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Вероятностная модель напряженно-деформированного состояния заряда прочно скрепленного по наружной поверхности с корпусом РДТТ..pdf

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)0 60)0.$ <0%'-0
0
1 P
1N r = P,
11 P
M 2 +1
(1)
N
=
P
,
2 M
2
'
M
1
1
2M 2 (1 ' µ ) +
1 P
2µP *
,1 —
-,
1N z = 2
M ' 1 .,
1+ M 2 (1 ' 2µ ) /31
0
2 (1 ' µ )
P
1N rP = 2
,
M ' 11+ M 2 (1 – 2µ )
1
1
2
2P *, (1 ' µ ) M ' 1 +1 P
1'
,
2N M = 2
2
,
M
1
1
+
M
1
2µ
'
'
(
)
1
.
/
1
2
*
1N P = 2µP 1 — 2M (1 ' µ ) + ,
2
1 z M 2 ' 1 ,,
1
+
M
1
2µ
'
(
)
.
/3
(
66
)
(2)
)0 60)0.$ <0%'-0
0
1
1N r 4 0,
1
E 5O5T
2M 2 ,
2N M 4
2
1
M
1
2
µ
6
'
7
(
)
1
1
E 5O5T
* M 2 6 1+ ,
1N z 4
2
/
1 6 M (1 ' 27µ ) .
3
(3)
0
EPOPT
* M 2 ' 1+ ,
1N r =
2
/
1
+
M
1
2µ
'
(
).
1
1
EPOPT
* M 2 +1+ ,
2N M =
2
/
1+ M (1 ' 2µ ) .
1
1
EPOPT
* M 2 +1+ .
1N z =
2
/
1+ M (1 ' 2µ ) .
3
(4)
:*=&.4<;' -$($%,/)/%&20))+$ <02/*/,&*(/, =&.;7/, 2+%0>$)/'
-.' 20%/09/B 6&,=&)$)( )0=%'>$)/B / @62/20.$)()+? )0=%'>$)/B &(
20%/09/B 2);(%$))$E& -02.$)/' 60,$%+ *E&%0)/'(QP ), 6&@88/9/$)(0
F;0**&)0 (Qµ) / ,&-;.' ;=%;E&*(/ (&=./20 (QE), E$&,$(%/7$*6/? =0%0,$(%&2 <0%'-0 (QM2). # 8&%,;.0? (5) / (6) =%$-*(02.$)+ <02/*/,&*(/
20%/09/B 6&,=&)$)( )0=%'>$)/B =%/ -$B*(2// 2);(%$))$E& -02.$)/'
60,$%+ *E&%0)/' )0 60)0.$ / 2)$5)$B =&2$%?)&*(/ <0%'-0, (7) / (8) –
=%/ -$B*(2// ($,=$%0(;%)&B )0E%;<6/ )0 60)0.$ / 2)$5)$B =&2$%?)&*(/ <0%'-0 *&&(2$(*(2$))&:
0
1 Q2 P = Q2P ,
1 Nr
2
1
2M 2 ! 2
1 2
2
(5)
2 QN P = Q P + # 4
$ QM 2 ,
% M —1&
1 M
1 2
1
* M 2 +1 2 Q2 + M 4 2µ ' 1 2 Q 2 + ,
2
(
) M2 µ
1 QN P = Q P +
2
,
2
.
/
z
1+ M (1 ' 2µ )
13
(
)
(
)
67
2
0
2
!
Rµ
4M 4 *
R + 2
2
2
1Q = Q + #
$ Qµ2 +
'
1
Q 2,
P
P
,
2
2
1 Nr
# (1 ' µ )2 $
2
'
1
M
.
/
'
1
M
%
&
1
2
1
2
*
+
*
+
2
11
2 ( µ ' 1)
M '1
M4
2
2
2
,
,1 '
Qµ +
R - Q2 2 ,
2 QNMP = Q P + ,R
2
2
2
2
,
( µ ' 1) 2 ' µ M +1 /1
M ' 1 . 2 ' µ M +1 /.,
1
1
* M 2 +1 2 Q2 + M 4 2µ ' 1 2 Q2 + ,
1 Q2 = Q2 +
(
) 2µ
P
2 ,
1 N Pz
2
/
1+ M (1 ' 2µ ) .
