%% Step 6: Navier solution for simply supported plate under sinusoidal load % w(x,y) = w0 * sin(pi x/a) * sin(pi y/b) % Coefficients alpha = pi / a; beta = pi / b; term1 = D_bend(1,1) * alpha^4; term2 = 2 * (D_bend(1,2) + 2*D_bend(3,3)) * alpha^2 * beta^2; term3 = D_bend(2,2) * beta^4; denom = term1 + term2 + term3; w0 = q0 / denom; % central deflection (m)
% z at top of this ply z_top = z_coords(i+1); eps_global = eps0 + z_top * k; sigma_global = Qbar * eps_global; Composite Plate Bending Analysis With Matlab Code
| Feature | Implementation Strategy | |---------|------------------------| | Arbitrary boundary conditions | Use Rayleigh-Ritz method or finite element discretization in MATLAB PDE Toolbox | | Transverse shear deformation | Implement First-Order Shear Deformation Theory (FSDT) — requires (A_55, A_44) | | Multiple loads (point, uniform) | Use Fourier series expansion for load shape | | Variable stacking sequences | Add command-line input for layup angles | | Failure analysis | Integrate Tsai-Wu or Tsai-Hill criteria for each ply | %% Step 6: Navier solution for simply supported
To analyze the bending of a composite plate, engineers typically use for thin plates or First-order Shear Deformation Theory (FSDT) for thicker ones. These theories calculate how various lamina properties and stacking sequences contribute to the overall stiffness, often represented by the [ABD] matrix . 1. Define Material and Geometry Define Material and Geometry The deflection $w$ within
The deflection $w$ within an element is approximated using shape functions $N_i$: $$ w(x,y) = \sum_i=1^4 N_i q_i $$ Where $q_i$ is the displacement vector at node $i$.
% Reduced stiffness in global coordinates: Qbar = T1 * Q * T1^T Qbar = T1 * Q * T1';