montecarlo.m

% This script uses a Mote Carlo model to determine mean and standard
% deviation for the maximum deflection if b and h are normally distributed
% random variables with 0.1% standard deviation at q = 50 N/m
clear
clc
% Length of the beam [meters]:
L = 1;
% Prescribed distributed loading:
q = 50;
% Young's Modulus for aluminum [Pascals]:
E = 70e9;
% x_max is the maximum deflection
x_max = 0.5;
% Width of beam [meters]:
b = 0.1;
% Height of beam [meters]:
h = 0.01;
% Standard deviation is 0.1%:
stdev = 0.1;
% Number of iterations:
N = 50;
for i = 1:N
    b_mont = normrnd(b,stdev*b);
    h_mont = normrnd(h,stdev*h);
    I = (b_mont*h_mont^3)/12;
    % Derived equation for vertical deflection:
    w = (q/(24*E*I)).*x_max.^4 - ((q*L)/(12*E*I)).*x_max.^3 + ((q*L^3)/(24*E*I)).*x_max;
    w_mont(i) = w;
end

mean = mean(w_mont);
stand_dev = std(w_mont);