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I. STRUCTURE CAD “ ” .........................................................................................................15
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Windows..................................................................................................22
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1.1 .............................................................................................................................24
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2. ...............................................................................................................41
2.1 ............................................................................................42
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2
- .............................................................................. 45
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, ........................................................................ 48
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2.2 .............................................................. 51
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2.3 ................................................................................................................................ 56
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2.4 , .................................................... 61
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2.6 ............................................................................................................ 64
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2.7 .................................................................................................................. 69
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2.9 .................................................................... 73
2.10 ............................................................................................................. 74
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( ) ............................................................................................................................. 76
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2.11 ( ) ....................................................................... 80
2.12 ...................................................................................... 82
3. ............................................................................................... 83
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3.1 ........................................................................................................................................ 86
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3
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3.2 ...............................................................................................................................95
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( )........................................................99
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( - ) ...........................................................................100
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3.3 .........................................................................................................................105
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4. ........................................................................107
4.1 ..............................................................................................108
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, ......................................................................114
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- ................................................................................................116
4.2 ........................................................................................................................117
4.3 .....................................................................................................118
4.4 ........................................................................................................................119
4.5 ................................................................................120
4.6 ................................................................121
4.7 1 .......................................122
4.8 ........................................................................................................................122
4.9 ........................................................................................................................123
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4.10 ...................................................................................... 124
4.11 Z1 .............................................. 125
4.12 ......................................................................... 125
4.13 ............................................................................................................................... 125
5. ................................................................................................................ 127
5.1 ........................................................................................................... 128
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5.2 ...................................................................................................................................... 136
5.3 .......................................................................................................................................... 138
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5.4 .................................................... 142
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, ................................................................................................................................................. 148
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6. .......................................................................................................................... 151
7. .......................................................................... 153
7.1 ................................................................. 154
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7.2 .................................................................................................................................... 159
7.3 ........................................................................................................................ 161
7.4 ................................................................ 162
7.5 ...................................................................................... 164
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7.6 .............................................................................................................. 169
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8. ................................................................. 171
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8.1 ............................................................................171
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( ) ............................................................................177
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8.2 ....................................................................................179
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8.3 ................................................................................................................. 203
8.4 .................................................................. 206
, ............................................... 207
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8.5 ........................................................................................ 208
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9. .......................... 213
9.1 ................................................................................................. 213
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9.2 .............................................................................................................................................. 217
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10. ................................................................................................................ 221
11. ( ) ........................................................................................ 223
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12. .............................................................................. 231
12.1 .................................................. 233
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12.2 ............................................................................................ 237
12.3 ................................... 237
13. .......................................................................................................................................... 241
13.1 ................................................................................................................................... 241
13.2 ....................................................................................... 242
13.3 .................................................................................................................. 243
13.4 ...................................................................................................................................... 243
13.5 ............................................................................................................................................... 244
14. ...................................................................................................................................... 245
14.1 .................................................................................................. 245
14.2 ................................................................................. 248
14.3 ....................................................................................................... 249
14.4 ..................................................................................................... 250
15. .................................................................................. 251
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15.1 ............................................................................................................................252
15.2 ..............................................................................................................................254
16. ..................................................255
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16.1 ............................................................................................257
1 ( 2D) ...............................................................................................................................257
2 ( 3D) ...............................................................................................................................258
11 ( . ) .......................................................................................................................259
21 ( - ) ..............................................................................................................................259
16.2. ....................................................................................................................260
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16.3 ....................................................................................................................268
1 ( 2D) ........................................................................................................268
2 ( 3D) ......................................................................................................269
11 ( . ) ................................................................................................269
21 ( - ) ......................................................................................................271
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17. .................................................275
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18. ........................................................................................289
- SCAD
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19. .....................................................................................................................295
19.1. .......................................................................................................295
19.1.1. ....................................................................................................................................295
19.1.2. ............................................................................................296
19.1.3. .......................................................................................298
19.1.4. ..............................................................................................................298
19.1.5. .........................................................................299
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19.1.6. , , ........................................................................................... 300
19.1.7. ...................................................................................................................... 300
19.2. .................................................................... 301
19.2.1. .......................................................................................................... 301
19.2.2. ............................................................................................................ 302
19.2.3. .......................................................................................................................... 303
19.3. .................................................................................................................... 305
19.4. ........................................................................... 306
19.4.1. .............................................................................................................................. 306
19.4.2. .............................................................................................................................................. 307
19.4.3. .......................................................................................................................... 307
19.4.4. ............................................................................................................. 308
19.4.5. ................................................................................................................ 308
19.5. ( )..................................................................................................... 309
19.5.1. .............................................................................................................................................. 309
19.5.2. ( ) ................................................................................ 309
19.5.3. .................................................................................................................................................. 310
19.5.4. .............................................................................................................................................. 310
19.5.5. ........................................................................................................................... 310
19.5.6. .......................................................................................................................................... 311
20. ........................................................................ 313
20.1. ........................................................................................................ 313
20.1.1. ................................................................................................................................ 313
20.1.2. ............................................................................................................. 315
20.1.3. ............................................................................... 316
20.1.4. ........................................................................................................................... 320
20.2. ........................................................................................................................................... 320
20.2.1. ................................................................................................................... 320
20.2.2. ........................................................................................................................ 321
20.2.3. .................................................................................................................... 322
20.3. .................................................................................................................................... 323
20.3.1. .............................................................................................................. 323
20.3.2. .......................................................................... 324
20.3.3. ............................................................................................... 326
20.4. ................................................................................................... 329
20.4.1. ......................................................... 329
20.4.2. ............................................................................................ 330
20.4.3. ................................................................................................................... 331
20.5. .................................................................................... 332
20.6. ........................................................................................................ 335
20.7. ................................................................................................................................. 336
20.8. ............................................................................................................... 337
19 20............................................................................................................................ 339
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53
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.
