How would I properly go about creating this function?

I am doing a project to practice matlab and thought it would be best to be put into a function. This is my function and the rest of my code, I have variables t_values, height_values, and width_values that need to be used outside of the function, but I do not know how to use them from inside the function. These equations are going to be different for the different beams which is why I decided to create a general function. Thanks!

l = 70*12;          %length
maxHeight = 12;     %maximum height of beam
maxWidth = 10;      %maximum width of beam
minHeight = 3;      %minimum height of beam
minWidth = 3;       %minimum width of beam
maxDef = 10;        %maximum beam deformation
w = 3;              %distributed load
p = 500;            %point force
a = l/3;            %distance to point force

E_alum = 9.9*10^6;  %aluminum stiffness
E_steel = 28*10^6;  %steel stiffness
E_ti = 16*10^6;     %titanium stiffness

den_alum = .098;    %aluminum density
den_steel = .286;   %steel density
den_ti = .16;       %titanium density

E = [E_alum, E_steel, E_ti];
density = [den_alum, den_steel, den_ti];

%For combined load
I_min = (w*(l^4)./(E.*30.*maxDef))...
    - ((p*(a^2)*((3*l)-a))./(E.*6.*maxDef));

disp('I-Beam');

I-Beam

A_horizI = width_values.*t_values; %Area of flanges

Unrecognized function or variable 'width_values'.

A_vertI = t_values.*(height_values-(2.*t_values)); %Area of web

I_horizI = width_values.*t_values.^3; %Moment of flanges
I_vertI = (t_values.*(height_values-(2.*t_values)).^3)./12; %Moment of web

I_I_beam = I_vertI + 2.*(I_horizI + A_horizI.*((height_values./2)-(t_values./2)).^2); %I for I beam

weightIbeam = @(t, h, w, l, density) (2*w.*t + t.*(h-2.*t))*l*density; %Weight equation for I beam

beamoptimize(I_min, l, density,I_I_beam,weightIbeam);


function beamoptimize( I_min, l, density, I1, weightFunc)

t = 0.1:0.05:1;
height = minHeight:0.05:maxHeight;
width = minWidth:0.05:maxWidth;
V = {t, height, width};

C = cell(1, numel(V));
[C{:}] = ndgrid(V{:});
C = cellfun(@(X) reshape(X, [], 1), C, 'UniformOutput', false);
C = horzcat(C{:});

t_values = C(:, 1);
height_values = C(:, 2);
width_values = C(:, 3);


for i = 1:length(I_min)

    I = I1;

    valid_I = I(I >= I_min(i));
    valid_t = t_values(I >= I_min(i));
    valid_height = height_values(I >= I_min(i));
    valid_width = width_values(I >= I_min(i));
    
    % Calculate weight using the provided weight function
    weight = weightFunc(valid_t, valid_height, valid_width, l, density(i));

    [min_weight, min_index] = min(weight);

    optimal_I = valid_I(min_index);
    optimal_t = valid_t(min_index);
    optimal_height = valid_height(min_index);
    optimal_width = valid_width(min_index);

    disp(['For I_min = ', num2str(I_min(i))]);
    disp(['Minimum weight: ', num2str(min_weight)]);
    disp(['Optimal valid_I: ', num2str(optimal_I)]);
    disp(['Minimum thickness: ', num2str(optimal_t)]);
    disp(['Optimal height: ', num2str(optimal_height)]);
    disp(['Optimal width: ', num2str(optimal_width)]);
    disp('---------------------------------------');
end
end

[Dyuman Joshi]

What is the objective here? What are you trying to do?

Which values are the inputs? Which parameters are outputs? Which quantities are constants?

