Civil Engineering Reference
In-Depth Information
have to consider that only
U
xx
and
U
yy
have a logarithmic and non-logarithmic part. The
logarithmic part is integrated with
Gauss-Laguerre,
for example:
1
(1
Q
) (3
4
Q
)
§·
1
d
[
e
xx ni
³
'
U
N
[
ln
P
,
[[ [
J
d
¨¸
n
i
4
S
E
1
Q
[
d
[
©¹
0
(6.44)
M
(1
Q
)(3
4
Q
)
d
[
¦
|
N
[
J
[
W
nm
m m
4
S
E
1
Q
d
[
m
1
The non-logarithmic part is integrated using Gauss Quadrature.
Zero coefficient arrays ['
U
] and ['
T
]
Colloc_Points: DO i=1,Number of points Pi
Determine distance of Pi to Element, R/L and No. of Gauss points
Gauss_Points: DO m=1,Number of Gauss points
Determine r,dsxr,Jacobian etc. for kernel computation
Node_Points: DO n=1,Number of Element Nodes
Direction_P: DO j=1,2 (direction of force at P)
Direction_Q: DO k=1,2 (direction of U,T at Q)
Sum coefficients ['
U
] and ['
T
]
Figure 6.12
Structure chart for SUBROUTINE Integ2E
A SUBROUTINE for integrating over one-dimensional elements for elasticity is
written. The main differences to the previous subroutine are that the Kernels
U
and
T
are
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