拉伸薄板中椭圆孔的拉伸屈曲
Tensional Buckling Around an Elliptic Hole in a Stretched Sheet
摘要：
众所周知，环形板在边缘处施加轴对称拉伸载荷时会起皱。在该系统中，由于泊松效应，在方位角方向上出现了受压区域，产生了不相容的长度过剩，使得膜不得不屈曲出平面。然后，沿拉伸主应力方向出现径向褶皱。这种所谓的Lamé组态已被广泛地用作计算非线性不稳定性的理论和实验范例。在这项工作中，我们探讨的后果，考虑在无限拉伸膜的椭圆形孔改变这个模型配置的几何形状。使用Kolosoff-Inglis解决方案，我们分析了孔周围的应力场，并确定了三个可能的区域：拉紧，单向拉伸和松弛区域。根据这些定义，我们在相图中将板的不同应力状态分类为孔偏心率和所施加的张力的函数。最后，我们量化了张力线如何随孔的几何形状而变化，并讨论了可能出现的屈曲模式的结果。
英文摘要：
It is well known that an annular sheet could wrinkle as a result of axisymmetric tensile loads applied at the edges. In this system, regions under compression appear due to Poisson effect in the azimuthal direction yielding an incompatible excess in length, so that the membrane has to buckle out of the plane. Then, radial wrinkles emerge following the direction of the tensile principal stress. This so called Lamé configuration has been widely used as theoretical and experimental paradigms for wrinkling instabilities. In this work, we explore the consequences of changing the geometry of this model configuration by considering an elliptic hole in an infinite stretched membrane. Using the Kolosoff-Inglis solution, we analyse the stress field around the hole and identify three possible regions: taut, unidirectionally tensioned and slack regions. According to these definitions, we classify in a phase diagram the different stress states of the sheet as function of the hole eccentricity and of the applied tensions. Finally, we quantify how the tension lines vary with the geometry of the hole and discuss possible outcomes on the emerging buckled patterns.
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