2012/09/08 by Gabor Csanyi, Gábor Cśanyi, Gabor Domokos +4
Biochemistry, Genetics and Molecular Biology · Chemistry · Engineering · Materials Science · Mathematics · Physics and Astronomy · #Advanced Physical and Chemical Molecular Interactions #Cellular Mechanics and Interactions #FOS: Physical sciences #Force Microscopy Techniques and Applications #High-Velocity Impact and Material Behavior #Mathematical Physics (math-ph) #Structural Analysis and Optimization #Structural Response to Dynamic Loads #math-ph #math.MP
paper · pdf · doi:10.48550/arxiv.1209.1758
openalex publication_date 2012/09/08 · arxiv created 2013/02/01 · arxiv updated 2013/02/04 · openalex created_date 2022/09/01 · openalex updated_date 2026/07/28
While static equilibria of flexible strings subject to various load types (gravity, hydrostatic pressure, Newtonian wind) is well understood textbook material, the combinations of the very same loads can give rise to complex spatial behaviour at the core of which is the unilateral material constraint prohibiting compressive loads. While the effects of such constraints have been explored in optimisation problems involving straight cables, the geometric complexity of physical configurations has not yet been addressed. Here we show that flexible strings subject to combined smooth loads may not have smooth solutions in certain ranges of the load ratios. This non-smooth phenomenon is closely related to the collapse geometry of inflated tents. After proving the nonexistence of smooth solutions for a broad family of loadings we identify two alternative, critical geometries immediately preceding the collapse. We verify these analytical results by dynamical simulation of flexible chains as well as with simple table-top experiments with an inflated membrane.