Composite Plate Bending Analysis With Matlab Code | PREMIUM × 2026 |

For a simply supported cross-ply laminate, this simplifies to ( w = 0 ) and ( \partial^2 w / \partial n^2 = 0 ) on edges.

N = length(layup); z = cumsum([-sum(thicknesses)/2, thicknesses]); % interfaces ABD = zeros(6,6); for k = 1:N theta = layup{k} * pi/180; m = cos(theta); n = sin(theta); T = [m^2, n^2, 2 m n; n^2, m^2, -2 m n; -m n, m n, m^2-n^2]; Qbar = T \ Q * T; % transformed stiffness hk = z(k+1) - z(k); ABD(1:3,1:3) = ABD(1:3,1:3) + Qbar * hk; ABD(1:3,4:6) = ABD(1:3,4:6) + Qbar * (z(k+1)^2 - z(k)^2)/2; ABD(4:6,1:3) = ABD(4:6,1:3) + Qbar * (z(k+1)^2 - z(k)^2)/2; ABD(4:6,4:6) = ABD(4:6,4:6) + Qbar * (z(k+1)^3 - z(k)^3)/3; end A = ABD(1:3,1:3); B = ABD(1:3,4:6); D = ABD(4:6,4:6); Composite Plate Bending Analysis With Matlab Code

% If symmetric, use D matrix. For unsymmetric, we could solve full system. % Here we proceed with D (bending only) for simplicity. For a simply supported cross-ply laminate, this simplifies

% w_xxxx term if i-2 >= 1, A_mat(idx, node(i-2,j)) = A_mat(idx, node(i-2,j)) + Dxx/dx^4; end A_mat(idx, node(i-1,j)) = A_mat(idx, node(i-1,j)) -4*Dxx/dx^4; A_mat(idx, node(i,j)) = A_mat(idx, node(i,j)) +6*Dxx/dx^4; A_mat(idx, node(i+1,j)) = A_mat(idx, node(i+1,j)) -4*Dxx/dx^4; if i+2 <= nx, A_mat(idx, node(i+2,j)) = A_mat(idx, node(i+2,j)) + Dxx/dx^4; end % w_yyyy term if j-2 >= 1, A_mat(idx, node(i,j-2)) = A_mat(idx, node(i,j-2)) + Dyy/dy^4; end A_mat(idx, node(i,j-1)) = A_mat(idx, node(i,j-1)) -4*Dyy/dy^4; A_mat(idx, node(i,j)) = A_mat(idx, node(i,j)) +6*Dyy/dy^4; A_mat(idx, node(i,j+1)) = A_mat(idx, node(i,j+1)) -4*Dyy/dy^4; if j+2 <= ny, A_mat(idx, node(i,j+2)) = A_mat(idx, node(i,j+2)) + Dyy/dy^4; end % w_xxyy term coef = 2*Dxy/(dx^2 * dy^2); if i-1>=1 && j-1>=1, A_mat(idx, node(i-1,j-1)) = A_mat(idx, node(i-1,j-1)) + coef; end if i-1>=1, A_mat(idx, node(i-1,j)) = A_mat(idx, node(i-1,j)) -2*coef; end if i-1>=1 && j+1<=ny, A_mat(idx, node(i-1,j+1)) = A_mat(idx, node(i-1,j+1)) + coef; end if j-1>=1, A_mat(idx, node(i,j-1)) = A_mat(idx, node(i,j-1)) -2*coef; end A_mat(idx, idx) = A_mat(idx, idx) +4*coef; if j+1<=ny, A_mat(idx, node(i,j+1)) = A_mat(idx, node(i,j+1)) -2*coef; end if i+1<=nx && j-1>=1, A_mat(idx, node(i+1,j-1)) = A_mat(idx, node(i+1,j-1)) + coef; end if i+1<=nx, A_mat(idx, node(i+1,j)) = A_mat(idx, node(i+1,j)) -2*coef; end if i+1<=nx && j+1<=ny, A_mat(idx, node(i+1,j+1)) = A_mat(idx, node(i+1,j+1)) + coef; end end end % Here we proceed with D (bending only) for simplicity