A New Boundary Element for Plane Elastic Problems Involving Cracks and Holes |
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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: | By applying the new boundary integral formulation proposed recently by Chau and Wang (1997) for two-dimensional elastic bodies
containing cracks and holes, a new boundary element method for calculating the interaction between cracks and holes is presented
in this paper. Singular interpolation functions of order r-1/2 (where r is the distance measured from the crack tip) are introduced for the discretization of the crack near the crack tips,
such that stress singularity can be modeled appropriately. A nice feature for our implementation is that singular integrands
involved at the element level are integrated analytically. For each of the hole boundaries, an additional unknown constant
is introduced such that the displacement compatibility condition can be satisfied exactly by the complex boundary function
H(t), which is a combination of the traction and displacement density. Another nice feature of the present formulation is
that the stress intensity factors (both K_I and K_II) at crack tips are expressed in terms of the nodal unknown of H(t) exactly, and no extrapolation of numerical data is required.
To demonstrate the accuracy of the present boundary element method, various crack problems are considered: (i) the Griffith
crack problem, (ii) the interaction problem between a circular hole and a straight crack subject to both far field tension
and compression, and (iii) the interaction problem between a circular hole and a kinked crack subject to far field uniaxial
tension. Excellent agreement with existing results is observed for the first two problems and also for the last problem if
the crack-hole interaction is negligible.
This revised version was published online in August 2006 with corrections to the Cover Date. |
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Keywords: | plane elastic problems cracks holes boundary elements singular integrals stress intensity factors |
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