ISSN 1812-3368. ȼɟɫɬɧɢɤ ɆȽɌɍ ɢɦ. ɇ.ɗ. Ȼɚɭɦɚɧɚ. ɋɟɪ. «ȿɫɬɟɫɬɜɟɧɧɵɟ ɧɚɭɤɢ». 2012
12
3
,
,
ij
ij pq
p q
!
¦
V
V
( ) .
k
ij pq
ij pq
ij pq
V
dV
³
[
[
V
V
V
[
(9)
Ɍɨɝɞɚ ɤɨɦɩɨɧɟɧɬɵ ɬɟɧɡɨɪɚ ɷɮɮɟɤɬɢɜɧɵɯ ɦɨɞɭɥɟɣ ɭɩɪɭɝɨɫɬɢ
ɤɨɦɩɨɡɢɬɚ
,
ij pq
ijpq
pq
C
V
H
(10)
ɝɞɟ ɩɨ
p
ɢ
q
ɫɭɦɦɢɪɨɜɚɧɢɹ ɧɟɬ. ɉɨɫɥɟ ɪɚɫɱɟɬɚ ɬɟɧɡɨɪɚ ɦɨɞɭɥɟɣ ɭɩɪɭ-
ɝɨɫɬɢ
ijpq
C
ɧɚɯɨɞɢɥɢ ɷɮɮɟɤɬɢɜɧɵɣ ɬɟɧɡɨɪ ɭɩɪɭɝɢɯ ɩɨɞɚɬɥɢɜɨɫɬɟɣ
,
ijpq
3
ɹɜɥɹɸɳɢɣɫɹ ɨɛɪɚɬɧɵɦ ɤ
.
ijpq
C
Ȼɵɥɢ ɩɨɥɭɱɟɧɵ ɞɟɜɹɬɶ ɬɟɯɧɢɱɟ-
ɫɤɢɯ ɭɩɪɭɝɢɯ ɤɨɧɫɬɚɧɬ ɤɨɦɩɨɡɢɬɚ:
1
E
3
D
DDDD
—
ɷɮɮɟɤɬɢɜɧɵɟ ɦɨ-
ɞɭɥɢ ɭɩɪɭɝɨɫɬɢ;
v
E
3
DDEE
DE
D
—
ɷɮɮɟɤɬɢɜɧɵɟ ɤɨɷɮɮɢɰɢɟɧɬɵ ɉɭɚɫ-
ɫɨɧɚ;
G C
DE
DEDE
—
ɷɮɮɟɤɬɢɜɧɵɟ ɦɨɞɭɥɢ ɫɞɜɢɝɚ.
Ʉɨɦɩɨɧɟɧɬɵ ɬɟɧɡɨɪɨɜ ɤɨɧɰɟɧɬɪɚɰɢɣ ɧɚɩɪɹɠɟɧɢɣ
ɜ ɦɚɬɪɢɰɟ
ɢ ɜ ɧɢɬɹɯ.
Ʉɨɦɩɨɧɟɧɬɵ ɬɟɧɡɨɪɨɜ ɤɨɧɰɟɧɬɪɚɰɢɣ ɧɚɩɪɹɠɟɧɢɣ
ijkl
B
D
ɫɜɹɡɵɜɚɸɬ ɦɢɤɪɨɧɚɩɪɹɠɟɧɢɹ ɜ ɦɚɬɪɢɰɟ ɢ ɜ ɧɢɬɹɯ ɫɨ ɫɪɟɞɧɢɦɢ
ɧɚɩɪɹɠɟɧɢɹɦɢ
3
( )
,
( )
( )
ij
k
k
ij pq
p q
D
V
[
V
[
¦
ɜ ɤɨɦɩɨɡɢɬɟ:
( )
( )
( )
( ) ,
,
1, ..., 3.
ij
k
ijkl
k kl
k
B
V

D
D
[
D
V
[
[
V
[
D
(11)
Ʉɨɦɩɨɧɟɧɬɵ
ijkl
B
D
ɜ ɦɚɬɪɢɰɟ ɢ ɜ ɧɢɬɹɯ ɜɵɱɢɫɥɹɸɬ ɩɨ ɮɨɪɦɭɥɚɦ
[4—10]
( )
( )
( )
( )
,
,
1, ..., 3.
ijpq k
ij kl
k klpq k
B
ɉ
V

D
[
D
[
V
[
[
D
(12)
Ʉɨɷɮɮɢɰɢɟɧɬɵ ɤɨɧɰɟɧɬɪɚɰɢɢ ɧɚɩɪɹɠɟɧɢɣ ɜ ɬɨɣ ɱɚɫɬɢ ɦɚɬɪɢɰɵ,
ɤɨɬɨɪɚɹ ɧɚɯɨɞɢɬɫɹ ɜ ɫɨɫɬɚɜɟ ɧɢɬɢ, ɪɚɫɫɱɢɬɵɜɚɸɬ ɫɥɟɞɭɸɳɢɦ ɨɛɪɚ-
ɡɨɦ [12]:
1
;
m
m
t
E B
E
2
;
m
m
l
E B
E
3
;
m
m
l
G B
G
4
tg .
m
f
B
M
(13)
ɇɚɩɪɹɠɟɧɢɹ
( )
( )
ij
k
c
D
V
[
ɜ ɧɢɬɹɯ ɜ ɫɨɛɫɬɜɟɧɧɨɣ ɫɢɫɬɟɦɟ ɤɨɨɪɞɢɧɚɬ
ɜɵɱɢɫɥɹɸɬɫɹ ɫ ɩɨɦɨɳɶɸ ɦɚɬɪɢɰ ɩɨɜɨɪɨɬɚ:
( )
( )
( )
( )
( )
( )
( )
( ).
l
n
ij
k
ln k
i
k
j
k
Q Q
c
c
D
D
D
D
V
[
V
[
[
[
(14)