论文标题
具有调节刚度的弹性曲线分叉
Bifurcation of elastic curves with modulated stiffness
论文作者
论文摘要
我们研究了固定长度的封闭平面弹性曲线的平衡构型，其刚度（也称为弯曲刚度）取决于额外的密度变量。潜在的变分模型依赖于形状和密度的弯曲能量最小化，并且可以被视为用于异质生物膜的Canham-Helfrich模型的一维类似物。我们提出了具有密度依赖性刚度系数的广义Euler-Bernoulli Elastica功能。为了治疗问题的固有非凸度，我们通过密度梯度项在模型中引入了一个额外的长度比例。我们得出了Euler-Lagrange方程的系统，并研究了有关模型参数的解决方案的分叉结构。介绍了分析结果和数值结果。
We investigate the equilibrium configurations of closed planar elastic curves of fixed length, whose stiffness, also known as the bending rigidity, depends on an additional density variable. The underlying variational model relies on the minimization of a bending energy with respect to shape and density and can be considered as a one-dimensional analogue of the Canham-Helfrich model for heterogeneous biological membranes. We present a generalized Euler-Bernoulli elastica functional featuring a density-dependent stiffness coefficient. In order to treat the inherent nonconvexity of the problem we introduce an additional length scale in the model by means of a density gradient term. We derive the system of Euler-Lagrange equations and study the bifurcation structure of solutions with respect to the model parameters. Both analytical and numerical results are presented.
