Composite Plate Bending Analysis With Matlab Code Direct

Do you need to modify the code for (such as fully clamped edges)? Share public link

for different loading types (e.g., concentrated load). Add stress calculations ( ) at specific ply layers.

% ========================================================================= % Composite Plate Bending Analysis using Classical Laminate Plate Theory % Boundary Conditions: Simply Supported on all edges (Navier's Method) % ========================================================================= clear; clc; close all; %% 1. Geometry and Load Data a = 0.5; % Plate length along x-axis (m) b = 0.5; % Plate width along y-axis (m) q0 = -10000; % Uniform transverse load (Pa) %% 2. Material Properties (E1, E2, nu12, G12) E1 = 140e9; % Longitudinal elastic modulus (Pa) E2 = 10e9; % Transverse elastic modulus (Pa) nu12 = 0.3; % Major Poisson's ratio G12 = 5e9; % In-plane shear modulus (Pa) nu21 = nu12 * E2 / E1; %% 3. Layup Configuration % Define ply orientations (degrees) and thicknesses (m) theta = [0, 90, 90, 0]; ply_t = 0.00125 * ones(1, length(theta)); % 1.25 mm per ply total_h = sum(ply_t); % Calculate Z-coordinates for each ply interface relative to mid-plane z = zeros(1, length(theta) + 1); z(1) = -total_h / 2; for k = 1:length(theta) z(k+1) = z(k) + ply_t(k); end %% 4. Calculate Laminate Bending Stiffness Matrix [D] Q = zeros(3,3); Q(1,1) = E1 / (1 - nu12*nu21); Q(1,2) = nu21 * E1 / (1 - nu12*nu21); Q(2,1) = Q(1,2); Q(2,2) = E2 / (1 - nu12*nu21); Q(3,3) = G12; D = zeros(3,3); for k = 1:length(theta) t = deg2rad(theta(k)); % Transformation matrix components m = cos(t); n = sin(t); T = [m^2, n^2, 2*m*n; n^2, m^2, -2*m*n; -m*n, m*n, m^2-n^2]; % Transformed reduced stiffness matrix Qbar = T \ Q * (T^-1).'; % Accumulate into bending stiffness matrix D D = D + (1/3) * Qbar * (z(k+1)^3 - z(k)^3); end %% 5. Navier's Solution for Deflection Nx = 50; Ny = 50; % Grid resolution for plotting x = linspace(0, a, Nx); y = linspace(0, b, Ny); [X, Y] = meshgrid(x, y); W = zeros(Nx, Ny); % Initialize deflection matrix M_max = 30; N_max = 30; % Fourier series truncation limits for m = 1:2:M_max for n = 1:2:N_max % Load coefficient for uniform distribution Qmn = (16 * q0) / ((pi^2) * m * n); % Denominator based on governing equation denom = (pi^4) * (D(1,1)*(m/a)^4 + 2*(D(1,2) + 2*D(3,3))*(m/a)^2*(n/b)^2 + D(2,2)*(n/b)^4); % Deflection amplitude Wmn = Qmn / denom; % Construct displacement field W = W + Wmn * sin(m * pi * X / a) .* sin(n * pi * Y / b); end end %% 6. Visualization figure('Color', 'w'); surf(X, Y, W*1000, 'EdgeColor', 'interp'); colormap jet; colorbar; title('Transverse Deflection of Composite Plate'); xlabel('Length a (m)'); ylabel('Width b (m)'); zlabel('Deflection w (mm)'); view(-37.5, 30); grid on; % Display max deflection in command window fprintf('Maximum central deflection: %.4f mm\n', min(W(:))*1000); Use code with caution. Result Analysis and Interpretation Composite Plate Bending Analysis With Matlab Code

% Layup Definition % Format: [Angle (deg), Thickness (m)] % Symmetric 4-layer layup [0/90]_s layup = [ 0, thick/4; 90, thick/4; 90, thick/4; 0, thick/4 ];

This article has presented a complete, ready‑to‑use Matlab code for the bending analysis of simply supported composite plates using Classical Lamination Theory and the Navier solution. The code is well‑commented and modular, making it easy to modify for different laminates, loads, and plate geometries. Users can obtain deflection, curvature, strain and stress distributions with just a few input changes. Do you need to modify the code for

To solve this in MATLAB, we discretize the plate into elements.

Q12=ν12E21−ν12ν21,Q66=G12cap Q sub 12 equals the fraction with numerator nu sub 12 cap E sub 2 and denominator 1 minus nu sub 12 nu sub 21 end-fraction comma space cap Q sub 66 equals cap G sub 12 2. Transformation to Global Coordinates When fibers are oriented at an angle Layup Configuration % Define ply orientations (degrees) and

if abs(D16) > 1e-3 || abs(D26) > 1e-3 warning('D16 or D26 not zero – using specially orthotropic formula may be inaccurate.'); end

[NM]=[ABBD][ϵ0κ]the 2 by 1 column matrix; cap N, cap M end-matrix; equals the 2 by 2 matrix; Row 1: cap A, cap B; Row 2: cap B, cap D end-matrix; the 2 by 1 column matrix; epsilon to the 0 power, kappa end-matrix; For a simple bending analysis (where ), you solve for mid-plane curvatures ( ) to find the plate's deflection. 3. MATLAB Code Implementation