A Variational Rod Model with a Singular Nonlocal Potential
A Variational Rod Model with a Singular Nonlocal Potential
复制标题
具有奇异非局部势的变分杆模型
DOI：
10.1007/s00205-010-0368-9
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发表时间：
2011
影响因子：
2.5
通讯作者：
T. Seidman
中科院分区：
文献类型：
--
作者：
Kathleen A. Hoffman;T. Seidman
弹性杆的经典理论没有考虑到这样的可能性，即大变形可能涉及沿杆沿着占据相同物理空间的不同点。我们发展了一个弹性杆模型与成对排斥的潜力，这样，如果两个非相邻点沿着杆是接近的物理空间，有一个能量障碍，防止接触，而附近的点沿着杆的潜力是可描述的经典。这个框架的发展证明存在的极小值内的每个同伦类，其中的拓扑同伦的概念的曲线被推广到弹性杆的框架曲线。最后，导出了相应的一阶最优性条件，并用于研究极小解的正则性。
The classical theory of elastic rods does not account for the possibility that large deformations may involve distinct points along the rod occupying the same physical space. We develop an elastic rod model with a pairwise repulsive potential such that, if two non-adjacent points along the rod are close in physical space, there is an energy barrier which prevents contact while for points nearby along the rod the potential is describable classically. This framework is developed to prove the existence of minimizers within each homotopy class, where the idea of topological homotopy of a curve is generalized to elastic rods as framed curves. Finally, the relevant first-order optimality conditions are derived and used to investigate the regularity of minimizers.