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.
% Define material stiffness matrix Q11 = E1 / (1 - nu12^2); Q22 = E2 / (1 - nu12^2); Q12 = nu12 * Q11; Q66 = G12; Q16 = 0; Q26 = 0; Composite Plate Bending Analysis With Matlab Code
% Solve for deflection and rotation w = q / (D11 * (1 - nu12^2)); theta_x = - (D12 / D11) * w; theta_y = - (D26 / D22) * w; where $M_x$, $M_y$, and $M_{xy}$ are the bending
% 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) $q$ is the transverse load
% 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);
% 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.