论文标题
在伸展的弹性字符串上
On stretch-limited elastic strings
论文作者
论文摘要
比起从凯奇弹性中，构成关系对非隔离材料建模的兴趣增加，我们启动了对一类伸展限制的弹性字符串的研究：无法压缩该字符串小于一定长度小于其自然长度，也不能比其自然长度大的长度小。特别是，我们考虑了在重力（catenies）下悬浮在两个点之间的弦的平衡状态。我们研究了在两种情况下含有可扩展和不可扩展段的拉伸状态的支撑状态的位置：当弦是垂直的弦和非排定情况时的退化情况时，当支架处于相同的高度处时。然后，我们研究了平衡状态的存在和多样性，总体上的多样性与满足经典构成关系的字符串明显不同。
Motivated by the increased interest in modeling nondissipative materials by constitutive relations more general than those from Cauchy elasticity, we initiate the study of a class of stretch-limited elastic strings: the string cannot be compressed smaller than a certain length less than its natural length nor elongated larger than a certain length greater than its natural length. In particular, we consider equilibrium states for a string suspended between two points under the force of gravity (catenaries). We study the locations of the supports resulting in tensile states containing both extensible and inextensible segments in two situations: the degenerate case when the string is vertical and the nondegenerate case when the supports are at the same height. We then study the existence and multiplicity of equilibrium states in general with multiplicity differing markedly from strings satisfying classical constitutive relations.
