End effects for plane Stokes flow along a semi-infinite strip

1997 ◽  
Vol 48 (6) ◽  
pp. 905 ◽  
Author(s):  
R. J. Knops ◽  
C. Lupoli
Keyword(s):  
Stokes Flow ◽  
Infinite Strip ◽  
End Effects

ON THE SPATIAL DECAY OF ILL-POSED PARABOLIC PROBLEMS

1993 ◽  
Vol 03 (04) ◽  
pp. 563-575 ◽  
Author(s):  
CHANGHAO LIN ◽  
L.E. PAYNE
Keyword(s):  
Stokes Flow ◽  
Parabolic Problems ◽  
Infinite Cylinder ◽  
Infinite Strip ◽  
Spatial Decay ◽  
Flow Equations ◽  
Decay Of Solutions ◽  
Ill Posed

This paper investigates the spatial decay of solutions to two ill-posed parabolic initialboundary value problems: 1) the backward heat equatoin defined on a semi-infinite cylinder in ℝN and 2) the backward Stokes flow equations defined on a semi-infinite strip in ℝ2.

Saint-Venant End Effects for Incremental Plane Deformations of Incompressible Nonlinearly Elastic Materials

1985 ◽  
Vol 52 (4) ◽  
pp. 847-852 ◽  
Author(s):  
R. Abeyaratne ◽  
C. O. Horgan ◽  
D.-T. Chung
Keyword(s):  
Plane Deformation ◽  
Tensile Load ◽  
Infinite Strip ◽  
End Effects ◽  
Short Side ◽  
Incompressible Materials ◽  
Constitutive Parameters ◽  
Small Deformations ◽  
Nonlinearly Elastic ◽  
Plane Deformations

This paper is concerned with assessing the extent of Saint-Venant end effects within the theory of small deformations superposed on a large deformation for plane strain of homogeneous, isotropic, incompressible materials. The problem considered is that of plane deformation of a body which in its undeformed configuration, occupies a semi-infinite strip. The long sides of the strip are free of traction while the short side is subjected to prescribed normal and shear tractions. A purely normal tensile traction is applied uniformly at the remote end. For the case of slightly nonuniform end tractions at the near end, it is shown that the resulting stress distribution differs from that of homogeneous uniaxial tension by an exponentially decaying function of the distance from the end of the strip. The decay rate is characterized explicitly in terms of the strip width, the remotely applied tensile load, and constitutive parameters. Numerical results are provided for the Mooney-Rivlin material and power-law materials which either harden or soften in tension.

End Effects of Symplectic Solution to Stokes Flow in a Rectangular Cavity

2012 ◽  
Vol 166-169 ◽  
pp. 3258-3264
Author(s):  
Shi Hua He ◽  
Li Xiang Zhang ◽  
Liang Cao
Keyword(s):  
Stokes Flow ◽  
Interaction Mechanism ◽  
Longitudinal Direction ◽  
Rectangular Cavity ◽  
Symmetric Problem ◽  
Direct Solution ◽  
End Effects ◽  
Hamilton System ◽  
Resultant Velocity ◽  
Expansion Coefficients

The end effects of symplectic direct solution to Stokes flow in a rectangular cavity are considered. Based on establishing the dual equations for Stokes flow in Hamilton system, the non-zero eigenvalues and their eigensolutions for an anti-symmetric problem were obtained. Expanding the solutions of dual equations by non-zero eigensolutions and determining the expansion coefficients by the end boundary conditions, the decay tendency and interaction mechanism of end effects were discussed and the end boundary errors were investigated. The resultant velocity caused by tangentially driving lid is gradually decayed along the longitudinal direction of cavity. The more number of the expansion items are superposed, the more accurate the solutions are. The smaller the depth-to-width ratios are, the stronger the interference between the end velocities is. The error of ends moving in the same directions is bigger than that in opposite directions.

Chaotic Advection by Two-Dimensional Stokes Flow in a Semicircle

2004 ◽  
Vol 31 (4) ◽  
pp. 344-357
Author(s):  
T. A. Dunaeva ◽  
A. A. Gourjii ◽  
V. V. Meleshko
Keyword(s):  
Stokes Flow ◽  
Chaotic Advection ◽  
Two Dimensional
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