A generalized computational approach to stability of static equilibria of nonlinearly elastic rods in the presence of constraints
A generalized computational approach to stability of static equilibria of nonlinearly elastic rods in the presence of constraints
复制标题
存在约束时非线性弹性杆静平衡稳定性的通用计算方法
DOI：
10.1016/j.cma.2010.02.007
复制
发表时间：
2010
影响因子：
7.2
通讯作者：
T. Healey
中科院分区：
文献类型：
--
作者：
Ajeet Kumar;T. Healey
基于线性化动力学稳定性准则，提出了非线性弹性杆在一般载荷、边界条件和约束（点式和积分型）下的静态平衡稳定性的一般方法。离散化的控制方程导致一个非标准的（奇异）广义特征值问题。提出了一种新的有效的稀疏矩阵友好的算法来确定其最左边的几个特征值，这反过来又产生稳定/不稳定的信息。对于保守的问题，所产生的线性化动力学稳定性准则的特征值问题也被证明是等价的，所产生的约束局部极小值的势能的测定。我们用几个例子来说明该方法。一种新的变分制定可扩展和不可剪切杆的范围内的一个例子问题。
We present a generalized approach to stability of static equilibria of nonlinearly elastic rods, subjected to general loading, boundary conditions and constraints (of both point-wise and integral type), based upon the linearized dynamics stability criterion. Discretization of the governing equations leads to a non-standard (singular) generalized eigenvalue problem. A new efficient sparse-matrix-friendly algorithm is presented to determine its few left-most eigenvalues, which, in turn, yield stability/instability information. For conservative problems, the eigenvalue problem arising from the linearized dynamics stability criterion is also shown to be equivalent to that arising in the determination of constrained local minima of the potential energy. We illustrate the method with several examples. A novel variational formulation for extensible and unshearable rods is also proposed within the context of one of the example problems.
DNA 弹性杆模型及其在单核小体 DNA 小环三级结构中的应用。
影响因子：
3.4
作者：
Swigon,D;Coleman,BD;Tobias,I
通讯作者：
Tobias,I