Existence of a weak solution to a steady 2D fluid-1D elastic structure interaction problem with Tresca slip boundary condition

2021 ◽  
Author(s):  
Hela Ayed ◽  
Leonardo Baffico ◽  
Taoufik Sassi
Keyword(s):  
Boundary Condition ◽  
Weak Solution ◽  
Slip Boundary Condition ◽  
Elastic Structure ◽  
Structure Interaction ◽  
Slip Boundary ◽  
Interaction Problem

Regularity of a weak solution to a linear fluid-composite structure interaction problem

2021 ◽  
Vol 56 (2) ◽  
pp. 407-440
Author(s):  
Marija Galić ◽  
Keyword(s):  
Weak Solution ◽  
Composite Structure ◽  
Contact Forces ◽  
Elastic Structure ◽  
Compatibility Conditions ◽  
Fluid Structure ◽  
Structure Interaction ◽  
Additional Regularity ◽  
Interaction Problem ◽  
Standard Techniques

In this manuscript, we deal with the regularity of a weak solution to the fluid-composite structure interaction problem introduced in [12]. The problem describes a linear fluid-structure interaction between an incompressible, viscous fluid flow, and an elastic structure composed of a cylindrical shell supported by a mesh-like elastic structure. The fluid and the mesh-supported structure are coupled via the kinematic and dynamic boundary coupling conditions describing continuity of velocity and balance of contact forces at the fluid-structure interface. In [12], it is shown that there exists a weak solution to the described problem. By using the standard techniques from the analysis of partial differential equations we prove that such a weak solution possesses an additional regularity in both time and space variables for initial and boundary data satisfying the appropriate regularity and compatibility conditions imposed on the interface.

NEW MODELS IN MICROPOLAR FLUID AND THEIR APPLICATION TO LUBRICATION

2005 ◽  
Vol 15 (03) ◽  
pp. 343-374 ◽  
Author(s):  
GUY BAYADA ◽  
NADIA BENHABOUCHA ◽  
MICHÈLE CHAMBAT
Keyword(s):  
Boundary Condition ◽  
Friction Coefficient ◽  
Boundary Conditions ◽  
Existence And Uniqueness ◽  
Micropolar Fluid ◽  
Reynolds Equation ◽  
Slip Boundary Condition ◽  
Slip Boundary ◽  
New Models ◽  
Uniqueness Of The Solution

A thin micropolar fluid with new boundary conditions at the fluid-solid interface, linking the velocity and the microrotation by introducing a so-called "boundary viscosity" is presented. The existence and uniqueness of the solution is proved and, by way of asymptotic analysis, a generalized micropolar Reynolds equation is derived. Numerical results show the influence of the new boundary conditions for the load and the friction coefficient. Comparisons are made with other works retaining a no slip boundary condition.

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