Answer 1

[Walter Roberson]

l = 70*12;          %length
maxHeight = 12;     %maximum height of beam
maxWidth = 10;      %maximum width of beam
minHeight = 3;      %minimum height of beam
minWidth = 3;       %minimum width of beam
maxDef = 10;        %maximum beam deformation
w = 3;              %distributed load
p = 500;            %point force
a = l/3;            %distance to point force

E_alum = 9.9*10^6;  %aluminum stiffness
E_steel = 28*10^6;  %steel stiffness
E_ti = 16*10^6;     %titanium stiffness

den_alum = .098;    %aluminum density
den_steel = .286;   %steel density
den_ti = .16;       %titanium density

E = [E_alum, E_steel, E_ti];
density = [den_alum, den_steel, den_ti];

%For combined load
I_min = (w*(l^4)./(E.*30.*maxDef))...
    - ((p*(a^2)*((3*l)-a))./(E.*6.*maxDef));

disp('I-Beam');

I-Beam

[height_values, width_values, t_values] = calculate_height_width(minHeight, maxHeight, minWidth, maxWidth);

A_horizI = width_values.*t_values; %Area of flanges
A_vertI = t_values.*(height_values-(2.*t_values)); %Area of web

I_horizI = width_values.*t_values.^3; %Moment of flanges
I_vertI = (t_values.*(height_values-(2.*t_values)).^3)./12; %Moment of web

I_I_beam = I_vertI + 2.*(I_horizI + A_horizI.*((height_values./2)-(t_values./2)).^2); %I for I beam

weightIbeam = @(t, h, w, l, density) (2*w.*t + t.*(h-2.*t))*l*density; %Weight equation for I beam

beamoptimize(height_values, width_values, t_values, I_min, l,  density, I_I_beam, weightIbeam);

For I_min = 355.0754
Minimum weight: 1193.64
Optimal valid_I: 355.2708
Minimum thickness: 0.5
Optimal height: 12
Optimal width: 9
---------------------------------------
For I_min = 125.5445
Minimum weight: 1244.4432
Optimal valid_I: 125.6859
Minimum thickness: 0.2
Optimal height: 12
Optimal width: 7.15
---------------------------------------
For I_min = 219.7029
Minimum weight: 1177.344
Optimal valid_I: 220.2674
Minimum thickness: 0.3
Optimal height: 12
Optimal width: 8.9
---------------------------------------

function [height_values, width_values, t_values] = calculate_height_width(minHeight, maxHeight, minWidth, maxWidth)
    t = 0.1:0.05:1;
    height = minHeight:0.05:maxHeight;
    width = minWidth:0.05:maxWidth;
    V = {t, height, width};
    
    C = cell(1, numel(V));
    [C{:}] = ndgrid(V{:});
    C = cellfun(@(X) reshape(X, [], 1), C, 'UniformOutput', false);
    C = horzcat(C{:});
    
    t_values = C(:, 1);
    height_values = C(:, 2);
    width_values = C(:, 3);
end

function beamoptimize( height_values, width_values, t_values, I_min, l, density, I1, weightFunc)

    for i = 1:length(I_min)
    
        I = I1;
    
        valid_I = I(I >= I_min(i));
        valid_t = t_values(I >= I_min(i));
        valid_height = height_values(I >= I_min(i));
        valid_width = width_values(I >= I_min(i));
        
        % Calculate weight using the provided weight function
        weight = weightFunc(valid_t, valid_height, valid_width, l, density(i));
    
        [min_weight, min_index] = min(weight);
    
        optimal_I = valid_I(min_index);
        optimal_t = valid_t(min_index);
        optimal_height = valid_height(min_index);
        optimal_width = valid_width(min_index);
    
        disp(['For I_min = ', num2str(I_min(i))]);
        disp(['Minimum weight: ', num2str(min_weight)]);
        disp(['Optimal valid_I: ', num2str(optimal_I)]);
        disp(['Minimum thickness: ', num2str(optimal_t)]);
        disp(['Optimal height: ', num2str(optimal_height)]);
        disp(['Optimal width: ', num2str(optimal_width)]);
        disp('---------------------------------------');
    end
end

[Oliver Ries]

This worked very well, thank you!

Answer 2

[Image Analyst]

What is "width_values"? You never set it equal to anything so of course it complains.

[Oliver Ries]

Width_ values was set in the function. So that’s what I’m trying to figure out is how to use it with the equations that need it outside the function as well as the other equations that use it within the function.

[Image Analyst]

It was not set before you tried to use it. Maybe you set it later but if you use it it must be assigned first. Tell me the line of code where you actually assigned values to width_values.