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P1-mw.pdf

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P1-mw.pdf
> restart; x1 dK1eK6 : x2 d 0.0 : x3 d 1eK6 :
> r1 d sqrt x Kx1 2 Cy2 Cz2 :
x Kx1 $z
x Kx1
P1
> ux1 d
$
K 1 K2$nu $
3
4$Pi$G
r1$ r1 Cz
r1
P1
y$z
y
> uy1 d
$
K 1 K2$nu $
:
3
4$Pi$G
r1$ r1 Cz
r1
P1
z2
2$ 1 Knu
> uz1 d
$
C
:
3
4$Pi$G
r1
r1
> r2 d sqrt
> ux2 d
> uy2 d
> uz2 d
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
P2
z2
2$ 1 Knu
$
C
3
4$Pi$G
r2
r2
2
2
2
:
:
x Kx3 Cy Cz :
P3
x Kx3 $z
x Kx3
ux3 d
$
K 1 K2$nu $
:
3
4$Pi$G
r3$ r3 Cz
r3
P3
y$z
y
uy3 d
$
K 1 K2$nu $
:
3
4$Pi$G
r3$ r3 Cz
r3
P3
z2
2$ 1 Knu
uz3 d
$
C
:
3
4$Pi$G
r3
r3
ux d ux1 Cux2 Cux3 :
uy d uy1 Cuy2 Cuy3 :
uz d uz1 Cuz2 Cuz3 :
exx d diff ux, x : eyy d diff uy, y : ezz d diff uz, z : theta d exxCeyyCezz :
1
exy d $ diff ux, y Cdiff uy, x :
2
1
eyz d $ diff uy, z Cdiff uz, y :
2
1
exz d $ diff ux, z Cdiff uz, x :
2
E
E$nu
Gd
: lambda d
:
2$ 1 C nu
1 Cnu $ 1 K2$nu
sx d lambda$theta C2$G$exx :
sy d lambda$theta C2 $G$eyy :
sz d lambda$theta C2$G$ezz :
sxy d 2$G$exy : syz d 2$G$eyz : sxz d 2$G$exz :
E d 2e11 : nu d 0.3 : P1 d 1 : P2 d 1 : P3 d 1 :
plot subs y = 0, z = 1eK7 , sx , x =K5eK6 ..5eK6 ;
> r3 d sqrt
>
x Kx2 2 Cy2 Cz2 :
x Kx2 $z
x Kx2
P2
$
K 1 K2$nu $
3
4$Pi$G
r2$ r2 Cz
r2
P2
y$z
y
$
K 1 K2$nu $
:
3
4$Pi$G
r2$ r2 Cz
r2
:
3.# 1012
2.# 1012
1.# 1012
K4.# 10 - 6
K2.# 10 - 6
0
K1.# 1012
2.# 10 - 6
x
K2.# 1012
K3.# 1012
K4.# 1012
K5.# 1012
K6.# 1012
> plot subs
x = 0, z = 1eK6 , sy , y =K1eK5 ..1eK5 ;
4.# 10 - 6
2.# 1010
K0.000010
K0.000005
0
0.000005
y
K2.# 1010
K4.# 1010
K6.# 1010
K8.# 1010
K1.# 1011
> plot subs
y = 0, z = 1eK6 , sz , x =K5eK6 ..8eK6 ;
0.000010
K2.# 10 - 6
0
2.# 10 - 6 4.# 10 - 6 6.# 10 - 6 8.# 10 - 6
x
K1.# 1011
K2.# 1011
K3.# 1011
K4.# 1011
K5.# 1011
K6.# 1011
> plot subs
y = 0, z = 1eK7 , uz , x =K5eK6 ..5eK6 ;
0.000025
0.000020
0.000015
0.000010
0.000005
K4.# 10 - 6
> plot subs
K2.# 10 - 6
0
x
2.# 10 - 6
x = 0, y = 0 , sz , z = 1eK6 ..2eK5 ;
4.# 10 - 6
z
0.000002 0.000006 0.000010
0.000016 0.000020
K1.# 1011
K2.# 1011
K3.# 1011
K4.# 1011
K5.# 1011
K6.# 1011
> Qx1 d 1 : Qx2 d 1 : Qx3 d 1 :
> r1 d sqrt x Kx1 2 Cy2 Cz2 :
Qx1
1
x Kx1 2
1
x Kx1 2
> uux1 d
$
C
C
1
K2$nu
$
K
4$Pi$G
r1
r1 Cz
r13
r1$ r1 Cz 2
Qx1
x Kx1 $y
1 K2$nu $ x Kx1 $y
> uuy1 d
$
K
:
3
4$Pi$G
r1
r1$ r1 Cz 2
Qx1
x Kx1 $z
1 K2$nu $ x Kx1
> uuz1 d
$
C
:
3
4$Pi$G
r1$ r1 Cz
r1
> r2 d sqrt
> uux2 d
> uuy2 d
> uuz2 d
> r3 d sqrt
Cy2 Cz2 :
1
x Kx2 2
1
x Kx2 2
$
C
C
1
K2$nu
$
K
r2
r2 Cz
r23
r2$ r2 Cz 2
x Kx2 $y
1 K2$nu $ x Kx2 $y
$
K
:
3
r2
r2$ r2 Cz 2
x Kx2 $z
1 K2$nu $ x Kx2
$
C
:
3
r2$ r2 Cz
r2
x Kx3 2 Cy2 Cz2 :
x Kx2
Qx2
4$Pi$G
Qx2
4$Pi$G
Qx2
4$Pi$G
:
2
:
2
Qx3
1
x Kx3 2
1
x Kx3
$
C
C
