I am trying to write code for the buckling of composite plates using the Ritz approximation but I can't understand something. According to Reddy (Mechanics of laminated composites), this is the equation of the principle of minimum potential energy (since we are concerned with buckling, q = 0 and the frequency omega = 0):
And the Ritz approximation
But after substituting 6.6.5 in 6.6.4 we get
It seems that delta w_0 has been substituted with X and Y but with indexes p and q, but it seems we do not sum over them. If that is the case, how do we go around solving this? Do we iterate over them but for some reason it is not written explicitly?