Composite Plate Bending Analysis With Matlab Code -

% Define material stiffness matrix Q11 = E1 / (1 - nu12^2); Q22 = E2 / (1 - nu12^2); Q12 = nu12 * Q11; Q66 = G12; Q16 = 0; Q26 = 0;

% Define flexural stiffness matrix D11 = (1/3) * (Q11 * h^3); D22 = (1/3) * (Q22 * h^3); D12 = (1/3) * (Q12 * h^3); D66 = (1/3) * (Q66 * h^3); D16 = (1/3) * (Q16 * h^3); D26 = (1/3) * (Q26 * h^3);

% Define plate properties a = 10; % plate length (m) b = 10; % plate width (m) h = 0.1; % plate thickness (m) E1 = 100e9; % Young's modulus in x-direction (Pa) E2 = 50e9; % Young's modulus in y-direction (Pa) G12 = 20e9; % shear modulus (Pa) nu12 = 0.3; % Poisson's ratio q = 1000; % transverse load (Pa) Composite Plate Bending Analysis With Matlab Code

where $M_x$, $M_y$, and $M_{xy}$ are the bending and twisting moments, $q$ is the transverse load, $D_{ij}$ are the flexural stiffnesses, and $\kappa_x$, $\kappa_y$, and $\kappa_{xy}$ are the curvatures.

The following MATLAB code performs a bending analysis of a composite plate using FSDT: % Define material stiffness matrix Q11 = E1

% Assemble global stiffness matrix K = [D11, D12, D16; D12, D22, D26; D16, D26, D66];

% Solve for deflection and rotation w = q / (D11 * (1 - nu12^2)); theta_x = - (D12 / D11) * w; theta_y = - (D26 / D22) * w; Q12 = nu12 * Q11

% Display results fprintf('Deflection: %.2f mm\n', w * 1000); fprintf('Rotation (x): %.2f degrees\n', theta_x * 180 / pi); fprintf('Rotation (y): %.2f degrees\n', theta_y * 180 / pi); This code defines the plate properties, material stiffness matrix, and flexural stiffness matrix. It then assembles the global stiffness matrix and solves for the deflection and rotation of the plate under a transverse load.