σ0
+ ,
.
( )σ σ σ σ σe nf k k= ≤ +1 2 3 1 0, , , ,..., , ,
k1,...,kn – ,
.
:
σ σ σ σ0 1 2 31
3= + +( ) –
( );
[ ]σ σ σ σ σ σ σi = − + − + −1
31 2
22 3
23 1
2( ) ( ) ( ) -
;
σ σ τ0 0 0+ −, , –
,
;
χ σ σ= + −0 0/ ;
ϕ σ τ= +0 0/ ;
ψ σ τ= −0 0/ ;
λ σ= −1 0/ .
σ0− ,
.
S .
, .
,
1 2 .
242
.
12.1
/n .
1
- = 1
s=| 3| ( ,
).
2 - = 1 – ( 2+ 3)
s=| 3 – ( 1+ 2)|
3
- = 1 – 3
s= ,
( ).
4
-
-
[σ σ σ σe i= = − +⎧⎨⎩1
21 2
2( )
]}+ − + −( ) ( )/
σ σ σ σ2 32
3 12
1 2
s= e
-
( ,
, ).
1 2 .
243
12.3
. 12.3.1.
-
( . 12.3.1),
.
, .
, ,
,
. , ,
.
.
,
.
1 3 .
245
13.
( ) SCAD :
;
(
);
.
13.1,
( ,
)
. ,
( ) -
, , -
—
( ). ( ) = Ao - B( )
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B( ),
, -
. . , -
,
u
( ,
,
,
, ).
,
( ),
( -
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.
, -
.
,
,
,
1 3 .
246
(
). ,
,
.
(
), ,
, , > .
13.2
( )
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, ( ,
)
, .
, ( ).
( )
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),
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= ( . . ( )).
, ,
.
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),
( /2),..., . .
.
, ( 1,
2) , 2 - 1 ( 1)
, ( 2) .
1 .
( )
,
. min < ,
, , min
, .
1 3 .
247
13.3
,
, SCAD
(A - B( 1)) u = 0. ( )
, , . .
-
u, -
. ,
,
. ( )
,
.
( ).
13.4
,
, . . ,
,
N
(N = 1*N).
N = 2EJ / l2,
lo = ( 1N / 2EJ )1/2,
EJ -
( - ).
1 3 .
248
13.5
. 13.5.1.
( . 13.5.1),
.
:
-
,
;
( 2 0.01);
,
,
:
,
( ) ;
( ).
-
. ,
.
-
.
.
.
1 4 .
249
14.
14.1
,
,x x x+ + =2 02ϕ ω ω (14.1)
–
( / );
– . < 1
(1)
x Ae ttD= +−ϕω ω αsin( ) ,
ω ω ϕD = −1 2 – ,
, – ,
.
<<1
ω ωD ≈ .
F(t),
( t) / ,x x x F m+ + =2 2ϕ ω ω (14.2)
e
( ) ( )[ ] ( )xm D
F t t z t z dz
t
D= − − −∫1
0ω
ρω ωexp sin (14.3)
( t)x 0
( ) m
F mx(t) ( t)= − 0 .
,
, ,
(t)x x x x+ + = −2 20ϕω ω , (14.4)
x x e z dzD
t zD
t
= − −− −∫1
0ω
ωϕω(t) sin (t )( ) (14.5)
x x xα = + 0 ,
x xDα ω≈ − 2 (14.6)
1 4 .
250
,
( ).
[ ]{ } [ ]{ } { }M u K u ,+ = 0 (14.7)
{u} – ;
[M] – ;
[K] – .
-
[ ] { } [ ] { } [ ] { } { (t)}M u C u K u F+ + = , (14.8)
[C] – ;
{F(t)} – .
(14.8)
[ ] { } [ ] { } [ ] { } [ ] { } (t)M u C u K u M I x+ + = − 0 , (14.9)
{u} – ( ,
xOy, );
{I} – ,
;
( t)x 0 - .
