Euler-Lagrange Equations for Nonlinearly Elastic Rods with Self-Contact
Euler-Lagrange Equations for Nonlinearly Elastic Rods with Self-Contact
复制标题
自接触非线性弹性杆的欧拉-拉格朗日方程
DOI：
10.1007/s00205-003-0253-x
复制
发表时间：
2003
影响因子：
2.5
通讯作者：
H. Mosel
中科院分区：
文献类型：
--
作者：
F. Schuricht;H. Mosel
摘要：我们推导了自接触非线性弹性杆的欧拉-拉格朗日方程。 排除体积约束制定的上限的中心线的全球曲率。这个条件被证明是为了保证全球注射的弹性杆的变形。拓扑约束，例如规定的结和链接类，以模拟观察到的打结和超螺旋现象，例如，在DNA分子中，通过使用同位素和高斯连接数的概念来包括。作为非光滑侧边条件的整体曲率界限需要使用Clarke广义梯度来获得接触力的显式结构，其自然地表现为欧拉-拉格朗日方程中的拉格朗日乘数。讨论了横截性条件，给出了应变、力矩、中心线和指向矢的较高规律性。
Abstract. We derive the Euler-Lagrange equations for nonlinearly elastic rods with self-contact. The excluded-volume constraint is formulated in terms of an upper bound on the global curvature of the centre line. This condition is shown to guarantee the global injectivity of the deformation of the elastic rod. Topological constraints such as a prescribed knot and link class to model knotting and supercoiling phenomena as observed, e.g., in DNA-molecules, are included by using the notion of isotopy and Gaussian linking number. The bound on the global curvature as a nonsmooth side condition requires the use of Clarke's generalized gradients to obtain the explicit structure of the contact forces, which appear naturally as Lagrange multipliers in the Euler-Lagrange equations. Transversality conditions are discussed and higher regularity for the strains, moments, the centre line and the directors is shown.
影响因子：
56.9
作者：
WASSERMAN, SA;COZZARELLI, NR
通讯作者：
COZZARELLI, NR
通过计算机模拟的超螺旋 DNA 能量学和动力学。
影响因子：
5.6
作者：
Schlick,T;Olson,WK
通讯作者：
Olson,WK