This paper is dedicated to the investigation of simultaneous homogenization and dimension reduction of textile structures as elasticity problem with an energy in the von-Kármán-regime. An extension for deformations is presented allowing to use the decomposition of plate-displacements. The limit problem in terms of displacements is derived with the help of the unfolding operator and yields in the limit the von-Kármán plate with linear elastic cell-problems. It is shown, that for homogeneous isotropic beams in the structure, the resulting plate is orthotropic. As application of the obtained limit plate we study the buckling behavior of orthotropic textiles.

本文致力于研究在von-Kármán体制下同时具有能量弹性问题的纺织品结构的同时均质化和尺寸减小。提出了变形的扩展，允许使用板位移的分解。关于位移的极限问题是在展开算子的帮助下得出的，并在极限情况下产生具有线性弹性单元问题的von-Kármán板。结果表明，对于结构中的均质各向同性梁，所得板是正交各向异性的。作为获得的极限板的应用，我们研究了正交各向异性纺织品的屈曲行为。