Civil Engineering Reference
In-Depth Information
where
1
ª
(
n
) s(
TG QG G
C
r
(
r
r
)
C r r r
)
º
3,
ij
k
ik
,
j
jk
,
i
6 ,
i
j
k
«
»
C
(9.47)
5
R
(
n
)
Q
(
n r r
n r r
)
«
»
kij
i
,
j
,
k
j
,
i
,
k
n
1
r
«
»
Cn nrr n
((
1)
G
n
G
)
Cn
G
«
»
¬
¼
3
k
,
i
,
j
j
ik
i
jk
7
k
ij
x, y, z
may be substituted for
i, j, k
and
cos
T
has been defined previously. Values of the
constants are given in Table 9.1.
Table 9.1
Constants for fundamental solutions
S
and
R
Plane strain
Plane stress
3-D
n
1
1
2
C
2
1/4
SQ
(1+
QS
1/8
SQ
C
3
1-2
Q
(1-
QQ
1-2
Q
C
5
G/(2
S
(1-
Q
Q
G/2
S
G/(4
S
(1-
Q
C
6
4
4
15
C
7
1-4
Q
(1-3
Q
1+
Q
1-4
Q
For plane stress assumptions the stresses perpendicular to the plane are computed
by
V
, whereas for plane strain
.
Subroutines for calculating Kernels
S
and
R
are added to the Elasticity_lib.
0
VQVV
(
)
z
x
y
SUBROUTINE
SK(TS,DXR,R,C2,C3)
!------------------------------------------------------------
! KELVIN SOLUTION FOR STRESS
! TO BE MULTIPLIED WITH t
!------------------------------------------------------------
REAL, INTENT(OUT) ::
TS(:,:) !
Fundamental solution
REAL, INTENT(IN) ::
DXR(:) !
r
x
,
r
y
,
r
z
REAL, INTENT(IN) ::
R !
r
REAL, INTENT(IN) ::
C2,C3 !
Elastic constants
REAL ::
Cdim !
Cartesian dimension
INTEGER ::
NSTRES !
No. of stress components
INTEGER ::
JJ(6), KK(6) !
sequence of stresses in pseudo-vector
REAL ::
A,C2,C3
INTEGER ::
I,N,J,K
Cdim=
UBOUND
(DXR,1)
IF
(CDIM == 2)
THEN
NSTRES= 3
JJ(1:3)= (/1,2,1/)
KK(1:3)= (/1,2,2/)
ELSE
NSTRES= 6
JJ= (/1,2,3,1,2,3/)
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