scholarly journals Weakly-singular traction and displacement boundary integral equations and their meshless local petrov-galerkin approaches

2005 ◽  
Vol 10 (1) ◽  
pp. 1-7 ◽  
Author(s):  
Zhidong Han ◽  
Zhenhan Yao ◽  
S. N. Atluri
Keyword(s):  
Integral Equations ◽  
Boundary Integral Equations ◽  
Boundary Integral ◽  
Displacement Boundary ◽  
Weakly Singular

scholarly journals Regularization of the Divergent Integrals. II. Application in Fracture Mechanics.

2007 ◽  
Vol 4 (2) ◽  
Author(s):  
Vladimir Zozulya
Keyword(s):  
Fracture Mechanics ◽  
Integral Equations ◽  
Convex Polygon ◽  
Boundary Integral Equations ◽  
Boundary Integral ◽  
Hypersingular Integrals ◽  
Divergent Integral ◽  
Contour Integrals ◽  
Weakly Singular ◽  
Arbitrary Convex

In this article the methodology for divergent integral regularization developed in [8] is applied for regularization of the weakly singular and hypersingular integrals, which arise when the boundary integral equations (BIE) methods are used to solve problems in fracture mechanics. The approach is based on the theory of distribution and the application of the Green theorem. The weakly singular and hypersingular integrals over arbitrary convex polygon have been transformed to the regular contour integrals that can be easily calculated analytically or numerically.

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