1
13
(6)
0
1
1 Q2 = 0,
1 Nr
2
2
1
*
+ 2 *
+ 2
2M 2 µ
1
1 2
2
2
2
- Qµ + ,
- Q 2,
2 QNM = Q E + Q5T + Q5O + ,
2
2
1
.,1+ M (1 ' 2µ ) /.,1+ M (1 ' 2µ ) /1
2
*
+ 2 *
1 2
2M 2 µ
2M 2 µ
2
2
2
,
+
Q
1 QN z = Q E + Q5T + Q5O + ,
µ
2
, M 2 +1 1+ M 2 (1 ' 2µ )
,.1+ M (1 ' 2µ ) -/
.
31
(7)
(
(
(
)
(
))
)
(
(
(
)
)
)
(
)(
2
)
+
- Q2 2 ,
/
2
2
0
2
2
*
+
*
+
M
'
2
µ
1
(
)
M
2
µ
2
2
2
2
2
1Q = Q + Q + Q + ,
- Q2 2 ,
- Qµ + ,
E
5T
5O
2
2
2
1 Nr
,. ( M ' 1) (1 + M (1 ' 2µ ) ) -/ M
,.1 + M (1 ' 2µ ) -/
1
2
2
1
+
*
+ 2 *
2M 2 µ
2M 2 µ
1 2
2
2
2
- Q2 2 , (8)
2 QNM = Q E + Q5T + Q5O + ,
- Qµ + ,
2
2
2
+
M
1
1
2µ
'
M
+
+
M
1
1
1
2µ
(
)
'
,. (
(
) ) -/ M
)(
1
.,
/2
1
2
+
*
+ 2 *
1 2
2M 2 µ
2M 2 µ
2
2
2
- Q2 2 ,
- Qµ + ,
1 QN z = S E + S 5T + S 5O + ,
2
2
2
M
+
M
1
1
2µ
'
M
(
)
+
1
1
+
M
1
2µ
'
,
(
)
,
(
)
(
)
.
/
13
.
/
E-$ R =
(1 ' µ ) ( M 2 ' 1)
.
1 + M 2 (1 ' 2µ )
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6&,=&)$)( )0=%'>$)/B. L0*7$( @62/20.$)()+? )0=%'>$)/B *&*(&/( /<
)$*6&.46/? 50E&2, =&@(&,; -.' 60>-&E& 50E0 )$&3?&-/,& 2+2$*(/ 20%/09//. H/>$ =%/2&-/, 6&@88/9/$)(+ 20%/09/' -.' 60>-&E& 50E0.
H0 =$%2&, 50E$ =&.;7/, 20%/09// &*)&2)+? )0=%'>$)/B:
68
0 DN' DN M
=
,
1
NM
1 N'
1
1 DN''
(9)
=
*.( N'' ' N z ) DN r + ( N'' ' N r ) DN z + 2T rz DT rz +/ ,
2
1 N'' N'' ( 2N'' ' N r ' N z )
1
1 DN'''
1 N''' = N''' 2N''' + N + N *.( N''' + N z ) DN r + ( N''' + N r ) DN z ' 2T rz DT rz +/ .
(
r
z)
3
#0%/09// E.02)+? )0=%'>$)/B (9) )$&3?&-/,& *&=&*(02/(4 * 20%/09/',/ &*)&2)+? )0=%'>$)/B, /*?&-' /< ;*.&2/' N1>N2>N3.
!0.$$ 2+2$-$, 20%/09// 50%&2&E& ($)<&%0 (10), =0%0,$(%0 U&-$H0-0/ (11), /)($)*/2)&*(/ )0=%'>$)/B (12) / 6&@88/9/$)(0 k (13):
DN 0
N DN1 N 2 DN 2 N 3 DN 3
= 1
+
+
,
N0
3N 0 N1 3N 0 N 2 3N 0 N 3
(10)
2 ( N3 ' N 2 )
Dµ N N1
DN1
=
+
µN
µ N ( N 3 ' N1 )( N 3 ' 2N 2 + N1 ) N1
N
2 DN 2 N 3 2 ( N 2 ' N1 ) DN 3
,
67 2
2
µ N N1 ' N 3 N 2 µ N ( N 3 ' N1 ) N 3
(11)
DN i
1 N ( 2N1 ' N 2 ' N 3 ) DN1 N 2 ( 2N 2 ' N 3 ' N1 ) DN 2
= 2# 1
+
+
Ni
Ni %
2
N1
2
N2
N ( 2N 3 ' N 2 ' N1 ) DN 3 !
6 3
$,
2
N3 &
(12)
(
)
3 µ N +1
Dµ N DN 0 DN i
Dk'
.
