Composite Plate Bending Analysis With Matlab Code File

dx2 = dx^2; dy2 = dy^2; kxx = (w(i_center-1,j_center) - 2 w(i_center,j_center) + w(i_center+1,j_center)) / dx2; kyy = (w(i_center,j_center-1) - 2 w(i_center,j_center) + w(i_center,j_center+1)) / dy2; kxy = (w(i_center-1,j_center-1) - w(i_center-1,j_center+1) - w(i_center+1,j_center-1) + w(i_center+1,j_center+1)) / (4 dx dy);

[ D_{11} \frac{\partial^4 w}{\partial x^4} + 2(D_{12}+2D_{66}) \frac{\partial^4 w}{\partial x^2 \partial y^2} + D_{22} \frac{\partial^4 w}{\partial y^4} = q(x,y) ] Composite Plate Bending Analysis With Matlab Code

% 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) dx2 = dx^2; dy2 = dy^2; kxx =

%% Stress Recovery % Compute curvatures at center element (using central diff) i_center = round(Nx/2); j_center = round(Ny/2); if mod(Nx,2)==0, i_center=i_center+1; end if mod(Ny,2)==0, j_center=j_center+1; end dx2 = dx^2

% 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.

boundary_nodes = []; for i = 1:Nx for j = [1, Ny] boundary_nodes = [boundary_nodes, idx(i,j)]; end end for j = 2:Ny-1 boundary_nodes = [boundary_nodes, idx(1,j), idx(Nx,j)]; end boundary_nodes = unique(boundary_nodes);

Boundary conditions (simply supported): [ w = 0,\quad M_{xx}=0 \Rightarrow \frac{\partial^2 w}{\partial x^2}=0 \text{ on } x=0,a ] (same for y-direction)