Composite Plate Bending Analysis With Matlab Code <PC>

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

[ \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} ]

%% Finite Difference Grid Nx = 41; Ny = 25; % odd numbers to include center dx = a/(Nx-1); dy = b/(Ny-1); x = linspace(0, a, Nx); y = linspace(0, b, Ny); Composite Plate Bending Analysis With Matlab Code

[ \left(\frac{\partial^4 w}{\partial x^4}\right) {ij} \approx \frac{w {i-2,j} - 4w_{i-1,j} + 6w_{i,j} - 4w_{i+1,j} + w_{i+2,j}}{\Delta x^4} ]

% Load (uniform pressure) F(n) = 1000; % Pa end end % Reduced stiffness matrix (plane stress) Q11 =

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);

% Max deflection fprintf('Max deflection = %.2e m\n', max(w(:))); Q12 = nu12 E2/(1-nu12 nu21)

kappa = [kxx; kyy; 2*kxy]; % engineering curvatures

%% 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