finite element to calculate deflection of fixed beam in matlab

main.m
% Define the properties of the fixed beam
L = 1; % Length of beam
E = 200e9; % Young's Modulus in Pa
I = 4.17e-6; % Area moment of inertia in m^4

% Create finite element model 
num_elements = 10;
elements = linspace(0, L, num_elements + 1);
nodes = elements(1:end-1);

% Construct global stiffness matrix
K_global = zeros(num_elements + 1, num_elements + 1);

for i = 1:num_elements
    length = elements(i + 1) - elements(i);
    Ke = [12, 6*length, -12, 6*length; 
          6*length, 4*length^2, -6*length, 2*length^2; 
          -12, -6*length, 12, -6*length; 
          6*length, 2*length^2, -6*length, 4*length^2];
      
    index = [i, i+1, i, i+1];
    
    for j = 1:4
        for k = 1:4
           K_global(index(j), index(k)) = K_global(index(j), index(k)) + (E*I/length^3) * Ke(j, k);
        end
    end
end

% Apply boundary conditions for fixed beam (simulating fixed support)
K_reduced = K_global(2:end, 2:end);

% Calculate deflection (displacement) by solving for the nodal displacements
F = zeros(num_elements, 1); % Assuming no external forces applied
U = K_reduced\F;

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