𝜕Mxy𝜕x+𝜕My𝜕y−Qy=0the fraction with numerator partial cap M sub x y end-sub and denominator partial x end-fraction plus the fraction with numerator partial cap M sub y and denominator partial y end-fraction minus cap Q sub y equals 0
Here ( \barQ_ij^(k) ) are the transformed reduced stiffnesses of the ( k)-th ply. Composite Plate Bending Analysis With Matlab Code
% Loop over odd m and n (others zero for uniform load) for m = 1:2:Mmax for n = 1:2:Nmax % Determine Qmn based on load type if strcmp(load_type, 'sinusoidal') if m == 1 && n == 1 Qmn(m,n) = q0; else Qmn(m,n) = 0; end elseif strcmp(load_type, 'uniform') Qmn(m,n) = 16 * q0 / (pi^2 * m * n); else error('Load type not recognized. Use ''sinusoidal'' or ''uniform''.'); end B (Coupling Stiffness):
the 2 by 1 column matrix; cap N, cap M end-matrix; equals the 2 by 2 matrix; Row 1: cap A, cap B; Row 2: cap B, cap D end-matrix; the 2 by 1 column matrix; epsilon to the 0 power, kappa end-matrix; A (Extensional Stiffness): Relates in-plane loads to in-plane strains. B (Coupling Stiffness): n) = q0