Next: FM-BIEM with hypersingluar integral Up: Crack problems for three-dimensional Previous: Crack problems for three-dimensional

## Integral equation

Our problem is to find a solution of the equation of elastostatics

subject to the boundary condition

 (3.42)

regularity condition

 := (3.43)

and an asymptotic condition

where , Cijkl, , and stand for the displacement, elasticity tensor, traction vector, a solution of the equation of elastostatics in the whole space and the crack opening displacement, respectively. The components of Cijkl are expressed with Lame's constants and Kronecker's delta as

The solution to this problem has an integral representation given by (See (3.7))

 = (3.44)

where is the fundamental solution of the equation of elastostatics expressed as

 (3.45)

Using (3.42) and (3.44), one obtains the following hypersingular integral equation given by (See (3.9))

 (3.46)

where  stands for the finite part of a divergent integral and indicates the traction associated with . The hypersingular integral equation (3.46) can be regularised as (See Appendix L.2)

 (3.47)

where  stands for the Cauchy principal value of a singular integral. We use (3.47) for a direct computation of (3.46). In the following sections we describe two types of FM-BIEM; one is FM-BIEM with the hypersingular integral equation and the other is FM-BIEM with the regularised integral equation.

Next: FM-BIEM with hypersingluar integral Up: Crack problems for three-dimensional Previous: Crack problems for three-dimensional
Ken-ichi Yoshida
2001-07-28