Abstract 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 Foppl von Karman (FvK) or Extended Foppl von Karman (EFvK) shell models.

中文翻译：

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一种基于多尺度方法的变向皱纹降阶建模

摘要 我们讨论了一种基于傅立叶级数的降阶建模技术，当皱纹的方向不均匀时，薄膜起皱。事实上，褶皱的方向取决于几何形状和载荷，例如在穿孔膜或非均匀残余应力的情况下。这种基于傅里叶的缩减技术是著名的 Ginzburg-Landau 方程的扩展，它已应用于梁、板、夹层结构和薄膜基板系统的起皱。得到的简化宏观模型可以通过有限元进行离散化。在本文中，离散基尔霍夫三角 (DKT18) 类型的有限元用于数值应用，起始模型是 Foppl von Karman (FvK) 或扩展 Foppl von Karman (EFvK) 壳模型。