(14.9)
( “ ”)
{ } { } (t)u j j
j
n
==∑ Φ Ψ
1
, (14.10)
n – (
);
Φ j – j-
;
Ψ j ( t) – ,
.
, [ ]
{ } { } { } { }Φ Φ
Φ Φi
T
j
i i i
T
i
Ci j
M i j[ ]
,
[ ] ,=
≠
=
⎧⎨⎪
⎩⎪
0
2ϕ ω
i – i- .
(14.10) (14.9) (14.9)
{ }Φ i
T Ψi ( t)
( t)Ψ Ψ Ψ+ + = −2 20ϕ ω ωi i i i i iD x , (14.11)
1 4 .
251
{ }{ } { }
DM I
Mxi
i
T
i
T
i
=Φ
Φ Φ
[ ] { }
[ ](t)0
:
{ } { } { }( ) { }{ } (t) (t) (t) (t)u u I x D xa i
i
n
j i i
i
n
ja= + = + == =∑ ∑0
1
0
1
Φ Ψ Φ Ψ
[ ]{ } [ ]{ } [ ]{ } [ ]({ } ( ) { } ( ) { } ( )M u C u K u M I x t I y t I z tx y z+ + =− + +0 0 0 , (14.12)
(t) , (t)x y0 0 (t)z0 –
. -
, (14.12)
.
1 4 .
252
14.2-
-
.
– ,
.
:
( )
,
;
;
,
,
.
,
(2), :
;
;
14.1.
14.1.
( ) ( )
0.2 – 3.0
3.0 – 3.6
3.6 – 5.0
5.0 – 8.0
8.0 – 15.0
15.0 – 18.0
18.0 – 22.0
22.0 – 34.0
0.10
0.15
0.20
0.25
0.5
1.0
2.0
3.0
. 14.1
.
,
.
,
.
1 4 .
253
14.3
. 14.3.1.
. 14.3.2.
( . 14.3.1)
,
( ).
,
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( )
.
,
.
,
( 0 1) , ,
( ,
4- ).
, ,
.
, ,
, .
.
.
.
,
.
, .
( ) .
1 4 .
254
14.4 SCAD SPC.
.
:
c /(c*c)
.
– SH. M – 1c. Amax = 45.1 c /(c*c).
N = 2047; Dt = 0.05000 c.
#
0.01 2047 0.05
0.0 0.0 0.1 0.3 0.4 0.6 0.5 0.0 –2.1 –2.6 …
# :
/ce 2 ;
;
;
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( SPC
).
,
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SCAD .
1 5 .
255
15.
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.
, ,
.
, ,
, .
Z,
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1 5 .
256
15.1 , -
.
.
.
.
– ,
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.
:
– ;
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);
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– ;
,
;
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,
.
, .
,
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1 5 .
257
,
.
.
-
.
.
1 5 .
258
15.2
. 15.2.1.
,
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( / ),
, ,
, .
.
( . 15.2.1).
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;
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) ;
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;
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,
Z ( 0 ).
-
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. . OK
.
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.
.
,
.
.
1 6 .
259
16.
2.03.01-
84. .
p p -
, , p
p p p -I, A-II, A-
III, A-IV, A-V, A-VI p p p -I.
p p p
, p
.
p
:
1 ( 2D) –
,
p , p
;
2 ( 3D) –
p p
, ,
p ;
11 ( . ) –
.
21 ( - ) –
-
.
p
:
p p p ;
p ;
, ,
. .
.
" " .
,
p .
1 6 .
260
:
,
;
;
;
, ,
;
2.03.01-84
( . 16.17)
;
;
;
. 3.16
2.03.01-84;
s5
A-IV, A-V, A-VI, -11, -11, 7, -19
( . 24 2.03.01-84);
.
1 6 .
261
16.1
1 ( 2D)
( p ). p
, p , p
(p ) p .
.
:
p – N;
p – Mk;
p p – Qz;
– My.
p
p p ,
p p . . 16.1.1 -
, . 16.1.1 - –
p p . ,
Y1.
16.3.
.16.1.1. ( - ) ( - )
1 6 .
262
2 ( 3D)
( ). ,
,
( ) .
.
:
– N;
– Mk;
– Qz, Qy;
– My, Mz.
p p
, p p .
. 16.1.2 -
,
. 16.1.2 - –
p p . C
, Y1.
. 16.1.2. ( - ) ( - )
1 6 .
263
11 ( . )
. 16.1.3.
(
p ). p -
p ,
p :
p p – Nx, Ny;
p – Txy;
p – Mxy;
p p – Qx, Qy;
– Mx, My.
p p
p p p ,
p p . . 16.1.3
p
p p p ,
.
21 ( - )
. 16.1.4.
-
-
( , )
(
p ).
-
, :
– Nx, Nz;
p – Txz.
p p
p p ,
X1 Z1.
. 16.1.4 -
p
p p .
1 6 .
264
16.2.
. 16.2.1.
. 16.2.2.
-
.
