subject to the boundary condition

regularity condition

and an asymptotic condition

where ,

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

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

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

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)

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.