For a complete, runnable version with correct DOF mapping, please refer to the full implementation notes or contact the author.
[ \beginBmatrix \mathbfN \ \mathbfM \endBmatrix = \beginbmatrix \mathbfA & \mathbfB \ \mathbfB & \mathbfD \endbmatrix \beginBmatrix \boldsymbol\varepsilon^0 \ \boldsymbol\kappa \endBmatrix ] Composite Plate Bending Analysis With Matlab Code
function Bs = shear_Bmatrix(dNdxi, invJ, ndof, nNodes) % Shear strain-displacement matrix Bs = zeros(2, ndof*nNodes); for i = 1:nNodes dNdx = invJ(1,1)*dNdxi(1,i) + invJ(1,2)*dNdxi(2,i); dNdy = invJ(2,1)*dNdxi(1,i) + invJ(2,2)*dNdxi(2,i); % DOF order: w, thetax, thetay Bs(1, (i-1)*ndof + 1) = dNdx; % gamma_xz = dw/dx + thetax Bs(1, (i-1)*ndof + 2) = 1; % thetax Bs(2, (i-1)*ndof + 1) = dNdy; % gamma_yz = dw/dy + thetay Bs(2, (i-1)*ndof + 3) = 1; % thetay end end For a complete, runnable version with correct DOF
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 Apply Loads and Solve: Define the transverse load
Link between stretching and bending (zero for symmetric laminates). D (Bending stiffness): Resistance to bending and twisting. Apply Loads and Solve: Define the transverse load ( ) and solve the governing differential equation (e.g., ) for displacement (