.
:
( ) -
( . 7);
;
( . 16.2.1) -
;
,
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;
( . 16.2.2)
;
( . 16.2.3)
. ,
21 ( - )
1,
– Z1;
( -
),
( . 16.2.4);
,
;
;
.
, -
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.
1 6 .
265
. 16.2.3.
. 16.2.4.
,
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,,
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, (144)
(152) [1].
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.
1 6 .
266
. 16.2.5.
-
.
.
( . 16.2.5)
( , , ,
). ,
,
.
,
.
:
2D – AS1, AS2, AS3, AS4
. 16.1.1 -
S1 = S2, AS3 AS4 ,
S3 ( . . 16.1.1 - ).
3D – AS1, AS2, AS3, AS4
. 16.1.2 -
S1 = S2, AS3 AS4 ,
S3 ( . .16.1.2 - ).
AS1 – AS4
AS1
( X), AS2 ( X), AS3 ( Y),
AS4 ( Y) .16.1.3.
- AS1 AS2
S1 ( X) S2 ( Z) ( . . 16.1.16). –
.
ASW1, , ASW2,
. ASW1 –
X1 Z1 ;
ASW2 – X1 Y1
Y1 Z1 – . –
, .
1 6 .
267
. 16.2.6.
, . ,
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1 6 .
268
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.
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1.2 0.9.
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)
X1OZ1 X1OY1.
. . 3.25 [1].
.
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( - );
EAY EAZ
X1OZ1 X1OY1.
.1.21 [1].
h/30 b/30. – ;
– 1 3.
1- ,
1 6 .
269
;
. .1
2 [1]
.
. – ;
.
(145) [1].
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. – .
,
,
.
16.1
Eb Rb Rbt Rs, Rsc Rsw
+
b2 = 1.1* v v
b2** v v
b b2 + +
+
+
v w
v w
,
( . ).
.
.
* – b2 . 2 15 ;
** – b2 . 2 15 (
);
+ – ;
v –
;
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1 6 .
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1 6 .
272
16.3
1
( 2D)
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( )
.
1- - :
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(AS1, AS2, AS3, AS4)
(AS1, AS3) ( –
,
,
);
;
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(ACR2) ;
(
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-
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Z1 (ASW1, );
(
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1).
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4- .
( )
1
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(
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– 1: ASW1 (ASWx)
1 6 .
274
. 16.3.3.
20
(Sx); Y1: ASW2 (ASWy) Y (Sy)
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1, 2- –
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Y1.
Y, CY, TY.
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,
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1 6 .
275
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,
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X1);
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X1 – AS1.
RTF 2-
( 1).
3- –
Z1 – AS3 .
RTF 3- Z
( Z1);
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Z1 – AS3.
RTF 4- Z
( Z1).
,
2 4- .
( )
,
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1 - .
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Y, Y
TY Z, Z Z.
1 6 .
276
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p
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1 6 .
277
1. .
. 2.03.01-84. M.,
C , 1985.
2. .
. II-7-81. M., , 1982.
3.
( 2.03.01 –
84). ,
. .: , 1986.
4. . .
. .: , 1976.
1 7 .
279
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( )
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.
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( . 17.1)
:
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;
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1 7 .
280
– ;
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.
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281
. 17.2.
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:
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0.7 1.2, –
120 400.
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:
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( . 17.3).
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1 7 .
282
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283
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284
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1 7 .
287
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5.25;
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. 17.15.
,
.17.11-17.12,
.
-
, .
.
( . 17.14).
( . 17.15),
.
1 8 .
293
18.
. 18.1.
,
.
,
.
:
-
;
;
- .
( . 18.1. )
,
,
.
,
.
.
( . 18.1. ),
.
,
,
( . 18.1. ).
( ,
)
. ,
, .
( )
.
.
, . .
. ,
,
,
" - ".
.
-
1 8 .
294
. 18.2.
,
.
,
,
,
,
( . 4).
.
-
( . 18.2),
(
).
,
,
,
, .
, .
:
;
;
,
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,
);
-
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);
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;
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;
;
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;
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1 8 .
295
;
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.
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.
1 9 .
297
« – ,
- ,
,
.
,
.
.»
. .
. – - : , 1998, .5
-
SCAD
,
SCAD. ,
,
.
, ,
.
, .
,
( , ) ( ) ,
, .
, - SCAD. ,
, ,
,
.
1 9 .
298
1 9 .
299
19.
1 9 .
300
19.1.
19.1.1.
,
, .
,
.
,
, .
(
; ;
, , ; .).
.
,
( – , !)
.
,
.
*. , ( ) ,
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.
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,
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.
.
, , ,
, , .
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,
( ),
( ),
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, (
).
, , ,
.
* -
. . [28],
. ,
. . , . . . . [1].
1 9 .
301
, . .
, ( !) .
.
.
, ,
.
. “ ” ( ., , [8])
.
, ,
,
.
.
19.1.2.
