A new boundary element for plane elastic problems involving cracks and holes

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.