Analysis With Matlab Code - Composite Plate Bending

The code is structured into main script and functions. It performs:

% Post‑process: extract nodal w, phix, phiy w = zeros(nNodes,1); phix = zeros(nNodes,1); phiy = zeros(nNodes,1); for i = 1:nNodes base = (i-1)*5; w(i) = U(base+3); phix(i) = U(base+4); phiy(i) = U(base+5); end

% Initialize global stiffness and force K_global = sparse(n_dof, n_dof); F_global = zeros(n_dof, 1);

[ \boldsymbol\varepsilon^0 = \beginBmatrix \frac\partial u_0\partial x \[4pt] \frac\partial v_0\partial y \[4pt] \frac\partial u_0\partial y + \frac\partial v_0\partial x \endBmatrix, \qquad \boldsymbol\kappa = \beginBmatrix \frac\partial \phi_x\partial x \[4pt] \frac\partial \phi_y\partial y \[4pt] \frac\partial \phi_x\partial y + \frac\partial \phi_y\partial x \endBmatrix. ] Composite Plate Bending Analysis With Matlab Code

clear; clc; close all;

We assume the plate has a displacement field based on First-Order Shear Deformation Theory (FSDT). This accounts for transverse shear deformation, which is critical for thick composite plates.

for k = 1:nlayers theta = pliesk * pi/180; c = cos(theta); s = sin(theta); The code is structured into main script and functions

Bs(1, col_w) = dN_dx(1,i); Bs(1, col_phix) = N(i); Bs(2, col_w) = dN_dx(2,i); Bs(2, col_phiy) = N(i);

where [D] is the 3×3 bending stiffness matrix from laminate theory, and [B] relates curvatures to nodal displacements (w and rotations θₓ, θᵧ). For a 4-node rectangle with 3 DOF per node (w, θₓ, θᵧ), the element has 12 DOFs.

fprintf('Layer %d (%.0f deg):\n', k, layers(k)); fprintf(' Top (z=%.4f): Sx=%.2f MPa\n', z_top_k, stress_top(1)/1e6); end This accounts for transverse shear deformation, which is

z_prev = -h/2; for i = 1:nlayers theta = layers(i) * pi/180; m = cos(theta); n = sin(theta);

% Build finite difference matrix N_total = nx * ny; A_mat = sparse(N_total, N_total); F = zeros(N_total,1);

Relates bending to in-plane forces (zero for symmetric layups).