create a system matrix that had a "finite element" structure/property in matlab

main.m
% Define the problem domain
x = [0 1 0 1];  % x-coordinates of the nodes
y = [0 0 1 1];  % y-coordinates of the nodes
elements = [1 2 3; 2 3 4];  % element connectivity

% Assign element properties
E = 1;  % Young's modulus
A = 1;  % cross-sectional area

% Assemble the stiffness matrix
numNodes = size(x, 2);
numElements = size(elements, 1);
numDOFs = numNodes * 2;  % number of degrees of freedom

K = zeros(numDOFs);  % initialize the system matrix

for elem = 1:numElements
    % Get the element connectivity
    nodes = elements(elem, :);
    x_elem = x(nodes);
    y_elem = y(nodes);
    
    % Calculate the element stiffness matrix
    [Ke] = calculateElementStiffness(x_elem, y_elem, E, A);
    
    % Assemble the element stiffness matrix into the global stiffness matrix
    for i = 1:3
        for j = 1:3
            K(2*nodes(i)-1, 2*nodes(j)-1) = K(2*nodes(i)-1, 2*nodes(j)-1) + Ke(2*i-1, 2*j-1);
            K(2*nodes(i), 2*nodes(j)) = K(2*nodes(i), 2*nodes(j)) + Ke(2*i, 2*j);
        end
    end
end

% Display the system matrix
disp(K);
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