% Compute ply positions (z coordinates) z_coords = linspace(-h_total/2, h_total/2, n_layers+1);
% Build finite difference matrix N_total = nx * ny; A_mat = sparse(N_total, N_total); F = zeros(N_total,1); Composite Plate Bending Analysis With Matlab Code
% Laminate layup: symmetric [0/90/90/0] (4 layers) layup_angles = [0, 90, 90, 0]; % degrees n_layers = length(layup_angles); t_layer = h_total / n_layers; % each layer thickness % Compute ply positions (z coordinates) z_coords =
w(x,y)=∑m=1∞∑n=1∞Wmnsin(mπxa)sin(nπyb)w open paren x comma y close paren equals sum from m equals 1 to infinity of sum from n equals 1 to infinity of cap W sub m n end-sub sine open paren the fraction with numerator m pi x and denominator a end-fraction close paren sine open paren the fraction with numerator n pi y and denominator b end-fraction close paren A_mat = sparse(N_total
For numerical integration we use 2×2 Gauss quadrature (full integration) which works well for bending‑dominated problems; however, for very thin plates, shear locking may appear, which can be alleviated by selective reduced integration (2×2 for bending, 1×1 for shear) – we implement the latter.