= 'µ N
+
'
2
k'
( µ N ' 3) µ N + 3 µ N N 0 N i
(
)
(13)
#0%/09// @62/20.$)()+? )0=%'>$)/B, /*=&.4<;' (10)–(13), 3;-;(
/,$(4 *.$-;1C/B 2/- (14):
V
@62
V
@62
DN
N
DN 0
1 Dk'
0
1N 0 8 0 N — k' +1 k' ,
1
0
=2
a k' 2 + ( 2k' + c* )( a*c* +b* ) Dk'
DN
0
1N 0 < 0
.
' *
N0
13
( k' + c* )( a*k' + a*c* +b* ) k'
(14)
"&@88/9/$)( 20%/09// -.' @62/20.$)()+? )0=%'>$)/B 3;-$(
/,$(4 2/- (15):
69
QN2 V
@62
0
1N 0 8 0,
1
=2
1
1N 0 < 0,
3
2
DN 0 !
1
Dk' !
#
$ +
2 #
$ ,
N
k'
1
k'
+
%
&
(
)
% 0 &
2
2
DN 0 ! * a*k' + ( 2k' + c* )( a*c* +b* ) + Dk' !
+
- #
#
$ ,
$ .
% N 0 & . ( k' + c* )( a* k' + a*c* +b* ) / % k' &
2
2
2
(15)
F& =&.;7$))+, <02/*/,&*(', )$&3?&-/,& =%&2$*(/ %0*7$( 6&@88/9/$)(&2 20%/09/B 6&,=&)$)( )0=%'>$)/B / @62/20.$)()+? )0=%'>$)/B. L0*7$( =%&2&-/.*' -.' 60)0.0 / -.' 6&)(06(0 <0%'-0 * 6&%=;*&,. F%/ =%&2$-$)// %0*7$(&2 /*=&.4<&20./*4 *.$-;1C/$ /*?&-)+$
-0))+$:
9 )&,/)0.4)+$ <)07$)/':
2);(%$))$$ -02.$)/$ 60,$%+ *E&%0)/' P"I=(5,5…6,5) WF0; ($,=$%0(;%0
&6%;>01C$B *%$-+: T = (–50, 20, 50) :C; 6&@88/9/$)( F;0**&)0 µ =
= 0,492; 0,494; 0,496; ,&-;.4 ;=%;E&*(/ E = (20…53) WF0; M2 = 9…14;
9 6&@88/9/$)(+ 20%/09/B:
2);(%$))$$ -02.$)/$ 60,$%+ *E&%0)/' QP6*=(1…3)%; 6&@88/9/$)(
F;0**&)0 Qµ = (0,01…0,03) %; ,&-;.4 ;=%;E&*(/ QE = (5…15) %;
QM2 = (0,04÷0,06) %.
H0 %/*. 1 =%/2$-$)+ %$<;.4(0(+ %0*7$(0 6&@88/9/$)(&2 20%/09/B @62/20.$)()+? )0=%'>$)/B &( 6&@88/9/$)(&2 20%/09/B 2);(%$))$E& -02.$)/' 60,$%+ *E&%0)/' )0 60)0.$ <0%'-0. :< E%08/60 2/-)&,
7(& 6&@88/9/$)( 20%/09// @62/20.$)()+? )0=%'>$)/B <02/*/( &( 6&@88/9/$)(0 20%/09// -02.$)/' 2 60,$%$ *E&%0)/' ./)$B)&. F%/ ;2$./7$)// 2);(%$))$E& -02.$)/' 60,$%+ *E&%0)/' )0 1…3 % @62/20.$)()+$ )0=%'>$)/' ;2$./7/201(*' 1…3 %. L0*7$(+ =%/ %0<./7)+?
)&,/)0.4)+? <)07$)/'? 8/</6&-?/,/7$*6/? =0%0,$(%&2 (&=./20 /
%0<,$%0? <0%'-0 =&60<0./, 7(& &)/ )$ &60<+201( <)07/($.4)&E& 2./')/' )0 &(6.&)$)/' @62/20.$)()+? )0=%'>$)/B =%/ /<,$)$)// -02.$)/' 2 60,$%$ *E&%0)/'. G06>$ )$ &60<+201( 2./')/' / )&,/)0.4)+$
<)07$)/' -02.$)/' 2 60,$%$ *E&%0)/'.
