A NEW BOUNDARY-ELEMENT FOR PLANE ELASTIC PROBLEMS INVOLVING CRACKS AND HOLES

By applying the new boundary integral formulation proposed recently by Chau and Wang (1997) for two-dimensional elastic bodies containing cr acks and holes, a new boundary element method for calculating the inte raction between cracks and holes is presented in this paper. Singular interpolation functions of order r(-1/2) (where r is the distance meas ured 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 in troduced such that the displacement compatibility condition can be sat isfied exactly by the complex boundary function H(t), which is a combi nation 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 unknow n of H(t) exactly, and no extrapolation of numerical data is required. To demonstrate the accuracy of the present boundary element method, v arious crack problems are considered: (i) the Griffith crack problem, (ii) the interaction problem between a circular hole and a straight cr ack subject to both far field tension and compression, and (iii) the i nteraction problem between a circular hole and a kinked crack subject to far field uniaxial tension. Excellent agreement with existing resul ts is observed for the first two problems and also for the last proble m if the crack-hole interaction is negligible.