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);
[ \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} ] Composite Plate Bending Analysis With Matlab Code
% 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
We’ll solve for deflection and then compute stresses in each ply. We discretize the plate into (N_x \times N_y) points. The biharmonic operator is approximated using central differences: % Pa end end
kappa = [kxx; kyy; 2*kxy]; % engineering curvatures
% Load (uniform pressure) F(n) = 1000; % Pa end end