A02/*/,&*(4 6&@88/9/$)(0 20%/09// @62/20.$)()+? )0=%'>$)/B
&( %0<3%&*&2 6&@88/9/$)(0 F;0**&)0 =%/2$-$)0 )0 %/*. 2. F%/ ;2$./7$)// %0<3%&*0 6&@88/9/$)(0 F;0**&)0 )0 0,01…0,03 % %0<3%&*+ @62/20.$)()+? )0=%'>$)/B ;2$./7/201(*' )0 1…2 %. H0 6&@88/9/$)(
20%/09// @62/20.$)()+? )0=%'>$)/B (06>$ &60<+201( 2./')/$ )&,/)0.4)+$ <)07$)/' 6&@88/9/$)(0 F;0**&)0 / E$&,$(%/7$*6/$ =0%0,$(70
%+ <0%'-0. A02/*/,&*(/ 6&@88/9/$)(0 20%/09// @62/20.$)()+? )0=%'>$)/B &( %0<3%&*0 6&@88/9/$)(0 F;0**&)0 )0 60)0.$ / )0 2)$5)$B
=&2$%?)&*(/ <0%'-0 *&2=0-01(.
QN@62
QM 2
L/*. 1. A02/*/,&*(4 6&@88/9/$)(&2 20%/09// @62/20.$)()+?
)0=%'>$)/B )0 60)0.$ <0%'-0 &( 6&@88/9/$)(0 20%/09//
-02.$)/' 2 60,$%$ *E&%0)/'
QN@62
Qµ
L/*. 2. A02/*/,&*(4 6&@88/9/$)(&2 20%/09// @62/20.$)()+?
)0=%'>$)/B )0 60)0.$ <0%'-0 &( 6&@88/9/$)(0 20%/09//
6&@88/9/$)(0 F;0**&)0: 1 – M2 = 9; 2 – M2=11; 3 – M2=14
71
!0.$$ 3+./ =%&2$-$)+ /**.$-&20)/' <02/*/,&*(/ 6&@88/9/$)(0
20%/09// @62/20.$)()+? )0=%'>$)/B &( 6&@88/9/$)(0 20%/09// M2.
L$<;.4(0(+ %0*7$(0 =%/2$-$)+ )0 %/*. 3. :< E%08/60 2/-)&, 7(& 6&@88/9/$)( 20%/09// @62/20.$)()+? )0=%'>$)/B )$ <02/*/( &( 6&@88/9/$)(0 20%/09// %0<,$%&2 <0%'-0. A02/*/,&*(4 )03.1-0$(*' &( /<,$)$)/'
)&,/)0.4)&E& <)07$)/' M2, (. $. &( %0<,$%&2 <0%'-0. F%/ ;2$./7$)//
)&,/)0.4)&E& <)07$)/' M2 )0 35…40 % 20%/09// @62/20.$)()+? )0=%'>$)/B ;2$./7/201(*' )0 0,3…0,5 %. H0 20%/09// @62/20.$)()+?
)0=%'>$)/B &60<+20$( 2./')/$ )&,/)0.4)&$ <)07$)/$ 6&@88/9/$)(0
F;0**&)0: ;2$./7$)/$ 6&@88/9/$)(0 F;0**&)0 )0 0,7…0,9 % 2$-$( 6
;2$./7$)/1 20%/09/B @62/20.$)()+? )0=%'>$)/B )0 0,08…1 %.
H0 2)$5)$B =&2$%?)&*(/ <0%'-0 <02/*/,&*(4 6&@88/9/$)(0 20%/09/B
@62/20.$)()+? 20%/09/B ;2$./7/20$(*' )0 1,2…1,4 %.
QN@62
QM 2
L/*. 3. A02/*/,&*(4 6&@88/9/$)(0 20%/09// @62/20.$)()+?
)0=%'>$)/B )0 60)0.$ <0%'-0 &( 6&@88/9/$)(0 20%/09/B M2:
1 – M2=9; 2 – M2=11; 3 – M2=14
:< %/*. 4 2/-)&, 7(& =%/ -$B*(2// ($,=$%0(;%)&B )0E%;<6/ )0/3&.45$$ 2./')/$ )0 6&@88/9/$)( 20%/09// @62/20.$)()+? )0=%'>$)/B &60<+201( %0<3%&*+ ,&-;.' ;=%;E&*(/. I ;2$./7$)/$, 6&@88/9/$)(0 20%/09// ,&-;.' ;=%;E&*(/ -& 15 % 6&@88/9/$)( 20%/09// @62/20.$)()+? )0=%'>$)/B (06>$ ;2$./7/201(*' -& 15 %. X0%06($%
<02/*/,&*(/ ./)$B)+B. H&,/)0.4)+$ <)07$)/' ,&-;.' ;=%;E&*(/, 6&72
@88/9/$)(0 F;0**&)0, E$&,$(%/7$*6/? =0%0,$(%&2 <0%'-0 / ($,=$%0(;%+ &6%;>01C$B *%$-+ <)07/($.4)&E& 2./')/' )$ &60<+201(.
