Functions with multiple variables

Hi

I am working on functions with multiple variables:

IFF1 = @(s22,s33) (s22+s33+sqrt((s22-s33)*(s22-s33)+4*s23*s23))/(2*St22)-1

I would like to gain all combinations of s22 and s33 so the function equals 0. Then i would like to plot these values, result should be an ellipsis.

Thank you for you help!

Greetings Ben

[Walter Roberson]

Is the St22 reference a typo, or a constant in the scope of the defining routine?

Likewise for the s23 and s33 references.

Answer 1

[Jonathan]

Ben,

Here is a neat way of solving your problem. There are certainly more efficient methods. This was the least amount of code for me to right, though. Let me know how it goes for you.

s23 = rand;
St22 = rand;
IFF1 = @(s22,s33) (s22+s33+sqrt((s22-s33)*(s22-s33)+4*s23*s23))/(2*St22)-1;
[X, Y, Z] = meshgrid(linspace(-10, 2, 50), linspace(-10, 2, 50), [0 0]);
V = nan(size(X));
for i = 1:numel(X)
  V(i) = IFF1(X(i), Y(i));
end
patch(isosurface(X,Y,Z,V,0))

Answer 2

[Ben]

Re

If i understand correct, your code plots my function. Though it does not solve my optimization problem. Any hints?

Thank you for your support!

Answer 3

[Walter Roberson]

There are an infinite number of solutions, not confined to any region of the graph. For any s33,

s22 = (s23^2+s33*St22-St22^2)/(s33-St22)

This is clearly an infinite curve with a discontinuity at s33 = St22

Answer 4

[Ben]

Sorry I should have added more information:

St22 = 73.00 [MPA]
s23 = 30 [MPA]

(s22+s33+sqrt((s22-s33)*(s22-s33)+4*s23*s23))/(2*St22) = 1

I have been able to solve this problem with an optimization approach. But was hoping to find an easyer way to visualize the result.

[Walter Roberson]

Same issue as before:

s22 = (-4429+73*s33)/(s33-73)

which is an infinite curve with a discontinuity at s33 = 73