Three‐dimensional crack analysis using singular boundary elements

Abstract

SUMMARYA multi-domain method of solving three-dimensional elastic crack problems in an infinite elastic body using the boundary element method is proposed. The 4 displacement and l/dL traction behaviours near a crack front are incorporated in special crack elements. The elimination of singularities arising from the l / f i term combined with Kelvin's kernel for displacement in the integrals is discussed in detail. Stress intensity factors of modes I, I1 and I11 are obtained directly from crack-front nodal values, without any extrapolation as in some other methods. No differentiation of conventional boundary integral equations (with Kelvin's tensor kernels) is necessary in the current approach. This method is applicable to cracks of arbitrary shape. Infinite bodies are modelled precisely as such, not approximated as large finite bodies. Numerical solutions of stress intensity factors are given for several problems involving a penny-shaped crack.

The Element Free Galerkin method for dynamic propagation of arbitrary 3-D cracks

“…We consider a ÿnite solid. As shown by Jia et al, 73 the di erence between the solution for the unbounded domain and for the ÿnite solid of dimension R is negligible for a=R ≈ 1=10, and small for a=R ≈ 1=5. We solve for the stress intensity factor in a cube of side length 20, with a penny-shaped crack inclined by !…”

“…We compare with the analytical solution, equation (22), and with the solution of Fedelinski et al 73 for a ÿnite cylinder with the ratio D=r ≈ 0·3 (r is the cylinder radius, 2r = w), which yields mode-I SIF approximately 2 per cent higher than equation (22). The comparison is shown in Figure 23 and is quite good.…”

“…Numerical solutions for this problem have been presented in Nikishkov and Atluri, 75 Jia et al, 73 Xu and Ortiz, 35 and Young. We consider a ÿnite solid.…”

Partitioning, boundary integral equations, and exact Green's functions

“…Having solved (23) for u l , we can calculate u(P) for P in D from (22). To do this, we need GE(q2; P ) , GE(ql; P ) and (a/an,)GE(q1; P).…”

Early Development of the BEM at the University of Kentucky

“…The final phase of our collaboration, begun before Frank left Kentucky, dealt with linear elastic fracture problems ( [33], [34], [35]). Knowing the limiting variation of displacement and traction with position in the region of a crack tip, we utilized special shape functions having the known variation (singular for traction).…”