MATLAB Cable Tension and Cost Optimization Script

MATLAB Cable Tension and Cost Optimization

This script calculates cable tensions and optimizes costs for a structural system by iterating through coordinate positions.

Initialization

ACMatrix = zeros(51,51);
ABMatrix = zeros(51,51);
ADMatrix = zeros(51,51);
CostMatrix = zeros(51,51);
countery = 0;
MinCost = 1;

A = [6 2 1]';
B = [3.5 0 -0.5]';
D = [0 -1 5.5]';
F = -[160 20 -30]';

rab = B - A;
rad = D - A;
ead = rad/norm(rad);
eab = rab/norm(rab);

Iterative Calculation

The following loop calculates tensions and costs across a range of Y and Z coordinates:

• C: Point position of the system.
• Tensions: Solved using the unit vector matrix.
• Cost: Calculated based on cable length and tension.

for y = 1:.1:6
    countery = countery + 1;
    counterz = 0;
    for z = -1:.1:4
        counterz = counterz + 1;
        C = [0 y z]';
        rac = C - A;
        NormRac = sqrt(rac(1)^2+rac(2)^2+rac(3)^2);
        eac = rac/NormRac;
        UnitVectorMatrix = [eab eac ead];
        Tensions = UnitVectorMatrix\F;
        ACMatrix(countery,counterz) = Tensions(2);
        ABMatrix(countery, counterz) = Tensions(1);
        ADMatrix(countery, counterz) = Tensions(3);
        CostMatrix(countery,counterz) = NormRac * Tensions(2);
    end
end

Visualization and Results

The script generates surface plots to visualize the effect of coordinate changes on cost and tension.

m = min(min(CostMatrix));
y = 1:.1:6;
z = -1:.1:4;

figure; surf(y,z,CostMatrix'); title('Effect on cost by changing y and z');
figure; surf(y,z,ACMatrix); title('Effect on Tension of AC');
figure; surf(y,z,ABMatrix); title('Effect on Tension of AB');
figure; surf(y,z,ADMatrix); title('Effect on Tension of AD');

Final Output

The script concludes by printing the minimum cost and the optimal position for point C, followed by the components of vector F.