Composite Plate Bending Analysis With Matlab Code -

%% 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

%% Geometry a = 0.5; % length (m) b = 0.3; % width ply_thick = 0.125e-3; % m num_plies = 4; h = num_plies * ply_thick; % total thickness

We assemble a sparse linear system ( [K] {w} = {f} ) and solve. Below is the complete code. It computes deflections, curvatures, and then stresses in each ply at Gauss points. Composite Plate Bending Analysis With Matlab Code

% Max deflection fprintf('Max deflection = %.2e m\n', max(w(:)));

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

strain_global_bot = [kxx; kyy; 2*kxy] * z_bot; stress_global_bot = Q_bar * strain_global_bot; stress_local_bot = T \ stress_global_bot;

% Central difference coefficients c1 = D(1,1)/dx^4; c2 = (2*(D(1,2)+2 D(3,3)))/(dx^2 dy^2); c3 = D(2,2)/dy^4; % Max deflection fprintf('Max deflection = %

% Reduced stiffness matrix (plane stress) Q11 = E1/(1-nu12 nu21); Q12 = nu12 E2/(1-nu12 nu21); Q22 = E2/(1-nu12 nu21); Q66 = G12;