Boundary Element Methods–Numerical Implementation - The Boundary Element Method with Programming - page 134

We see that since R cancels out, the integral is valid for any radius of the circle,
including a radius of infinity, so the method of computing the strongly singular terms by
rigid body translation is also valid for infinite domains.
For three-dimensional elasticity problems, the infinite domain is assumed to be a
sphere of radius R . Typical values of the azimuthal integral are (see Figure 6.4):

2 SS 2

C

³

³³

2 2

T P , Q dS C 3 cos I 1 Rd \ Rd I 1

(6.23)

xx 3

2

R

S 0 0

R

and

³

T P , Q dS

xy

S

R

(6.24)

2 SS 2

C

> @

³³

2

3 c os I sin I 1 C cos I sin I sin I cos I Rd \ Rd I 0

3

2

R

0 0

so equation (6.22) is equally valid for three-dimensional problems, except that I is a 3x3
unit matrix.

z

y

I

\

R

x

Rd \

Rd I

Figure 6.5 Rigid body mode for semi-infinite domain problem