For the same laminate but with a uniformly distributed load ( q_0 = -1\ \textMPa ), the centre deflection is – about 60% larger than under sinusoidal load, as expected because the uniform load contains higher‑frequency Fourier components that excite more bending modes.
figure; surf(X, Y, W_grid); xlabel('x (m)'); ylabel('y (m)'); zlabel('Deflection (m)'); title(sprintf('Composite Plate Deflection (Max = %.2e m)', max(abs(w_deflection)))); colorbar; colormap(jet); shading interp; view(45,30);
% Shape functions for w and slopes (σ = -dw/dx, τ = dw/dy) % Node 1 (xi=-1, eta=-1) N(1) = 1/8 * (1-xi) (1-eta) ( (1+xi)^2*(1+eta)^2 - (1+xi)*(1+eta) - (1+xi)^2 - (1+eta)^2 + 2 ); % Similar for others – too lengthy. Instead, we use a simplified approach: % For demonstration and educational clarity, we assume a reduced integration % and approximate B using bilinear w + constant slopes. Full derivation is long.
% ============================================================ % Composite Plate Bending Analysis using 4-node Rectangular Element % Classical Laminated Plate Theory (CLPT) % Degrees of freedom per node: w, theta_x, theta_y % ============================================================
The moment-curvature relation:
% Assemble global stiffness matrix K = [D11, D12, D16; D12, D22, D26; D16, D26, D66];
(Extensional Stiffness Matrix): Relates in-plane forces to in-plane strains.