Hello Juan,
I see that you intend to refine the `B0` matrix so that the stress ratio `RF` is constrained within 0.95 to 1.05, while also ensuring that the values of `B0` do not fall below the threshold of `1e-4`.
There are issues in the current code that might prevent it from converging and could lead to `B0` taking negative values.
Here are the steps to rectify the problem:
- Guarantee that `B0` doesn't decrease beneath `Bmin`.
- Implement proportional changes to `B0` contingent on the distance of `RF` from the target range.
- Re-evaluate `RF` after every modification to `B0`.
- Ensure `sigma_max` is accurately defined and incorporated.
Below is the modified function:
% Example inputs for y, x, Mx, and sigma_max
y = [0.1, 0.2, 0.3, 0.4, 0.5, 0.6]; % Sample y coordinates
x = [0.5, 0.4, 0.3, 0.2, 0.1, 0]; % Sample x coordinates
Mx = 100; % Sample bending moment
sigma_max = 200; % Sample maximum stress
% Convert y and x to column vectors if they aren't already
y = y(:);
x = x(:);
% Execute the function with the sample inputs
optimized_B0 = optimize_areas(y, x, Mx, sigma_max);
% Output the optimized boom areas
disp('Optimized B0:');
disp(optimized_B0);
% The function to optimize boom areas
function B0 = optimize_areas(y, x, Mx, sigma_max)
% Define minimum boom area, tolerance, and initial guess
Bmin = 1e-4;
tolRF = 0.05;
B0 = ones(size(y)) * 0.001;
sigma_max = sigma_max * 0.7; % Modify sigma_max as necessary
% Initial calculations for area, centroid, and stress
a = sum(B0, 2);
I = sum(B0 .* y.^2, 2);
sigma = (y .* Mx) ./ I;
RF = abs(sigma_max ./ sigma);
% Iteration counter and limit
count = 0;
maxIterations = 10000;
% Iterative process to adjust B0
while any(RF < (1 - tolRF) | RF > (1 + tolRF)) && count < maxIterations
count = count + 1;
for i = 1:numel(B0)
if RF(i) < (1 - tolRF)
B0(i) = B0(i) + B0(i) * 0.01; % Increment by 1%
elseif RF(i) > (1 + tolRF)
B0(i) = B0(i) - B0(i) * 0.01; % Decrement by 1%
end
B0(i) = max(B0(i), Bmin); % Enforce minimum value
end
% Recompute values after updating B0
a = sum(B0, 2);
I = sum(B0 .* y.^2, 2);
sigma = (y .* Mx) ./ I;
RF = abs(sigma_max ./ sigma);
end
% Check for convergence
if count == maxIterations
disp('Maximum iterations reached without convergence.');
else
disp('Convergence achieved.');
end
disp(['Iterations: ', num2str(count)]);
end
Hope this should help resolve the issues
Best regards,
Chetan