,
, , :
( , ,
. .), .
:
;
, , ,
, , ;
,
– (
) . . ( . );
,
, ( ), ;
( )
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;
,
, ;
-
;
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, .).
.
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, – ,
,
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( ).
1 9 .
302
.
. ,
, ( , )
.
,
( ) .
, .
,
. ,
,
.
. , , .19.1,
, ,
.19.1, .
, ,
,
( . .1.1.4).
, .
, , ,
( ), .
. 19.1
, , . ,
, , .
, , , ,
, ,
( , “ ” ).
, , -
. ,
( ) (
), .
19.1.3.
1 9 .
303
, ,
, .
, –
.
:
1 – X;
2 – Y;
3 – Z;
4 – X ( X);
5 – Y ( Y);
6 – Z ( Z).
( ), ,
, X, Y, Z, UX,
UY UZ .
-
, ( , ,
, ),
.
,
, , –
.
( )
. :
) , XOZ – ,
Y (UX, UY, UZ);
) XOY – X Y UZ.
( ),
, .
, , ( )
- .
19.1.4.
( ). , ,
( X=0 UY=0).
,
[17]. ,
. , ,
, ,
( , Xicos + Yisin =0 X). , ,
( )
.
, ,
, , ,
, . ,
.
1 9 .
304
, ,
, . . ,
. ,
, “ ”
. , ,
.
, , –
.
,
, .
, ,
, ,
. “ -
”, , , [17].
19.1.5.
( ) , ,
, . .
. , ,
, ( )
( .
3).
,
( ),
.
( )
. ,
,
,
.
,
– , – “ ” . .
“ ”, .
, ,
, ,
19.1. , -
1 4 7 8.
,
, ,
. (
, – .).
19.1.6. , ,
,
- .
( , )
1 9 .
305
( , ), , ,
( , ).
, , ,
, .
, ,
( , . .).
( , ).
. , ,
, . .
, ( ) ,
, .
, ,
, .
, .
, ,
, .
19.1.7.
, ( )
( ). ,
, .
. . .
, .
,
. , ,
, ,
,
.
,
, .
, ( ,
)
- ( ,
).
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.
( ) ,
,
.
( ). ,
,
.
( ) , , ,
. , , -
( ,
),
( ).
1 9 .
306
,
, ,
.
.
1 9 .
307
19.2.
19.2.1.
SCAD ( )
.
,
,
.
( ., , [10, 26, 27 .]).
.
- x ,
V S, (x) (x),
u(x) :
σ ε ε= =M Bu; , (19.1)
: B – ; M – ,
,
.
Π ( ) /e T
v
T
v
T
s
M dV u pdV u q dS= − −∫ ∫ ∫1 2 ε ε , (19.2)
p q – .
u( )
Z
u( ) = ϕ i
i
(x) Zi∑ = (x)Ze, (19.3)
: i(x) – , ,
[26]; (x) –
; Ze –
( “ ”).
(19.1) (19.3) (19.2) ( )
=1/2 Ze( ( ) ) ( )B MB dV Z p dV q dS ZT
e
v
T T
sv
eΦ Φ Φ Φ∫ ∫∫− + (19.4)
(19.4) ( )
= 1/2 Ze K(e)Ze - feTZe, (19.5)
: K(e) = ( )B T
v
Φ∫ MB dV – ; feT = pT
v
∫ dV + q T
s
∫ dS –
.
= Π (e)
e
∑ , (19.6)
KZ = f (19.7)
1 9 .
308
K f,
K(e) f(e) ,
.
.
,
( ), , .
, ,
, . ,
.
,
.
,
. ,
, , ,
– , , .
:
, , ;
, , .
.
, (
) . ,
, , , -
, , . ,
, ,
. , h τ,
h – , = 2 – , = 1 –
. , hτ ,
= 4 – , = 2 –
.
– (
) .
, h ( . .20.1).
19.2.2.
Z
CZ = 0, (19.8) Z ,
[17]
L = 1/2ZT(K + C
TDoC)Z - Z
Tf + T
CZ, (19.9)
Do , –
( ).
(19.9)
KZ + (CTDoC)Z + C
T = f;
CZ = 0. (19.10) , ,
( )
, ,
1 9 .
309
. (19.10)
, , (
), .
.
K CTDoC
(“ - ”),
. [17]
“ - ”,
SCAD.
19.2.3.
, . . f = f(t),
, dZ/dt
d2Z/dt2 .
J(t) = M(d2Z/dt
2) (19.11)
,
,
M(d2Z/dt
2) + KZ(t) = f(t). (19.12)
, ,
(
).
( )
,
Z(t) = sin( t + ). (19.13)
(19.13) (
), – , – . (19.13) (19.12) ,
f(t) = 0
(K - 2M) = 0, (19.14)
, i (i = 1,...,n),
, (K - 2M).
i .
, i .
,
, . .
i M j= 0 i K j= 0 i j. (19.15)
Z,
( ), ,
. ,
, . SCAD ,
,
, .
