% Displacements w = (q / (24 * D)) * (Lx^4 + Ly^4);
1m5the fraction with numerator 1 and denominator m to the fifth power end-fraction
If you can tell me the and load cases you are interested in, I can help modify the code for your project. I can also: Add a plot of the deflection surface. Implement FSDT for thicker laminates. Calculate buckling loads .
q(x,y)=∑m=1∞∑n=1∞Qmnsin(mπxa)sin(nπyb)q open paren x comma y close paren equals sum from m equals 1 to infinity of sum from n equals 1 to infinity of cap Q sub m n end-sub sine open paren the fraction with numerator m pi x and denominator a end-fraction close paren sine open paren the fraction with numerator n pi y and denominator b end-fraction close paren For a uniformly distributed load Composite Plate Bending Analysis With Matlab Code
If you want to modify this script for a different engineering application, let me know your target , boundary conditions , or material options , and I can adapt the source code for you.
matrix represents the bending stiffness of the laminate, mapping bending moments directly to plate curvatures.
The deflection w is approximated by a 12-term polynomial: % Displacements w = (q / (24 *
% 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
The execution of the script generates a displacement profile highlighting critical structural characteristics. Maximum Deflection Location
$$\beginbmatrix M_x \ M_y \ M_xy \endbmatrix = \beginbmatrix D_11 & D_12 & D_16 \ D_12 & D_22 & D_26 \ D_16 & D_26 & D_66 \endbmatrix \beginbmatrix \kappa_x \ \kappa_y \ \kappa_xy \endbmatrix$$ Calculate buckling loads
Q = [Q11, Q12, 0; Q12, Q22, 0; 0, 0, Q66];
Aij=∑k=1n(Q̄ij)k(zk−zk−1)cap A sub i j end-sub equals sum from k equals 1 to n of open paren cap Q bar sub i j end-sub close paren sub k open paren z sub k minus z sub k minus 1 end-sub close paren Coupling Stiffness Matrix (
% Plot deformed shape figure; trisurf(elements, nodeCoords(:,1), nodeCoords(:,2), W, W, 'EdgeColor', 'none'); colormap(jet); colorbar; title(sprintf('Deformed composite plate (max deflection = %.4f mm)', max(W)*1000)); xlabel('x (m)'); ylabel('y (m)'); zlabel('Deflection (m)'); axis equal; view(45,30);
end
This is the core logic.