QN@62
QE
L/*. 4. A02/*/,&*(4 6&@88/9/$)(0 20%/09// @62/20.$)()+? )0=%'>$)/B
)0 60)0.$ <0%'-0 &( 6&@88/9/$)(0 20%/09// ,&-;.' ;=%;E&*(/ (&=./20
=%/ -$B*(2// ($,=$%0(;%)&B )0E%;<6/ –50 °I
L0*7$(+ /<,$)$)/' 6&@88/9/$)(0 20%/09// @62/20.$)()+? )0=%'>$)/B &( 20%/09/B 6&@88/9/$)(0 F;0**&)0 / E$&,$(%/7$*6/? =0%0,$(%&2 =&60<0./, 7(& <02/*/,&*(/ )$(. G06>$ =%/ /<,$)$)// 20%/09/B 6&@88/9/$)(0 F;0**&)0 / =0%0,$(%0 M 2 )&,/)0.4)+$ <)07$)/'
8/</6&-,$?0)/7$*6/? / E$&,$(%/7$*6/? =0%0,$(%&2 <0%'-0 / ($,=$%0(;%0 &6%;>01C$B *%$-+ )$ &60<+201( <)07/($.4)&E& 2./')/'.
#+2&-+:
1. L0<%03&(0)0 2$%&'()&*()0' ,&-$.4 )0=%'>$))&--$8&%,/%&20))&E& *&*(&')/' <0%'-0, =%&7)& *6%$=.$))&E& * 6&%=;*&, %06$()&E&
-2/E0($.' =& 2)$5)$B =&2$%?)&*(/;
2. F%/ -$B*(2// 2);(%$))$E& -02.$)/' 60,$%+ *E&%0)/' )0/3&.45$$ 2./')/$ )0 6&@88/9/$)(+ 20%/09// 6&,=&)$)( )0=%'>$)/B /
@62/20.$)()+? )0=%'>$)/B &60<+201( 6&@88/9/$)(+ 20%/09// 2);(%$))$E& -02.$)/' 60,$%+ *E&%0)/' / )&,/)0.4)+$ <)07$)/' 8/</6&,$?0)/7$*6/? =0%0,$(%&2 (&=./20 / %0<,$%&2 <0%'-0.
73
3. F%/ -$B*(2// ($,=$%0(;%)&B )0E%;<6/ )0/3&.45$$ 2./')/$ )0
6&@88/9/$)(+ 20%/09// 6&,=&)$)( )0=%'>$)/B / @62/20.$)()+? )0=%'>$)/B &60<+201( 6&@88/9/$)(+ 20%/09// ,&-;.' ;=%;E&*(/ (&=./20.
!"#!$%&'(!)*+,!- +.!+$,
1. #$)(9$.4 Y.I., J270%&2 U.Z. G$&%/' 2$%&'()&*($B / $$ /)>$)$%)+$ =%/.&>$)/': ;7$3. =&*&3/$ -.' *(;-. 2(;<&2. – W.: Z60-$,/',
2003. – 464 *.
2. Y2E%05/) [.\. J*)&2+ ($&%// )0-$>)&*(/ L!GG. F0%0,$(%/7$*60' )0-$>)&*(4: ;7$3. =&*&3/$..– F$%,4: :<--2& F$%,. E&*. ($?). ;)(0, 2007. – 197 *.
3. I&%6/) L.Y. G$&%/' 2);(%/60,$%)+? =%&9$**&2 2 %06$()+?
*/*($,0? )0 (2$%-&, (&=./2$. – W.: H0;60, 1983. – 288 *.
4. ]0?%;(-/)&2 :.X., "&($.4)/6&2 Z.#. "&)*(%;69/' / =%&$6(/%&20)/$ %06$()+? -2/E0($.$B (2$%-&E& (&=./20: ;7$3)/6 -.' ,05/)&*(%&/($.4)+? 2;<&2. – W.: W05/)&*(%&$)/$, 1987. – 328 *.
F&.;7$)& 6.12.2010
74
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