, O,
, I, , (19.14)
KOO O + KOI I = 0;
KIO O + KII I = 2MII . (19.16)
O “
”
1 9 .
310
(KOO-1
MII - 2 I) I = 0, (19.17)
I – , = 1/ .
SCAD i
I (19.17). = 1/ ( / ), = /2 ( ) = 1/ .
Z(t) = yi
i
∑ (t) i (19.18)
(19.12)
yi(t). ,
,
d2yi /dt
2+ 2 i dyi /dt + i
2yi = Pi(t)/Mi. (19.19)
Pi(t) = 2 Ti f(t), (19.20)
Mi = ΨiT M i (19.21)
i , yoi y1
i , Zo = Z(0)
Z1 = dZ(0)/dt
yoi = Ψi
T MZo, y
1i = Ψi
T MZ1 (19.22)
.
yi = exp[- i i t] {[(yoi i i + y1
i)/ Di] sin Dit + yoi} +
+ (1/ DiMi) P (t)i
0
t
∫ exp[- i i (t - )] sin Di(t - )d , (19.23)
, .
(19.23)
Di = i (1 - I2)1/2
(19.24)
i
= 2 / D 2 . (19.25)
1 9 .
311
19.3.
, ,
KZ=F, (19.26)
: K – N N; F –
( ) N k (k – ); Z – k N.
K ,
,
(19.26) ( .19.2).
.19.2
SCAD , ,
- , - , x .
.
.
- , . . .
, . .
.
(19.26)
.
K
, . . , K – ,
, ,
.
, . ,
,
“ ” ( )
, .
1 9 .
312
,
.
.
(19.26).
, , ,
K,
, .
( ,
“ ” ) .
1 9 .
313
19.4.
SCAD :
– ;
– , [24];
– ;
– ;
– .
,
.
19.4.1.
10 [5],
.
, z ,
q(z,t) = qs(z) + q
p(z,t). (19.27)
, ,
, (z)
S( ) = 1200 5/3/[3vo(1 + 2
)4/3
], (19.28)
vo – 10 ; = vo/1200 – .
, (
)
j- Z
Z .j =
i
s
=∑
1
( 2ij 2
i)/ 4i . (19.29)
s – , ij – ,
ij = ( ij σk
k
∑ ik)/ Mr
r
∑ ir , (19.30)
:
2= (2/3) ε11 3
0
/
∞
∫ (1 + 2)-4/3
[ 4- 2(1 - 2
/2) 2 2i + 4
i]-1
d . (19.31)
= / , i
i = vo/1200 .
(19.27), –
(19.29). ( –
)
, .
X = Xc [ ( )Xi
d
i
2∑ ]1/2
, (19.32)
1 9 .
314
, ,
( ) .
Xid
(19.32), ,
Xc.
19.4.2.
[24] ,
( )
.
d2zo/dt2, ,
(19.11) ,
Jc(t) = M(d2Z/dt
2 - d
2zo/dt
2), (19.33)
(19.12)
fc(t) = M d2zo/dt
2. (19.34)
(19.34)
( . 3 [5])
Sik, k- i-
Sik = QkKc (Ti) ikcos ok. (19.35)
Qk – k- ; Kc – ,
( , )
; – ,
= a/T ( b), (19.36)
a b ; ik – (19.30); ok –
Zk.
(19.35) Xi ,
X = maxi Xi X = [X
2
( )Xii
2
≠∑
α]1/2
. (19.37)
19.4.3.
, 2,5 s, s ( . 5
[5]). , f(t)=0 t > ,
, ,
.
1 9 .
315
. 19.3
, f(t)
( . 19.3),
S = Po f t( )
0
τ
∫ dt. (19.38)
< 0,1Ts
f(t),
.
S = Movo(1 + ko), (19.39)
vo – , ko – ,
. ,
, (19.39),
.
, (
!). f(t)
( . 19.3,f).
19.4.4.
P(1)icos t + P(2)
isin t
S1 S2, ( )
( ) ,
S1 = a i
i
∑ M i, S2 = bi
i
∑ M i, (19.40)
ai = (P(1)i - P(2)
i i)/( 2i + 2
i),
bi = (P(2)i - P(1)
i i)/( 2i + 2
i),
i = / i, i = 1 - 2i. (19.41)
S = (S12+ S2
2)1/2
. (19.42)
, i,
, ( . [5, .53]).
19.4.5.
yi(t).
yi(t) .
, k-
t k fk = f(tk). (19.20) Pi,k = Pi(tk). (19.19)
. yi,k = yi(tk) Si,k = Si(tk),
Sj,o = maxk{ j yj(tk) }. (19.43)
1 9 .
316
19.5. ( )
SCAD .
( )
. 2 n ( n – ),
, ,
.
19.5.1.
( . 19.4).
