Composite Plate Bending Analysis With Matlab Code May 2026

%% 8. Postprocessing % Extract deflection at nodes W = zeros(nx, ny); for iy = 1:ny for ix = 1:nx node = (iy-1) nx + ix; W(ix, iy) = U(3 (node-1)+1); end end

% For a fully functional version, please contact author or % implement shape functions from "Analysis of Laminated Composite Plates" by Reddy.

Mxx ; Myy ; Mxy = [D] * κxx ; κyy ; κxy We use a 4-node rectangular element (size 2a×2b in local coordinates). Each node has 3 DOF: w, θx = ∂w/∂y, θy = -∂w/∂x. 2.1 Shape Functions (non-conforming but widely used) The deflection w is approximated by a 12-term polynomial: Composite Plate Bending Analysis With Matlab Code

% Dummy B (3x12) - replace with actual derivatives in real code B = zeros(3,12); % B matrix structure: row1: d2w/dx2, row2: d2w/dy2, row3: 2*d2w/dxdy % For actual implementation, please refer to standard FEA textbooks.

%% 3. Compute Laminate Bending Stiffness Matrix D (3x3) D = zeros(3,3); for k = 1:n_layers theta = layup_angles(k) * pi/180; m = cos(theta); n = sin(theta); Each node has 3 DOF: w, θx = ∂w/∂y, θy = -∂w/∂x

%% 6. Apply Boundary Conditions (Simply Supported) % Simply supported: w = 0, and Mxx=0, Myy=0 approximately enforced by free θ % At x=0 and x=a: w=0, Myy=0 -> θy free, θx free (if not clamped) % Standard SS: w=0, moment normal to edge zero. % Here we enforce w=0 on all edges and keep θx, θy free.

% Laminate layup: symmetric [0/90/90/0] (4 layers) layup_angles = [0, 90, 90, 0]; % degrees n_layers = length(layup_angles); t_layer = h_total / n_layers; % each layer thickness Compute Laminate Bending Stiffness Matrix D (3x3) D

% Jacobian for rectangular element detJ = a_elem * b_elem;