Looping over vectors with different sizes

Question

This code is meant to calculate the deflection of a beam with the principal of superposition, where for every given position og a beam, all the individual influences of forces are calculated, and then summed together.

function deflection = beamSuperposition(positions, beamLength,loadPositions, loadForces, beamSupport)
%If several loads are applied, calculate each one individually and end with sum

x = positions;
l = beamLength;
a = loadPositions;
W = loadForces;
E = 200*10^9;
I = 0.001;

%For every position(x) element calculate the expression for all
%loadPositions(a) and their respective loadForce(W)

%Make sure a and W are of same size
%Make sure neither x or a ever surpass l

%Go trhough each element of x
for i = 1:length(x)
   %For beamSupport = 1 only
   while beamSupport == 1
      %Go through each element of 'a' and calculate the deflection
      for n = 1:length(a)
          %There are two different equations to calculating the deflection depending on the position of the loadForce compared to the position of interest
         while true
            if x(i) < a(n)
               y = (W(n)*(l-a(n))*x(i))*(l^2-x(i)^2-(l-a(n))^2)/(6*E*I*l);
            end
            if x(i) >= a(i)
               y = (W(n)*a(n)*(l-x(i)))*(l^2-(l-x(i))^2-a(n)^2)/(6*E*I*l);
            end
            break
         end
      end
      break
   end
%Sum the values for each y element?!?
   deflection = y
   end

How can I make this work as intended? The output should be a vector y with the same size as x with the summed deflections for each x value.

In use;

 beamSuperposition([1,2,5],10,[6,5,3],[10,15,20],1)

Will return, if deflection = y is not supressed,

deflection =

   5.8333e-07


deflection =

   1.0967e-06


deflection =

   1.6500e-06


ans =

   1.6500e-06

But should return values as a vector instead of the last value only

Answer 1

I've made some small changes. Firstly I've changed the central two if statements to a single if else statement. This removed an error you had

if x(i) >= a(i)

which should have probably read

if x(i) >= a(n)

Whilst there I also removed some of your while break control flows which I didn't quite see the purpose of. You might want to compare.

Secondly I saved your outputs to the i-th entry of y. I also preallocated it so it doesn't change size in the loop.

Finally, as suggested by @StackPlayer I used ii for the loop variable instead of i. There is some discussion on the question Using i and j as variables in Matlab.

function deflection = beamSuperposition(positions, beamLength,loadPositions, loadForces, beamSupport)
%If several loads are applied, calculate each one individually and end with sum

x = positions;
l = beamLength;
a = loadPositions;
W = loadForces;
E = 200*10^9;
I = 0.001;

%For every position(x) element calculate the expression for all
%loadPositions(a) and their respective loadForce(W)

%Make sure a and W are of same size
%Make sure neither x or a ever surpass l

y = zeros(size(x));
%Go through each element of x
for ii = 1:length(x)
    %For beamSupport = 1 only
    if ( beamSupport == 1 )
        %Go through each element of 'a' and calculate the deflection
        for n = 1:length(a)
            %There are two different equations to calculating the deflection depending on the position of the loadForce compared to the position of interest
            if x(ii) < a(n)
                y(ii) = (W(n)*(l-a(n))*x(ii))*(l^2-x(ii)^2-(l-a(n))^2)/(6*E*I*l);
            else
                y(ii) = (W(n)*a(n)*(l-x(ii)))*(l^2-(l-x(ii))^2-a(n)^2)/(6*E*I*l);
            end
        end
    end
end
%Sum the values for each y element?!?
deflection = y;
end

Example use:

>> beamSuperposition([1,2,5],10,[6,5,3],[10,15,20],1)

ans =

   1.0e-05 *

    0.0583    0.1097    0.1650

Answer 2

First things first, avoid using i and j in MATLAB (they are used for the imaginary number).

In your second while loop, you have if conditions on "x" instead of "x(i)"