. 19.4
:
σ k
y
y
z
z
N
F
M z
I
M y
I= ± ± , (19.44)
: k – (k = 1 9).
yb= ±2
zh= ±2
σ k
y
z i
z
y i
F NM
l
M
l= ± +
, ,
, (19.45)
ly,i lz,i
(i=1,2).
.
:
τ y z
y z kp
y z y z
FQ M
l l,
,
, ,( )= ±
+2 2 1 1 1 2
. (19.46)
.
30 .
19.5.2. ( )
.
:
σ α α α α( ) cos sin sin= ⋅ + ⋅ + ⋅N N Tx z xz2 2 2 ; (19.47)
( )τ α α α( ) sin cos= − ⋅ + ⋅1
22 2N N Tz x xz . (19.48)
1 9 .
317
. 19.5
. 19.5.
900
900
, – 900
00
. 150.
19.5.3.
, , .19.5.2.
. , (19.47) (19.48)
M M M Mx y xy( ) cos sin sinα α α α= ⋅ + ⋅ + ⋅2 2 2 ; (19.49)
( )M M M Mk y x xy( ) sin cosα α α= − ⋅ + ⋅1
22 2 . (19.50)
, .
19.5.4.
, , .19.5.2.
:
σ
σ
τ
xH
xx
yH
y
y
Hxy
xy
NM
h
NM
h
TM
h
/
/
/
;
;
,
Β
Β
Β
= ±
= ±
= ±
6
6
6
2
2
2
(19.51)
: h – ; B H – ,
. =22.50
.
19.5.5.
: ) ( ); )
. .
:
σ σ σ σ τ τ τ= ⋅ + ⋅ + ⋅ + ⋅ ⋅ ⋅ + ⋅ ⋅ + ⋅ ⋅ ⋅x y z xy xz yzl m n l m l n m n2 2 2 2 2 2 ;
1 9 .
318
σ σ
τ τ τ
= +
= ⋅ + ⋅ + ⋅ + ⋅ ⋅ + ⋅ ⋅ + ⋅ ⋅
0
2 2 2 2 2 2
S
S S l S m S n l m l n m nx y z xy xz yz
;
,
: σ – l, m, n X1, Y1, Z1;
S – ; ( )σ σ σ σ0 3= + +x y z / – c
.
.
. n ,
3n . S
.
.
, .
1 6, :
1 – 1- ;
2 – 1- ;
3 4 – 2- ;
5 6 – 3- .
, , 143 , 2- 14-
. 076 , 3- 7-
.
, ,
7 8 .
19.5.6.
,
, .
:
– ( , . .);
– ( ,
. .);
– ( . .).
.
2 0 .
319
20.
20.1.
20.1.1.
, . .
. , ,
[26, . 195-196], (k-1) ,
2m, u*,
u
U(u-u*, u-u*) C2h2(k-m)||u||2k ,
h – ( ).
s- z
||z-z*||s Chk-s||z||k , s > 2m-k ;
||z-z*||s Ch2(k-s)||z||k , s 2m-k.
. . . .
( ., , [8], [13]).
SCAD, 20.1.
20.1.
:
- - - -
11,13 2 — 2 1
12,14 2 — 1 0
20 ( 4 8
)
2 — 1 0
21 2 1 — —
22 2 1 — —
23 2 1 — —
24 2 1 — —
27 ( 4 8
)
2 1 — —
29 ( 4 12
)
2 1 — —
2 0 .
320
:
- - - -
30 ( 4 8
)
2 1 — —
31 2 1 — —
32 2 1 — —
33 2 1 — —
34 2 1 — —
36 2 1 — —
37 2 1 — —
41 2 1 1 0
42 2 1 1 0
44 2 1 1 0
50 ( 4 8
)
2 1 1 0
61 2 1 — —
62 2 1 — —
64
( 4 8
)
2 1 — —
71
( , ,
)
2 1 — —
72
( , ,
)
2 1 — —
73
( ,
, )
2 1 — —
74 ( 4 8 )
(
, , )
2 1 — —
81
( )
2 1 — —
2 0 .
321
:
- - - -
82
( )
2 1 — —
83
( )
2 1 — —
84 ( 4 8 )
(
)
2 1 — —
, 20.1,
, [3, .55]: "...
, ,
ch/L,
, ; h — ; L — .
( ), ,
5%, 1/20
...", . . 400 ,
– 8000.
20.1.2.
,
,
, . ,
" -
",
, .
. ( [1, .52]):
"... , 1000n/n! n!/1000n,
... 999 999- ,
, . , ,
, 1000 ;
, 1000 ".
: " : —
, ".
- ,
,
. , , ,
.
.
,
,
, .
,
.
2 0 .
322
,
,
.
,
, . , ,
. : " ,
, . ,
,
.
, , , ." [10,
.257].
,
, ,
,
.
, ( ,
),
- ,
. , ,
,
, .
.
,
, .
( ),
,
( )
.
,
, ,
.
. .
20.1.3.
.
