论文标题
弹性膜跨越可变形边界
Elastic membranes spanning deformable boundaries
论文作者
论文摘要
我们对跨越封闭曲线的弹性膜进行各种分析，该曲线可以维持弯曲和扭转。首先，我们处理参数化的曲线和线性弹性膜，证明存在平衡并找到最小化计算第一个变化的一阶必需条件。其次，我们使用框架曲线方法研究了边界曲线和膜的更一般情况。应用Lagrange乘数方法的无限尺寸版本用于获得一阶必要条件。最后，在几个数值测试案例中提出并采用了一种数值方法。
We perform a variational analysis of an elastic membrane spanning a closed curve which may sustain bending and torsion. First, we deal with parametrized curves and linear elastic membranes proving the existence of equilibria and finding first-order necessary conditions for minimizers computing the first variation. Second, we study a more general case, both for the boundary curve and for the membrane, using the framed curve approach. The infinite dimensional version of the Lagrange multipliers' method is applied to get the first-order necessary conditions. Finally, a numerical approach is presented and employed in several numerical test cases.
