Degenerate scale problem for some configurations with rigid line tips in antiplane elasticity or Laplace equation

2021 ◽  
pp. 103697
Author(s):  
Y.Z. Chen
Keyword(s):  
Laplace Equation ◽  
Scale Problem ◽  
Degenerate Scale ◽  
Antiplane Elasticity ◽  
Rigid Line

Closed form Solution for Degenerate Scale Problem of Joukowcki Airfoil Configuration in Antiplane Elasticity

2013 ◽  
Vol 29 (4) ◽  
pp. N21-N23 ◽  
Author(s):  
Y. Z. Chen
Keyword(s):  
Conformal Mapping ◽  
Closed Form ◽  
Closed Form Solution ◽  
Mapping Function ◽  
Form Solution ◽  
Scale Problem ◽  
Thin Airfoil ◽  
Degenerate Scale ◽  
Antiplane Elasticity

ABSTRACTThis paper provides a closed form solution for degenerate scale problem of the Joukowcki thin airfoil configuration in antiplane elasticity. The solution depends on a conformal mapping function for the Joukowcki thin airfoil configuration.

Solution for the degenerate scale for a rigid curve in antiplane elasticity by using a weakly singular integral equation

2021 ◽  
pp. 108128652110112
Author(s):  
YZ Chen
Keyword(s):  
Integral Equation ◽  
Singular Integral Equation ◽  
Numerical Solution ◽  
Logarithmic Potential ◽  
Boundary Integral ◽  
Scale Problem ◽  
Numerical Examples ◽  
Weakly Singular ◽  
Degenerate Scale ◽  
Antiplane Elasticity

This paper provides a numerical solution for the degenerate scale for a rigid curve in antiplane elasticity. The degenerate scale problem for the rigid curve is formulated on the usage of the logarithmic potential. After assuming the displacement to be a vanishing value along the rigid curve, the boundary integral equation (BIE) is formulated. The problem can be first formulated in the degenerate scale. After making a coordinate transform, we can obtain the relevant BIE in the ordinary scale. Finally, a numerical solution is achieved. Several numerical examples are provided. In addition, the degenerate scale problem for the multiple rigid curves is also solved.

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