We discuss a reduced-order modeling technique based on Fourier series for membrane wrinkling when the orientation of the wrinkles is not uniform. Indeed, the orientation of the wrinkles depends on geometry and loading, for instance in the case of perforated membrane or with non uniform residual stresses. This Fourier-based reduction technique is an extension of the famous Ginzburg-Landau equation and it has been applied to the wrinkling of beams, plates, sandwich structures and film-substrate systems. The obtained reduced macroscopic models can be discretized by finite elements. In this paper, a finite element of type Discrete Kirchhoff Triangle (DKT18) is used in the numerical applications, the starting model being the Föppl von Karman (FvK) or Extended Föppl von Karman (EFvK) shell models.