scholarly journals Solutions of the interior and exterior boundary value problems in plane elasticity by using dislocation distribution layer

2010 ◽  
Vol 47 (3-4) ◽  
pp. 355-364 ◽  
Author(s):  
Y.Z. Chen ◽  
X.Y. Lin
Keyword(s):  
Boundary Value Problems ◽  
Boundary Value ◽  
Plane Elasticity ◽  
Dislocation Distribution ◽  
Exterior Boundary

A transform method for the biharmonic equation in multiply connected circular domains

2018 ◽  
Vol 83 (6) ◽  
pp. 942-976 ◽  
Author(s):  
Elena Luca ◽  
Darren G Crowdy
Keyword(s):  
Boundary Value Problems ◽  
Biharmonic Equation ◽  
Mixed Boundary ◽  
Boundary Value ◽  
Circular Domain ◽  
Plane Elasticity ◽  
Transform Method ◽  
Multiply Connected ◽  
Wide Range ◽  
Circular Domains

Abstract A new transform approach for solving mixed boundary value problems for the biharmonic equation in simply and multiply connected circular domains is presented. This work is a sequel to Crowdy (2015, IMA J. Appl. Math., 80, 1902–1931) where new transform techniques were developed for boundary value problems for Laplace’s equation in circular domains. A circular domain is defined to be a domain, which can be simply or multiply connected, having boundaries that are a union of circular arc segments. The method provides a flexible approach to finding quasi-analytical solutions to a wide range of problems in fluid dynamics and plane elasticity. Three example problems involving slow viscous flows are solved in detail to illustrate how to apply the method; these concern flow towards a semicircular ridge, a translating and rotating cylinder near a wall as well as in a channel geometry.

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