1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
| data1 = {{-90`, 15066`}, {-87.5`, 14530`}, {-85`, 14061`}, {-82.5`,
12789`}, {-80`, 12722`}, {-77.5`, 12186`}, {-75`,
10847`}, {-72.5`, 9776`}, {-70`, 9575`}};
data2 = {{-90`, 3821`}, {-87.5`, 4187`}, {-85`, 4320`}, {-82.5`,
6093`}, {-80`, 6160`}, {-77.5`, 7231`}, {-75`, 8303`}, {-72.5`,
9374`}, {-70`, 9572`}};
data3 = {{-90`, 2343`}, {-87.5`, 2410`}, {-85`, 2209`}, {-82.5`,
2343`}, {-80`, 2410`}, {-77.5`, 2410`}, {-75`, 2477`}, {-72.5`,
2544`}, {-70`, 2477`}};
Subscript[\[Nu], qt] = (3*6.2*10^6)/(2*Ii*(2*Ii - 1));
Subscript[\[Nu], L] = 104.286846*10^6;
a1 = 5/2*(5/2 + 1);
s = 1.5;
k = 1/2;
Clear[X1, X2, X3, X11, X22, X33, Z, M2, T2, n, \[Mu], F2];
X1 = {x11, x12, x13};
X2 = {0, 0, 1};
Z = {x21, x22, x23};
n = 1/Norm[X1]*X1;
M2 = X2*Cos[\[CapitalDelta] \[Degree]] + (1 -
Cos[\[CapitalDelta] \[Degree]])*(X2.n)*n + (Cross[n, X2])*
Sin[\[CapitalDelta] \[Degree]];
T2 = VectorAngle[Z, M2];
\[Mu]2 = Cos[T2];
F2 = -Subscript[\[Nu], qt]*(k - 1/2)*((3*\[Mu]2^2 - 1)/
2) + (Subscript[\[Nu], qt]^2/(
12*Subscript[\[Nu],
L]))*( (k*((3 \[Mu]2^2)/2*(1 - \[Mu]2^2)*(8*k^2 - 4*a1 + 1) +
3/8*(1 - \[Mu]2^2)^2*(-2*k^2 + 2*a1 - 1))) - ((k -
1)*((3 \[Mu]2^2)/
2*(1 - \[Mu]2^2)*(8*(k - 1)^2 - 4*a1 + 1) +
3/8*(1 - \[Mu]2^2)^2*(-2*(k - 1)^2 + 2*a1 - 1))) ) + 10000;
delta1[x11_?NumericQ, x12_?NumericQ, x13_?NumericQ, x21_?NumericQ,
x22_?NumericQ, x23_?NumericQ] =
Total@Cases[data1, {\[CapitalDelta]_, Fvalue_} -> (F2 - Fvalue)^2];
{d, xr} =
NMinimize[{delta1[x11, x12, x13, x21, x22, x23]}, {x11, x12, x13,
x21, x22, x23}];
X3 = {0, 1, 0};
M3 = X3*Cos[\[CapitalDelta] \[Degree]] + (1 -
Cos[\[CapitalDelta] \[Degree]])*(X3.n)*n + (Cross[n, X3])*
Sin[\[CapitalDelta] \[Degree]];
T3 = VectorAngle[Z, M3];
\[Mu]3 = Cos[T3];
F3 = -Subscript[\[Nu], qt]*(k - 1/2)*((3*\[Mu]3^2 - 1)/
2) + (Subscript[\[Nu], qt]^2/(
12*Subscript[\[Nu],
L]))*( (k*((3 \[Mu]3^2)/2*(1 - \[Mu]3^2)*(8*k^2 - 4*a1 + 1) +
3/8*(1 - \[Mu]3^2)^2*(-2*k^2 + 2*a1 - 1))) - ((k -
1)*((3 \[Mu]3^2)/
2*(1 - \[Mu]3^2)*(8*(k - 1)^2 - 4*a1 + 1) +
3/8*(1 - \[Mu]3^2)^2*(-2*(k - 1)^2 + 2*a1 - 1))) ) + 10000;
delta2[x11_?NumericQ, x12_?NumericQ, x13_?NumericQ, x21_?NumericQ,
x22_?NumericQ, x23_?NumericQ] =
Total@Cases[data2, {\[CapitalDelta]_, Fvalue_} -> (F3 - Fvalue)^2];
{d, xr} =
NMinimize[
delta2[x11, x12, x13, x21, x22, x23], {x11, x12, x13, x21, x22,
x23}];
X4 = {1, 0, 0};
M4 = X4*Cos[\[CapitalDelta] \[Degree]] + (1 -
Cos[\[CapitalDelta] \[Degree]])*(X4.n)*n + (Cross[n, X4])*
Sin[\[CapitalDelta] \[Degree]];
T4 = VectorAngle[Z, M4];
\[Mu]4 = Cos[T4];
F4 = -Subscript[\[Nu], qt]*(k - 1/2)*((3*\[Mu]4^2 - 1)/
2) + (Subscript[\[Nu], qt]^2/(
12*Subscript[\[Nu],
L]))*( (k*((3 \[Mu]4^2)/2*(1 - \[Mu]4^2)*(8*k^2 - 4*a1 + 1) +
3/8*(1 - \[Mu]4^2)^2*(-2*k^2 + 2*a1 - 1))) - ((k -
1)*((3 \[Mu]4^2)/
2*(1 - \[Mu]4^2)*(8*(k - 1)^2 - 4*a1 + 1) +
3/8*(1 - \[Mu]4^2)^2*(-2*(k - 1)^2 + 2*a1 - 1))) ) + 10000;
delta3[x11_?NumericQ, x12_?NumericQ, x13_?NumericQ, x21_?NumericQ,
x22_?NumericQ, x23_?NumericQ] =
Total@Cases[data3, {\[CapitalDelta]_, Fvalue_} -> (F4 - Fvalue)^2];
{d, xr} =
NMinimize[{delta3[x11, x12, x13, x21, x22, x23]}, {x11, x12, x13,
x21, x22, x23}];
NSolve[{NMinimize[
delta1[x11, x12, x13, x21, x22, x23], {x11, x12, x13, x21, x22,
x23}] NMinimize[
delta2[x11, x12, x13, x21, x22, x23], {x11, x12, x13, x21, x22,
x23}] NMinimize[{delta3[x11, x12, x13, x21, x22, x23]}, {x11,
x12, x13, x21, x22, x23}]}, {x11, x12, x13, x21, x22, x23}] |
(
