How do i correct my MATLAB Optimisation code

I have written a optimisation code for MATLAB to refine design parameters for Ri and Ro to calculate the minimum volume of a shaft of Length 1000mm. Torque of 5392Nm is applied to the shaft made of S235 Steel with a density of 7850kg/me, E of 230GPa, Shear stiffness of 95GPa and a shear yield strength of 140MPa and a Poisson ratio of 0.3 are used. RI and Ro are initially set as 70 and 100mm respectively. The length of the shaft and the position of a 30mm diameter rivet hole, placed halfway down the shaft and cuts through the entire shaft, must be kept fixed. The maximum shear stress in the bar must not exceed the shear yield stress and the twist angle should be kept below 1.5 degrees. Wall thickness must not be less than 5mm.

My code is as follows:

function shaft_optimization

% Given data

L = 1000; % Length of the shaft in mm

T = 5392; % Applied torque in Nm

r_hole = 15; % Radius of the rivet hole in mm

shearYieldStrength = 140e6; % Shear yield strength in Pascals

G = 95e9; % Shear modulus in Pascals

maxTwistAngle = 1.5; % degrees

% Objective function: minimize the volume of the shaft

objective = @(x) pi * (x(1)^2 - x(2)^2) * L;

% Constraint functions

constraints = @(x) deal([

% Shear stress constraint

16 * T / (pi * (x(1)^4 - x(2)^4)) - shearYieldStrength,

% Twist angle constraint

(T * L) / (G * (pi/2 * (x(1)^4 - x(2)^4))) - maxTwistAngle * (pi/180),

% Wall thickness constraint ensuring the hole is accounted for

x(1) - x(2) - r_hole,

% Ensuring the volume remains non-negative

pi * (x(1)^2 - x(2)^2) * L - 0

], []);

% Initial guesses for ro and ri

x0 = [100, 70]; % Based on initial dimensions provided

% Setting options for the optimizer

options = optimoptions('fmincon', 'Display', 'iter', 'Algorithm', 'sqp');

% Run the optimization

lower_bounds = [r_hole + 70, r_hole]; % Ensure ro > ri + r_hole

upper_bounds = [150, 95]; % Example upper bounds

[x_opt, fval] = fmincon(objective, x0, [], [], [], [], lower_bounds, upper_bounds, constraints, options);

% Display the results

fprintf('Optimal outer radius ro = %.2f mm\n', x_opt(1));

fprintf('Optimal inner radius ri = %.2f mm\n', x_opt(2));

fprintf('Minimum volume = %.2f cubic mm\n', fval);

end

I seem to get a negative value for minimum volume. Can anyone help me debug this issue and offer recommendations for corrections.

Thanks,

James

Answer 1

[Torsten]

Unit error. Convert all mm in m (or all m in mm).