论文标题
薄弹性结构中的各种问题
Variational problems in thin elastic structures
论文作者
论文摘要
对于由2D-FOPPL-VONKármán板模型描述的两种不同的有关薄弹性结构的情况，我们获得了能量缩放定律。首先，假设参考几何形状是奇异的多个多孔的几何形状，我们获得了相当最佳的上层和下部能量边界，我们突出显示了这些边界如何扩展WRT。厚度参数$ h。在这种情况下，我们为径向对称可允许的地图提供了一项能量尺度法律，这一次，取决于$ h $和凹痕深度$ d。
For two different scenarios regarding thin elastic structures, described by 2d-Föppl-von Kármán plate models, we obtain energy scaling laws. Firstly, assuming the reference geometry being that of a singular excess-cone, we obtain fairly optimal upper- and lower energy bounds and we highlight how those bounds scale wrt. the thickness-parameter $h.$ Secondly, we consider the half sphere, while being indented by a thin object at the top and perpendicular to its surface. In this situation we provide an energy-scaling law, for radial symmetric admissible maps, this time, depending on $h$ and the indentation depth $d.$
