Boundary Element Methods–Numerical Implementation - The Boundary Element Method with Programming - page 133

The integral over S R is known as the azimuthal integral 4 . Substituting cos

T and 1

for two-dimensional elasticity problems, typical integrals are given by (see
Figure. 6.3)

r cos I

, x

2 S

C

³ ³

(6.20)

2 2

TPQ S , C 2 cos I 1 d I 1

xx 3

R

S 0

R

and

2 S

C

³

³

2

> @

(6.21) T P , dS 2 c os I sin I 1 C sin I cos I cos I sin I Rd I 0

xy 3

R

S 0

R

The azimuthal integral of matrix T can therefore be written as

³ R

T P , Q dS I

(6.22)

S

where I is a 2x2 unit matrix.

z

Rd I

Rd \

R

y

\

I

x

Figure 6.4 Rigid body mode for three-dimensional infinite domain problem