2015/09/01 by A. Moore, Moore, Alexander, Timothy J. Healey +2 · 1 citation
Engineering · Physics and Astronomy · #Advanced Materials and Mechanics #Elasticity and Material Modeling #FOS: Physical sciences #Force Microscopy Techniques and Applications #Soft Condensed Matter (cond-mat.soft) #Structural Analysis and Optimization
paper · pdf · doi:10.48550/arxiv.1509.00147
openalex publication_date 2015/09/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Determining the equilibrium configuration of an elastic M "obius band is a\nchallenging problem. In recent years numerical results have been obtained by\nother investigators, employing first the Kirchhoff theory of rods and later the\ndevelopable, ruled-surface model of Wunderlich. In particular, the strategy\nemployed previously for the latter does not deliver an unconstrained\nequilibrium configuration for the complete strip. Here we present our own\nsystematic approach to the same problem for each of these models, with the\nultimate goal of assessing the stability of flip-symmetric configurations. The\npresence of pointwise constraints considerably complicates the latter step. We\nobtain the first stability results for the problem, numerically demonstrating\nthat such equilibria render the total potential energy a local minimum. Along\nthe way we introduce a novel regularization for the for the singular Wunderlich\nmodel that delivers unconstrained equilibria for the complete strip, which can\nthen be tested for stability.\n