Error using contour (line 48) Z must be at least a 2x2 matrix.

Hello i hope im not missing something obvious by putting this here but ive been stuck for hours. I am trying to solve this problem, basically i need to fill a zero matrix with different values for von mises stress and then plot it using a contour plot. I continue to encounter the error in the title, i am also not sure if maybe the problem is in my loop rather than Z.

function Hertz2DContour (P,R,ECM,nu,mu,N)
% Hertz2DContour (P,R,ECM,nu,mu,N)
%   Plots contours of von Mises equivalent stress
%   P    Load per unit length
%   R    Equivalent radius
%   ECM  Elastic contact modulus
%   mu   Friction coefficient
%   N    Number of points

% (1) Calculate and display semi-contact width, a
a = ((4*P*R)/(pi*ECM))^0.5

% (2) Calculate and display peak pressure, p0
p0 = (2*P/pi*a)

% Create vector of x values from -1.5a to 1.5a
X = linspace (-1.5*a,1.5*a,N);

% Create vector of z values fzom 0 to 3a
Z = ([1:N] - 0.5) * 3 * a / N;

% Create empty matrix for von Mises stress values
sv = zeros (N,N);
% (3) Loop through all X and Z values and calculate sv for each pair
for X=1:N
    for Z=1:N
        [sx,sz,tzx]=Hertz2DStress(P,R,ECM,nu,N)
        sy=nu*(sx+sz);
        I1=sx+sy+sz;
        I2=sx*sy+sy*sz+sz*sx-(tzx^2);
        I3=sx*sy*sz-(sy*tzx^2);
        J2=I2-((I1^2)/3);
        sv=sqrt(-3*J2);
    end
end

       
% (4) Create a contour plot of the X,Z,sv
[X,Z]=meshgrid(X,Z)
contour(Z,sv,X) 

Any help would be greatly appricated, thank you.

[Rena Berman]

(Answers Dev) Restored edit

Answer 1

[Star Strider]

I have no idea what the arguments to your function are, so I cannot run your code.

Try this:

% Create empty matrix for von Mises stress values
sv = zeros (N,N);
% (3) Loop through all X and Z values and calculate sv for each pair
for X=1:N
    for Z=1:N
        [sx,sz,tzx]=Hertz2DStress(P,R,ECM,nu,N)
        sy=nu*(sx+sz);
        I1=sx+sy+sz;
        I2=sx*sy+sy*sz+sz*sx-(tzx^2);
        I3=sx*sy*sz-(sy*tzx^2);
        J2=I2-((I1^2)/3);
        sv(X,Z)=sqrt(-3*J2);
    end
end
       
% (4) Create a contour plot of the X,Z,sv
[X,Z]=meshgrid(1:N)
contour(Z,sv,X) 

I cannot test this. It should work, although ‘sv(Z,X)’ mighty be correct instead. Experiment!

[Oscar Hales]

I get the same error message, ive put the other function bellow. Thank you.

function [sx,sz,tzx] = Hertz2DStress (p0,a,mu,x,z)
% [sx,sz,tzx] = str2d(p0,a,mu,x,z)
%    Routine to calculate stresses for Hertz 2D cylindrical contact
%    p0  Peak contact pressure
%    a   Semi-contact width
%    mu  Friction coefficient
%    x   Horizontal coordinate
%    z   Vertical coordinate (+ve is down)

% need to normalize x & z w.r.t. semi-contact width a
x   = x / a;
z   = z / a;

k1  = (1+x).^2 + z^2;
k2  = (1-x).^2 + z^2;
k   = sqrt(k2./k1);

s   = (pi./k1)./k./sqrt(2*k + (k1 + k2 - 4)./k1);
si  = s.*(1-k);
sib = s.*(1+k);

sx  =    - z/pi * ((1 + 2*x.^2 + 2*z^2).*sib - 2*pi - 3*x.*si);
sx  = sx - (2*mu/pi)*((x.^2 - 1 - 1.5*z^2).*si + pi*x);
sx  = sx - (2*mu/pi)*((1 - x.^2 - z^2).*x.*sib);

sz  =    - (z/pi).*(sib - x.*si) - (mu/pi).*si*z^2;

tzx =     - (z^2/pi).*si;
tzx = tzx - (mu/pi)*((1 + 2*x.^2 + 2*z^2)*z.*sib - 2*pi*z - 3*x*z.*si);

sx  = p0 * sx;
sz  = p0 * sz;
tzx = p0 * tzx;

[Star Strider]

First, it does not appear that you have included the loop that I posted. That appears to create the matrix that contour requires.

Second, without the necessary arguments, I cannot test the code I post. If you provide them, I may be able to solve the problem.

[Star Strider]

Creating ‘sv’ as a matrix eliminiated the error that contour threw, however ‘sv’ is not changing. This is most readily apparent if you calculate:

cv_lims = min(sv(:))-max(sv(:))

producing:

cv_lims =
     0

I am not certain what the problem is.

You will need to find that and fix it, since materials science is far from my areas of expertise.