Issue 52
O. Kryvyi et alii, Frattura ed Integrità Strutturale, 52 (2020) 33-50; DOI: 10.3221/IGF-ESIS.52.04
1, 00 2, 00 1, 00 2, 00 3, 00 3 00 ,
1, 01 2, 01 1, 01 2, 01 3, 01 3, 01
1, 10 2, 10 1, 10 2, 10 3, 10 3, 10
1, 11 2, 11 1, 11 2, 11 3, 11 3, 11
1, 20 2, 20 1, 20 2, 20 3, 20 3, 20
1, 21 2, 21 1, 21 2, 21 3, 21 3, 21
jk s
* jk s
1 S S * ,
S S S S
,
,
1 j
k
k
k
2
i
j
( )
j
j
i
i
i
j
j
j
2
1, 44 3 ( k c
, 2, 3 k
1,
2, jk
3, jk
k
i
),
,
,
jk
j
j
j
j
j
j
1, 1,
2, jk
3, jk
3, jk ) j 3
, 2, jk
2, jk
1,
, 3, jk
33 c
3
c
i
j
(
,
c
i
44 [
(
)]
jk
jk
j
13
jk
2
4
6
2
* s s q , 3, , p kn np k
* s s q , kn np
* s s q , kn np
s s
p
p
p
,
,
,
*
q
k
k
k
kn np
1,
2,
3,
n
n
n
n
1
3
5
1
3 ( ) V z
5 ( ) V z
3 ( ) V z
5 ( ) V z
The formulas for the definition
and
we obtain respectively from the formulas for
and
, by
permutations . Using expressions (A.9), we compose the transformants of the sums of limiting values: 0 z thermoelastic characteristics of the space, and proceed to the originals. As a result, we obtain singular integral relations in 3 ( ), connecting jumps and the sum of the components of the stress tensor, displacement vectors, temperature and heat flux in the plane: 2 3 , 4 5 , 1 2
5
1
1
1
1
1
15 7 q
1
11 1 q 13
j
3 1 ]
} , dtd
x y q
{ [ q
q
q
( , )
j
3
12 2 2
14 6
16 8
3
r
r
r
2
r
j
4
0
0
0
0
x t
x t
y
1
1
22 2 24 2 6 q
q
2
q
x y q
q
q
( , )
{
[
]
21 1 2
2 22 1
11 2
22 3 2
2
2
2
r
2
r
r
r
0
0
0
0
y
1
1
1
1
2 23 4 12 q
2
2
12 1 25 7 2 ] q q
} , dtd
q
q
[
5 23 2
26 8
2
r
r
r
r
r
0
0
0
0
0
x t
y
y
1
22 3 24 1 6 q
3
q
x y q
q
q
( , )
{
[
]
22 2 1
3 22 2
11 1
2
2
2
2
r
r
r
0
0
0
x t
1
1
1
1
1
2
2
2
} , dtd
q
q
q
q
q
q
[
]
4 23 1
12 2
21 1 1
23 5 12
25 7 1
26 8 2
r
r
r
r
r
r
0
0
0
0
0
0
x t
x t
y
y
1
1
q
4
q
34 6 1 q
( , ) x y
q
q
{
[
]
31 1
32 2 2
3 32 1
21 2
2
2
r
r
r
r
r
0
0
0
0
0
x t
x t
x t
x t
y
q
33 4
4 33 2 [ q
q
dtd q
q
q
]
}
,
22 1
33 5 2
35 7
36 8
2
2
2
2
r
r
r
r
r
0
0
0
0
0
48
Made with FlippingBook Publishing Software