F Ur Mathematik in Den Naturwissenschaften Leipzig Global Injectivity and Topological Constraints for Spatial Nonlinearly Elastic Rods Global Injectivity and Topological Constraints for Spatial Nonlinearly Elastic Rods
F Ur Mathematik in Den Naturwissenschaften Leipzig Global Injectivity and Topological Constraints for Spatial Nonlinearly Elastic Rods Global Injectivity and Topological Constraints for Spatial Nonlinearly Elastic Rods
复制标题
F Ur Mathematik in Den Naturwissenschaften Leipzig 空间非线性弹性杆的全局注入性和拓扑约束 空间非线性弹性杆的全局注入性和拓扑约束
DOI：
--
复制
发表时间：
--
期刊：
影响因子：
--
通讯作者：
F. Schuricht
中科院分区：
文献类型：
--
作者：
F. Schuricht
本文研究了可剪非线性弹性杆空间变形的局部和整体内射性。在非线性弹性力学中，我们采用了Ciarlet & Ne引入的一个分析条件来保证这种情况下的整体内射性。特别是，我们验证了存在的能量最小化的平衡状态，没有自穿透，这也可能是由一个刚性障碍物的限制。此外，我们考虑特殊情况下，杆的两端粘在一起。在这种情况下，我们仍然可以施加拓扑限制，例如，杆的形状属于给定的结类型。我们再次证明了一个全局内射能量极小的存在，现在除了尊重拓扑约束。请注意，超螺旋DNA分子的研究是所提出的结果的一个重要应用。
In this paper we study the local and global injectivity of spatial deformations of shearable nonlinearly elastic rods. We adopt an analytical condition introduced by Ciarlet & Ne cas in nonlinear elasticity to ensure global injectivity in that case. In particular we verify the existence of an energy minimizing equilibrium state without self-penetration which may be also restricted by a rigid obstacle. Furthermore we consider the special situation where the ends of the rod are glued together. In that case we can still impose topological restrictions as, e.g., that the shape of the rod belongs to a given knot type. Again we show the existence of a globally injective energy minimizer which now in addition respects the topological constraints. Note that the investigation of super-coiled DNA molecules is an important application of the presented results.