Civil Engineering Reference
In-Depth Information
S
-
½
xx
°
°
S
°
°
yy
-
S
½
°
°
xx
°
®
°
¾
°
S
°
zz
ˆ
ˆ
S
for
2
D
and
for
3
D
(13.16)
®
¾
yy
S
°
¯
°
¿
°
°
xy
S
°
°
°
°
xy
°
S
°
yz
°
°
°
°
S
¯
¿
xz
For 3-D problems we have
1
1
-
½
cos
T
(
br
b r
)
QG
cos
T \
cos
cos
I
°
°
ij
,
ji
,
j
1
°
°
1
Q
(13.17)
ˆ
S
®
¾
ij
8
S
1
r
°
°
ª
º
cos
\
(
nr
n r
)
(1
2 )(
Q
bn
b n
)
¬
¼
ij
,
ji
,
ij
ji
°
°
¯
2
¿
where cosT and cos\ have been defined previously,
i
G
is the Kronecker delta defined
in Chapter 4 and
cos
I
b
x
n
(13.18)
For plane strain problems we have
1
-
½
°
2cos (
T
br
b r
)
°
ij
,
ji
,
°
°
°
ª
2cos
T\ I
cos
cos
º
°
§
·
1
1
°
°
«
»
¨
¸
ˆ
S
QG
cos
\
(
n r
n r
)
(13.19)
®
1
¾
ij
«
ij
¨
¸
i
,
j
j
,
i
»
8
S
1
Q
(1
2 ln
) co s
I
¨
¸
°
°
«
»
©
r
¹
¬
¼
°
°
°
1
°
ª
º
cos
\
(
nr
n r
)
(1
2 )(
Q
bn
b n
)
°
°
¬
¼
ij
,
ji
,
ij
ji
2
¯
¿
Two subroutines
Grav_dis
and
Grav_stress
, which compute matrices
G
and
ˆ
needed for the gravity load case are added to the library
Elasticity.lib
. The subroutines
can be used to compute the element contributions for assembly of the right hand side.
Search WWH ::
Custom Search