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Minimization error: constraints are not valid

Felix Toperczer

Felix Toperczer, TU Wien

Posted 1 year ago

In the notebook above, I am attempting to minimize a function that depends on the function θ(x). The purpose is to solve this problem and extract the variable q3. However, I keep encountering an error message from Mathematica. Could you please help me identify the mistake I am making?

POSTED BY: Felix Toperczer

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Gianluca Gorni

Gianluca Gorni, University of Udine

Posted 1 year ago

`ClearAll`, without arguments, does not clear anything at all, I suspect. `Cos[\[Theta]], Sin[\[Theta]], (\[Theta]')^2` do nothing useful for you; you should use `Cos[\[Theta][x]], Sin[\[Theta][x]], (\[Theta]'[x])^2`. The quantity `U` is best written as a function of the parameters `q1,q2,q3`, not of `\[Theta]`. This works: Clear[q1, q2, q3, x, \[Theta], U] w = 4.7; h = 3.4; A = 25; \[Nu] = 0.45; L = 36Pi; R = 36; (Steifigkeiten) a1 = 4A\[Pi]wh^3; a2 = 4A\[Pi]w^3h; a3 = (2Ahw(h^2 + w^2))/(1 + \[Nu]); \[Theta][x_] = q1 + q2x + q3x^2; Solve[{\[Theta][0] == 0, \[Theta]'[0] == 0}] U[q1_, q2_, q3_] = Integrate[(1/2)(a1/R^2Cos[\[Theta][x]]^2 + a2/R^2Sin[\[Theta][x]]^2 + a3/L^2*(\[Theta]'[x])^2), {x, 0, 1}]; Plot[U[0, 0, q3], {q3, -2, 2}] result = NMinimize[U[0, 0, q3], q3]

ClearAll, without arguments, does not clear anything at all, I suspect. Cos[\[Theta]], Sin[\[Theta]], (\[Theta]')^2 do nothing useful for you; you should use Cos[\[Theta][x]], Sin[\[Theta][x]], (\[Theta]'[x])^2. The quantity U is best written as a function of the parameters q1,q2,q3, not of \[Theta]. This works:

Clear[q1, q2, q3, x, \[Theta], U]
w = 4.7;
h = 3.4;
A = 25;
\[Nu] = 0.45;
L = 36*Pi;
R = 36;
(*Steifigkeiten*)
a1 = 4*A*\[Pi]*w*h^3;
a2 = 4*A*\[Pi]*w^3*h;
a3 = (2*A*h*w*(h^2 + w^2))/(1 + \[Nu]);
\[Theta][x_] = q1 + q2*x + q3*x^2;
Solve[{\[Theta][0] == 0, \[Theta]'[0] == 0}]
U[q1_, q2_, q3_] =
  Integrate[(1/2)*(a1/R^2*Cos[\[Theta][x]]^2 +
      a2/R^2*Sin[\[Theta][x]]^2 +
      a3/L^2*(\[Theta]'[x])^2),
   {x, 0, 1}];
Plot[U[0, 0, q3], {q3, -2, 2}]
result = NMinimize[U[0, 0, q3], q3]

POSTED BY: Gianluca Gorni