figure; surf(x 1000, y 1000, w*1e3); xlabel('x (mm)'); ylabel('y (mm)'); zlabel('Deflection (mm)'); title('Composite Plate Bending — [0/90/90/0] Laminate'); colormap(jet); colorbar; axis equal;
N = length(layup); z = cumsum([-sum(thicknesses)/2, thicknesses]); % interfaces ABD = zeros(6,6); for k = 1:N theta = layupk * pi/180; m = cos(theta); n = sin(theta); T = [m^2, n^2, 2 m n; n^2, m^2, -2 m n; -m n, m n, m^2-n^2]; Qbar = T \ Q * T; % transformed stiffness hk = z(k+1) - z(k); ABD(1:3,1:3) = ABD(1:3,1:3) + Qbar * hk; ABD(1:3,4:6) = ABD(1:3,4:6) + Qbar * (z(k+1)^2 - z(k)^2)/2; ABD(4:6,1:3) = ABD(4:6,1:3) + Qbar * (z(k+1)^2 - z(k)^2)/2; ABD(4:6,4:6) = ABD(4:6,4:6) + Qbar * (z(k+1)^3 - z(k)^3)/3; end A = ABD(1:3,1:3); B = ABD(1:3,4:6); D = ABD(4:6,4:6); Composite Plate Bending Analysis With Matlab Code
% Material properties (example: T300/5208 Carbon-epoxy) E1 = 181e9; % Pa E2 = 10.3e9; G12 = 7.17e9; nu12 = 0.28; nu21 = nu12 * E2/E1; figure; surf(x 1000, y 1000, w*1e3); xlabel('x (mm)');
When the above code is completed with a correct B matrix, running it for a 0.2m square, 5mm thick, [0/90/90/0] graphite/epoxy plate under 1000 Pa gives: 1.2. Governing Equations for Bending
% Extract A, B, D A = ABD(1:3,1:3); Bmat = ABD(1:3,4:6); D = ABD(4:6,4:6);
The following MATLAB script calculates the ABD matrix for a composite laminate and solves for the maximum deflection of a simply supported plate under a uniform load q₀.
Matrix (Coupling Stiffness): Relates in-plane forces to curvatures (and moments to strains). For symmetric laminates, Matrix (Bending Stiffness): Relates moments to curvatures. 1.2. Governing Equations for Bending