完全Möbius带无约束弹性平衡的计算及其稳定性
Computation of Unconstrained Elastic Equilibria of Complete Möbius Bands and their Stability
摘要：
确定弹性莫比乌斯带的平衡构型是一个具有挑战性的问题。近年来，其他研究人员已经获得了数值结果，首先采用基尔霍夫理论的杆，后来的可发展，规则面模型的Wunderlich。特别是，以前采用的策略，后者不提供一个无约束的平衡配置为完整的带。在这里，我们提出了我们自己的系统的方法来解决这些模型中的每一个相同的问题，最终目标是评估翻转对称配置的稳定性。逐点约束的存在使后一步骤相当复杂。我们得到的第一个稳定性结果的问题，数值证明，这样的平衡使总势能的局部最小值。一路上，我们引入了一种新的正则化的奇异Wunderlich模型，提供了无约束的平衡，为完整的带，然后可以测试的稳定性。
英文摘要：
Determining the equilibrium configuration of an elastic Möbius band is a challenging problem. In recent years numerical results have been obtained by other investigators, employing first the Kirchhoff theory of rods and later the developable, ruled-surface model of Wunderlich. In particular, the strategy employed previously for the latter does not deliver an unconstrained equilibrium configuration for the complete strip. Here we present our own systematic approach to the same problem for each of these models, with the ultimate goal of assessing the stability of flip-symmetric configurations. The presence of pointwise constraints considerably complicates the latter step. We obtain the first stability results for the problem, numerically demonstrating that such equilibria render the total potential energy a local minimum. Along the way we introduce a novel regularization for the for the singular Wunderlich model that delivers unconstrained equilibria for the complete strip, which can then be tested for stability.
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