1
K2$nu
$
K
4$Pi$G
r3
r3 Cz
r33
r3$ r3 Cz 2
Qx3
x Kx3 $y
1 K2$nu $ x Kx3 $y
uuy3 d
$
K
:
3
2
4$Pi$G
r3
r3$ r3 Cz
Qx3
x Kx3 $z
1 K2$nu $ x Kx3
uuz3 d
$
C
:
3
4$Pi$G
r3$ r3 Cz
r3
uux d uux1 Cuux2 Cuux3 :
uuy d uuy1 Cuuy2 Cuuy3 :
uuz d uuz1 Cuuz2 Cuuz3 :
eexx d diff uux, x : eeyy d diff uuy, y : eezz d diff uuz, z :
1
eexy d $ diff uux, y Cdiff uuy, x :
2
1
eeyz d $ diff uuy, z Cdiff uuz, y :
2
1
eexz d $ diff uux, z Cdiff uuz, x :
2
psi d eexx Ceeyy Ceezz :
ssx d lambda$psi C2$G$eexx :
Qx
3$x3
x
3$x
x3
SSx d
$ K 5 C 1 K2$nu $ 3 K
C
3
2$Pi
rho$ rhoCz 2
ρ
ρ
ρ $ rhoCz 2
> uux3 d
>
>
>
>
>
>
>
>
>
>
>
>
C
>
>
>
>
2$x3
:
2
ρ $ rhoCz 3
ssy d lambda$psi C2$G$eeyy :
ssz d lambda$psi C2$G$eezz :
ssxy d 2$G$eexy : ssyz d 2$G$eeyz : ssxz d 2$G$eexz :
plot subs y = 0, z = 1eK6 , ssx , x =K1eK5 ..1eK5 ;
:
1.5 # 1011
1.# 1011
5.# 1010
K0.000010
K0.000005
0
0.000005
x
K5.# 1010
K1.# 1011
K1.5 # 1011
> plot subs
y = 0, z = 1eK6 , ssy , x =K1eK5 ..1eK5 ;
0.000010
2.# 1010
1.# 1010
K0.000010
K0.000005
0
0.000005
x
K1.# 1010
K2.# 1010
> plot subs
y = 0, z = 1eK6 , ssz , x =K1eK5 ..1eK5 ;
0.000010
1.5 # 1011
1.# 1011
5.# 1010
K0.000010
K0.000005
0
0.000005
x
K5.# 1010
K1.# 1011
K1.5 # 1011
> plot subs
y = 1eK6, z = 0 , uuz , x =K2eK5 ..2eK5 ;
0.000010
4.# 10 - 7
2.# 10 - 7
K0.00002
K0.00001
0
0.00001
x
K2.# 10 - 7
K4.# 10 - 7
> plot subs
y = 0, z = 1eK7 , sxCssx , x =K2eK6 ..4eK6 ;
0.00002
4.# 1012
2.# 1012
K1.# 10 - 6
0
K2.# 1012
1.# 10 - 6 2.# 10 - 6 3.# 10 - 6 4.# 10 - 6
x
K4.# 1012
K6.# 1012
K8.# 1012
K1.# 1013
K1.2 # 1013
K1.4 # 1013
> plot subs
y = 0, z = 1eK7 , syCssy , x =K1eK5 ..1eK5 ;
3.# 1012
2.# 1012
1.# 1012
K0.000010
K0.000005
0
0.000005
x
K1.# 1012
> plot subs
y = 0, z = 1eK7 , sz Cssz , x =K1eK5 ..1eK5 ;
0.000010
K0.000010
K0.000005
0
0.000005
x
K1.# 1013
K2.# 1013
K3.# 1013
K4.# 1013
K5.# 1013
> plot subs
y = 0, z = 1eK7 , uz Cuuz , x =K5eK6 ..5eK6 ;
0.000010
0.000025
0.000020
0.000015
0.000010
0.000005
K4.# 10 - 6
> evalf subs
> evalf subs
> evalf subs
> evalf subs
> evalf subs
> evalf subs
> evalf subs
> evalf subs
> evalf subs
K2.# 10 - 6
0
x
2.# 10 - 6
4.# 10 - 6
x = 0, y = 0, z = 1eK6 , ux Cuux ;
0.000003678329676
x = 0, y = 0, z = 1eK6 , uy Cuuy ;
0.
x = 0, y = 0, z = 1eK6 , uz Cuuz ;
0.000005262543738
x = 1eK6, y = 1eK6, z = 1eK6 , sxCssx ;
K1.070509466 1011
x = 1eK6, y = 1eK6, z = 1eK6 , syCssy ;
K1.210832959 1011
x = 0, y = 0, z = 1eK6 , sz Cssz ;
K6.462741387 1011
x = 1eK6, y = 1eK6, z = 1eK6 , sxy Cssxy ;
K8.970892805 1010
x = 1eK6, y = 1eK6, z = 1eK6 , syz Cssyz ;
K1.619071042 1011
x = 1eK6, y = 1eK6, z = 1eK6 , sxz Cssxz ;
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
K9.374613274 10
>
10
(9)
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