Composite Plate Bending Analysis With Matlab Code -

% Set rows for boundary to identity K(boundary_nodes, :) = 0; for n = boundary_nodes K(n,n) = 1; F(n) = 0; end

% Apply simply supported boundary conditions: w=0 and Mxx=0 => w,xx=0 on x-edges % We'll set w=0 on all edges and use ghost points to enforce curvature=0 % For simplicity, we set w=0 on boundary nodes and eliminate their equations. Composite Plate Bending Analysis With Matlab Code

[ \begin{Bmatrix} \mathbf{N} \ \mathbf{M} \end{Bmatrix} = \begin{bmatrix} \mathbf{A} & \mathbf{B} \ \mathbf{B} & \mathbf{D} \end{bmatrix} \begin{Bmatrix} \boldsymbol{\epsilon}^0 \ \boldsymbol{\kappa} \end{Bmatrix} ] % Set rows for boundary to identity K(boundary_nodes,

[ \frac{\partial^4 w}{\partial x^2 \partial y^2} \approx \frac{ w_{i-1,j-1} - 2w_{i-1,j} + w_{i-1,j+1} - 2w_{i,j-1} + 4w_{i,j} - 2w_{i,j+1} + w_{i+1,j-1} - 2w_{i+1,j} + w_{i+1,j+1} }{\Delta x^2 \Delta y^2} ] :) = 0

% Calculate stresses in each ply at top and bottom of ply fprintf('\nStress recovery at center (x=%.3f, y=%.3f):\n', x(i_center), y(j_center)); for k = 1:num_plies theta_k = theta(k) pi/180; m = cos(theta_k); n = sin(theta_k); T = [m^2, n^2, 2 m n; n^2, m^2, -2 m n; -m n, m n, m^2-n^2]; Q = [Q11, Q12, 0; Q12, Q22, 0; 0, 0, Q66]; z_top = z(k+1); z_bot = z(k); % Stress at top of ply (global coordinates) sigma_global_top = z_top * (D(1:3,1:3) \ kappa); % M = D kappa, sigma = M z/I?? Actually sigma_global = Q_bar * kappa * z % Correct method: curvatures -> strains = z kappa, then stress = Q_bar * strain strain_global = [kxx; kyy; 2*kxy] * z_top; stress_global_top = Q_bar * strain_global; stress_local_top = T \ stress_global_top; % transform to material coordinates (1,2,6)