Fracture fatigue problem, summation inside loops

Hello,

I am having a hard time trying to figure out how to setup a loop for this fatigue problem. Essentially, I am trying to solve the dK equation in iterations while adding the sum of da to ao. So, iteration one would be solving dK with ao=.125. Iteration 2 would be solving dK with ao=.125+sum(da) from the previous iteration. I am trying to run this process until dK reaches a value of 70. I think I am close, but I just can't get the loop to workout correctly.

dsigma=[46 26 16 12 24 26 16]';
R=[0 0.44 0.6 0.67 0.43 0.41 0.64]';
N=[1 2 3 17 3 1 2]';
ao=.125;
dK=dsigma.*sqrt(pi*ao)*((0.5*(3-(ao./(.125+ao)))*(1+1.243*(1-(ao./(.125+ao)))^3)))
da=(((3*10^-6).*(dK).^2.2)./((1-R)*70-dK)).*N
deltaa=sum(da);
while dK<70
  a1=ao+sum(da1);
  dK1=dsigma.*sqrt(pi*a1)*((0.5*(3-(a1./(.125+a1)))*(1+1.243*(1-(a1./(.125+a1)))^3)));
  da1=(((3*10^-6).*(dK1).^2.2)./((1-R)*70-dK1)).*N;
end

Answer 1

[Cedric]

You are setting a condition on dK in your WHILE statement, but you compute dK1 in the loop. Both should match (either use dK or dK1, but not both). If you wanted to save the "trajectory" of dK, you could define it as a 1D array and use a loop index to increment the index in dK at each iteration, e.g.

 ...
 k = 1
 dK(k) = dsigma.*sqrt(pi*ao)*((0.5*( .. etc
 ...

 while dK(k) < 70
    k = k + 1 ;
    ...
    dK(k) = dsigma.*sqrt(pi*a1)*((0.5*(3- .. etc
    ...
 end

This would not be optimal as dK should be preallocated, but let's not focus on that for now.