Composite Plate Bending Analysis With Matlab Code Now

We’ll solve for deflection and then compute stresses in each ply. We discretize the plate into (N_x \times N_y) points. The biharmonic operator is approximated using central differences:

%% Compute ABD Matrix A = zeros(3,3); B = zeros(3,3); D = zeros(3,3); for k = 1:num_plies theta_k = theta(k) * pi/180; m = cos(theta_k); n = sin(theta_k); % Transformation matrix T = [m^2, n^2, 2 m n; n^2, m^2, -2 m n; -m n, m n, m^2-n^2]; % Q_bar = T * Q * T_inv Q = [Q11, Q12, 0; Q12, Q22, 0; 0, 0, Q66]; Q_bar = T * Q * T'; % Integrate through thickness A = A + Q_bar * (z(k+1)-z(k)); B = B + Q_bar * 0.5 * (z(k+1)^2 - z(k)^2); D = D + Q_bar * (1/3) * (z(k+1)^3 - z(k)^3); end % For symmetric laminate, B should be zero (numerically small) B = zeros(3,3); % enforce symmetry Composite Plate Bending Analysis With Matlab Code

% Reduced stiffness matrix (plane stress) Q11 = E1/(1-nu12 nu21); Q12 = nu12 E2/(1-nu12 nu21); Q22 = E2/(1-nu12 nu21); Q66 = G12; We’ll solve for deflection and then compute stresses

fprintf('D Matrix (N.m):\n'); disp(D);

% Interior points for i = 3:Nx-2 for j = 3:Ny-2 n = idx(i,j); % w_xxxx K(n, idx(i-2,j)) = K(n, idx(i-2,j)) + c1; K(n, idx(i-1,j)) = K(n, idx(i-1,j)) - 4 c1; K(n, idx(i,j)) = K(n, idx(i,j)) + 6 c1; K(n, idx(i+1,j)) = K(n, idx(i+1,j)) - 4 c1; K(n, idx(i+2,j)) = K(n, idx(i+2,j)) + c1; % w_yyyy K(n, idx(i,j-2)) = K(n, idx(i,j-2)) + c3; K(n, idx(i,j-1)) = K(n, idx(i,j-1)) - 4 c3; K(n, idx(i,j)) = K(n, idx(i,j)) + 6 c3; K(n, idx(i,j+1)) = K(n, idx(i,j+1)) - 4 c3; K(n, idx(i,j+2)) = K(n, idx(i,j+2)) + c3; % w_xxyy K(n, idx(i-1,j-1)) = K(n, idx(i-1,j-1)) + c2; K(n, idx(i-1,j)) = K(n, idx(i-1,j)) - 2 c2; K(n, idx(i-1,j+1)) = K(n, idx(i-1,j+1)) + c2; K(n, idx(i,j-1)) = K(n, idx(i,j-1)) - 2 c2; K(n, idx(i,j)) = K(n, idx(i,j)) + 4 c2; K(n, idx(i,j+1)) = K(n, idx(i,j+1)) - 2 c2; K(n, idx(i+1,j-1)) = K(n, idx(i+1,j-1)) + c2; K(n, idx(i+1,j)) = K(n, idx(i+1,j)) - 2*c2; K(n, idx(i+1,j+1)) = K(n, idx(i+1,j+1)) + c2; B = zeros(3