o develop a linear beam bending analysis code in matlab

main.m
% Define beam properties
length = 1;                   % Length of the beam
E = 1e6;                      % Young's modulus
I = 1;                        % Moment of inertia

% Define boundary conditions
supportA = 0;                 % Support at left end
supportB = 1;                 % Support at right end
force = 1000;                 % Applied force at mid-span

% Discretization
numElements = 10;             % Number of elements
elementLength = length / numElements;

% Element stiffness matrix
k = E * I / elementLength^3 * [12, 6 * elementLength, -12, 6 * elementLength;
                              6 * elementLength, 4 * elementLength^2, -6 * elementLength, 2 * elementLength^2;
                              -12, -6 * elementLength, 12, -6 * elementLength;
                              6 * elementLength, 2 * elementLength^2, -6 * elementLength, 4 * elementLength^2];

% Global stiffness matrix and load vector
K = zeros(numElements + 1, numElements + 1);
F = zeros(numElements + 1, 1);

% Assemble global stiffness matrix and load vector
for i = 1:numElements
    % Add contribution from each element in global stiffness matrix
    K(i:i+1, i:i+1) = K(i:i+1, i:i+1) + k;
    
    % Add contribution from each element in global load vector
    F(i:i+1) = F(i:i+1) + force * elementLength / 2 * [1; 1];
end

% Apply boundary conditions
K(1, 1) = supportA;
K(end, end) = supportB;
F(1) = 0;
F(end) = 0;

% Solve the linear system
displacements = K \ F;

% Compute bending moment and shear force at mid-span
moment = E * I / elementLength^2 * (displacements(numElements + 1) - displacements(numElements));
shearForce = E * I / elementLength^3 * (displacements(numElements + 1) - 2 * displacements(numElements) + displacements(numElements - 1));

% Plot the deflection along the beam
x = linspace(0, length, numElements + 1);
y = [0; displacements];
plot(x, y)
xlabel('Position along beam')
ylabel('Deflection')
title('Deflection of the beam')
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