where
{ }{
}
T
ηP = ηi , η j
(108)
$
$$
C PJ = - α ∫ ~ i N iP + ~ j N P N IP N Pds
a
a j
I
J
P
LP ~ ~
(
)
α ai + a j + 2~I
-
a
for I = J
12
(I, J = i, j)
(109)
=
LP ~ ~
-
α ( aI + aJ )
for I ≠ J
12
When node i is at open boundary, boundary condition (Equation 74) applies, and
the first term in Equation 91 becomes
η
2
$
I = ∫~pη + q
- gN Pds
P
(110)
a $
Γi
i
θ2
P
Similar to ICP (Equations 107 and 108), the first term of the ith and jth Equation in
(110) is
[ ]= [ ] η }
Γ {$
P
P
P
I
(111)
Γ
1
1
where
LP
p~ i + ~ j + 2~I for I = J
a a
a
12
ΓIJ = P
P
(I, J = i, j)
(112)
1
L
p~I + ~ J
for I ≠ J
a a
12
34
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