, elastic plate of Koiter type.  ...  For that we introduce a methodology that overcomes the problem that the two (variable in time) domains of the fluid velocities and pressures are not the same.  ...  The fluid and the shell are coupled via a kinematic and a dynamic coupling condition on the moving interface.  ... 
arXiv:2003.04049v3 fatcat:7lzqlludcbgtvnf6hmwbvq3dca

Meshless techniques for anisotropic diffusion

Annamaria Mazzia, Giorgio Pini, Flavio Sartoretto
2014 Applied Mathematics and Computation  
Moreover, it would be good for the methods to be of high order accuracy.  ...  A good numerical method would be locally mass conservative, produce no or minimal over/under-shoots, produce minimal numerical diffusion, and require no CFL time-step limit for stability.  ...  We show how to solve the equations using a global implicit approach in an efficient way, and we present the derived computational results.  ... 
doi:10.1016/j.amc.2014.03.032 fatcat:c527226gyfgbffnq4p67qxd7wi

MATHICSE Technical Report : An adjoint-based method for the numerical approximation of shape optimization problems in presence of fluid-structure interaction

Andrea Manzoni, Luca Ponti
2019
As benchmark case, we consider an unsteady Stokes flow in an elastic channel with compliant walls, whose motion under the effect of the flow is described through a linear Koiter shell model.  ...  In this work, we propose both a theoretical framework and a numerical method to tackle shape optimization problems related with fluid dynamics applications in presence of fluid-structure interactions.  ...  Sandro Salsa (Politecnico di Milano) for his valuable insights, to Dr. Luca Dedè (EPFL) for his careful remarks and to Dr. Davide Forti (EPFL) for his useful suggestions.  ... 
doi:10.5075/epfl-mathicse-271083 fatcat:vl6j5c2qlbdfve4rthbn3o5yba

Existence of local strong solutions to fluid–beam and fluid–rod interaction systems

Céline Grandmont, Matthieu Hillairet, Julien Lequeurre
2018 Annales de l'Institut Henri Poincare. Analyse non linéar  
We study an unsteady nonlinear fluid-structure interaction problem.  ...  In the case of the wave equation or a beam equation with inertia of rotation, this is, to our knowledge the first result of existence of strong solutions for which no viscosity is added.  ...  We recall an elliptic regularity result for steady state Stokes-like equations obtained in [15] and other technical lemmas.  ... 
doi:10.1016/j.anihpc.2018.10.006 fatcat:ohnndna7obgknphrhbbdsar2wi

Decima giornata di studio Ettore Funaioli Decima giornata di studio Ettore Funaioli

A Cura Di, Umberto Meneghetti, Vincenzo Castelli, Umberto Meneghetti, Vincenzo Castelli, Alessandro Zanarini, Umberto Meneghetti, Vincenzo Castelli
2016 unpublished
Acknowledgements The authors want to acknowledge Dr Alberto Ferrari, for his help during experimental measurements.  ...  Wassermann and his staff, are kindly acknowledged for hosting the TEFFMA project of the author at the Schwingungs-und Strukturanalyse / Optical Vibration Measurement Laboratory.  ...  The shell dynamics is studied in the framework of the Sanders-Koiter shell theory and a multiple elastic shell model is considered.  ... 
fatcat:zyxtrkxx2bbm5agambnicdidwm

Fluid-Structure Interaction Problems in Hemodynamics:Parallel Solvers, Preconditioners, and Applications

Paolo Crosetto
2011
An estimate for the condition number of the preconditioned system is proposed, showing how preconditioners of this type depend on the coupling, and explaining the good performance they exhibit when increasing  ...  The fluid equations are derived in an arbitrary Lagrangian-Eulerian (ALE) frame of reference.  ...  Finally the existence of a strong solution for a 3D FSI problem is derived by Cheng et al. in [ACCS06] . The structure is modeled by a nonlinear Koiter shell model without the inertial term.  ... 
doi:10.5075/epfl-thesis-5109 fatcat:lw5jh7orgfdtbiscsgajvd4fr4