— 4 4, 8 8, 16 16 24 24 ( .20.1).
2 0 .
323
.20.1.
20.2 ,
, ,
, .20.2.
20.2
:
4x4 8x8 16x16 24x24
11/41 0,0180329 0,0172754 0,0170823 0,0170453
20/50 0,0166168 0,0169137 0,0169918 0,0170051
12/42 0,0161403 0,0168034 0,0169658 0,0169938
:
-11/41 0,04781 0,04509 0,04443 0,04443
-20/50 0,03991 0,04313 0,04393 0,04408
-12/42 0,04787 0,04528 0,04432 0,04448
:
Q -11/41 0,22 0,28 0,31 0,32
Q -20/50 0,37 0,4 0,43 0,44
Q -12/42 0,24 0,31 0,33 0,34
2 0 .
324
) )
)
:
.20.2.
: - , -
, -
,
,
11- , ,
. , 20/50 ,
, ( ).
,
, . ,
8 8 0,01701, - 0,0442 - 0,278.
,
, , 20.3 .20.3, .
, -
, ,
. - ,
.
.
2 0 .
325
20.3
:
4x4 8x8 16x16 24x24
11/41 0.511522 0.494164 0.488470 0.487183
20/50 0.466266 0.480460 0.484425 0.485222
12/42 0.432918 0.470046 0.481375 0.483493
:
-11/41 2.61566 3.27276 3.93364 4.32066
-20/50 2.31761 3.04494 3.72290 4.11309
-12/42 1.89259 2.52465 3.17713 3.56252
:
Q -11/41 7.26 14.58 29.18 43.77
Q -20/50 6.50 13.31 26.81 40.26
Q -12/42 11.37 25.59 53.21 80.42
) )
)
:
.20.3.
: -
, - , -
2 0 .
326
,
.
.
20.1.4.
, , ,
( ) ,
.
.
( ., . 20.2. ),
.
-
, , ,
. , ,
, .
, ,
, -
.
,
.
( , ),
( )
.
20.2.
20.2.1.
,
.
,
, .
,
. ,
, .
, - . , ,
[30]: 1 - ,
, ; 2 - ,
, ; 3 - .
.
:
)
, -
, ;
2 0 .
327
) , .
, , ,
.
,
, .
[28].
, .
.
20.2.2.
, ( ,
) ,
. .
[K]{u} = {p}. (20.1)
.
{uo}, {u},
{u} = [D]{uo}. (20.2)
[K]
[Ko] = [D]T[K][D], (20.3)
[Ko] - ,
[Ko]{uo} = [D]T{p} (20.4)
[Ko]-1
.
, {u} (20.4)
(20.2) {d},
{u} = [D]{uo} + {d} = [D][Ko]-1
[D]T + {d} (20.5)
(20.5) (20.1)
[K]{d} = ([E] - [K][D][Ko]-1[D]T){p} = [S]{p}. (20.6)
,
[D]T[S] = [D]T - [D]T[K][D][Ko]-1
[D]T =
= [D]T - [Ko][Ko]-1
[D]T = [D]T - [D]T = [0], (20.7)
{x} (20.1) {xo} (20.4)
([D]{xo}) () = {xo} [D] [S]{x} = 0. (20.8)
, {p} (20.6)
(20.2).
,
( ) ,
, [D].
(20.4), , ,
, .
, ,
. , ,
- , ( ,
[28, c.62])
2 0 .
328
. ,
(20.5).
(-0,5; +1,0; -0,5), s .
s -
. , ,
xx = -2/( x)[1 - 1/(1 + 2 2 + 4)], (20.9)
= s/x, = 3s
.
20.2.3.
,
( .20.6).
,
, .
[31]. SCAD
20, 30 50,
.
- (
).
.20.6.
2 0 .
329
20.3.
20.3.1.
— ,
, ( ,
) , ( ,
). ,
. , ,
. 20.7, .
, :
) , , (
, );
) , X Y.
99%.
, , SCAD
,
. , ,
:
- UX ,
YOZ, UY , XOZ;
,
.
.
. 20.7.
.
,
.
, ,
2 0 .
330
. ,
, .
- , ,
( ). ,
, - ,
. ,
. ,
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1960.
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18. . ., . . . p x p x .
.: p , 1991. 240 .
19. . ., . .
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21. . . . . , 1955.-475 .
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26. ., . .— .: , 1977.—350 .
27. . . .: , 1980. 512 .
28. . . - . - . , 1969
29. .- . ,
, 1973, 1, .125-127.
30. Sabahi D., Rose T. Special Applications of Global-Local Analysis, MSC/NASTRAN 1992 World Users`
Conference Proceedings.
31. Schiermeier J.E., Housner J.M., Ranson J.B., Aminpour M.A., Stroud W.J. The Application of Interface
Element to Dissimilar Meshes in Global/Local Analysis, MSC 1996 World Users` Conference Proceedings
32. . ., . ., - . ., . ., . .,
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