% Numerical integration for i = 1:2 xi = gauss_pts(i); wxi = gauss_wts(i); for j = 1:2 eta = gauss_pts(j); wet = gauss_wts(j); % Compute shape functions and derivatives at (xi, eta) [B, detJ] = compute_B_matrix(xi, eta, a_elem, b_elem); % Element stiffness contribution Ke = Ke + B' * D * B * detJ * a_elem * b_elem * wxi * wet; % Nodal load vector (uniform pressure p0 on w DOF) [Nw, ~] = shape_functions(xi, eta); Fe(1:3:end) = Fe(1:3:end) + Nw * p0 * detJ * a_elem * b_elem * wxi * wet; end end
% At each node i, shape function for w gives 1 at node i, 0 at others. % Using bilinear shape functions for w alone would cause incompatibility. % For a working element, we use the ACM element (12 DOF). Simplified here: Composite Plate Bending Analysis With Matlab Code
%% 5. Assemble Global Matrices K_global = sparse(n_dof, n_dof); F_global = zeros(n_dof, 1); % Numerical integration for i = 1:2 xi
%% 9. Plot Deflection Surface figure; surf(X, Y, W'); xlabel('x (m)'); ylabel('y (m)'); zlabel('Deflection (m)'); title('Composite Plate Bending Deflection'); colormap(jet); colorbar; view(120,30); grid on; Simplified here: %% 5
Introduction Composite materials, particularly laminated fiber-reinforced polymers, have revolutionized aerospace, automotive, and civil engineering due to their high stiffness-to-weight and strength-to-weight ratios. However, analyzing the bending behavior of composite plates is more complex than isotropic plates due to orthotropic properties, layup sequences, and coupling effects (bending-stretching coupling).