Related papers: Sagging Ropes Demonstrate the Transversality Condi…
The problem of a suspended rope wrapped around a fixed cylinder is studied. If the suspension force is larger than a certain threshold (which is larger than the weight of the rope), the rope would remain tightly wrapped around the cylinder.…
We address the mechanics of an elastic ribbon subjected to twist and tensile load. Motivated by the classical work of Green and a recent experiment that discovered a plethora of morphological instabilities, we introduce a comprehensive…
Many physical systems can be modelled as parameter-dependent variational problems. In numerous cases, multiple equilibria co-exist, requiring the evaluation of their stability, and the monitoring of transitions between them. Generally, the…
The application of variational principles for analyzing problems in the physical sciences is widespread. Cantilever-like problems, where one end is fixed and the other end is free, have received less attention in terms of their stability…
The morphology of an elastic strip subject to vertical compressive stress on a frictional rigid substrate is investigated by a combination of theory and experiment. We find a rich variety of morphologies, which -when the bending elasticity…
We investigate the tension distribution in systems of mass-less ropes under different loading conditions. For a two-rope system, we demonstrate how the breaking scenario depends on the applied force dynamics: rapid pulling causes the lower…
Functional structures from across the engineered and biological world combine rigid elements such as bones and columns with flexible ones such as cables, fibers and membranes. These structures are known loosely as tensegrities, since these…
To study vertical sag requirements and factors affecting the stretched wire alignment method, the vertical sag equation is first derived theoretically. Subsequently, the influencing factors,such as the hanging weight or tension, span…
We describe several configurations of clasped ropes which are balanced and thus critical for the Gehring ropelength problem of arXiv:math.DG/0402212.
A rope laid on the ground with one end subjected to time-dependent forcing is proposed as a prototypical elastic dynamical contact problem, which we study analytically, numerically, and experimentally. The dynamics is governed by an…
Many mechanical structures, both engineered and biological, combine heavy rigid elements such as bones and beams with lightweight flexible ones such as cables and membranes. These are referred to as tensegrities, reflecting that cables can…
The hanging chain is a very instructive system for demonstrating more advanced methods and ideas for the analysis of normal modes of one-dimensional systems, beyond the standard ordinary (horizontal) string. Accordingly, the normal modes of…
Motivated by observations of snap-through phenomena in buckled elastic strips subject to clamping and lateral end translations, we experimentally explore the multi-stability and bifurcations of thin bands of various widths and compare these…
We consider thin plates whose energy density is a quadratic function of the difference between the second fundamental form of the deformed configuration and a "natural" curvature tensor. This tensor either denotes the second fundamental…
We establish a sufficient condition for the tightness of a sequence of stochastic processes. Our condition makes it possible to study processes with accumulations of fixed times of discontinuity. Our motivation comes from the study of…
The ropelength problem asks for the minimum-length configuration of a knotted diameter-one tube embedded in Euclidean three-space. The core curve of such a tube is called a tight knot, and its length is a knot invariant measuring…
We analyze stability of a thin inextensible elastic rod which has non-vanishing spontaneous generalized torsions in its stress-free state. Two classical problems are studied, both involving spontaneously twisted rods: a rectilinear beam…
The surface texture of materials plays a critical role in wettability, turbulence and transport phenomena. In order to design surfaces for these applications, it is desirable to characterise non-smooth and porous materials by their ability…
We study ribbons of vanishing Gaussian curvature, i.e., flat ribbons, constructed along a curve in $\mathbb{R}^{3}$. In particular, we first investigate to which extent the ruled structure determines a flat ribbon: in other words, we ask…
Ribbons are a class of slender structures whose length, width, and thickness are widely separated from each other. This scale separation gives a ribbon unusual mechanical properties in athermal macroscopic settings, e.g. it can bend without…