A new boundary element method for mixed boundary value problems involving cracks and holes: Interactions between rigid inclusions and cracks |
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Authors: | YB Wang KT Chau |
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Affiliation: | (1) Department of Mechanics, Lanzhou University, Lanzhou, People's Republic of China;(2) Department of Civil and Structural Engineering, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong, China |
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Abstract: | This paper derives a new boundary integral equation (BIE) formulation for plane elastic bodies containing cracks and holes and subjected to mixed displacement/ traction boundary conditions, and proposes a new boundary element method (BEM) based upon this formulation. The basic unknown in the formulation is a complex boundary function H(t), which is a linear combination of the boundary traction and boundary displacement density. The present BIE formulation can be related directly to Muskhelishvili's formalism. Singular interpolation functions of order r
–1/2 (where r is the distance measured from the crack tip) are introduced such that singular integrand involved at the element level can be integrated analytically. By applying the BEM, the interaction between a rigid circular inclusion and a crack is investigated in details. Our results for the stress intensity factor are comparable with those given by Erdogan and Gupta (1975) and Gharpuray et al. (1990) for a crack emanating from a stiff inclusion, and with those by Erdogan et al. (1974) for a crack in the neighborhood of a stiff inclusion. |
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Keywords: | Boundary element method cracks holes mixed boundary value problems rigid inclusion |
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