Twisted elastic rings and the rediscoveries of Michell’s instability. (English) Zbl 1098.74034
Summary: Elastic rings become unstable when sufficiently twisted. This fundamental instability plays an important role in the modeling of DNA mechanics and in cable engineering. In 1962, E. E. Zajac computed the value of the critical twist for the instability [J. Appl. Mech. 29, 136–142 (1962; Zbl 0106.38005)]. This critical value was rediscovered in 1979 by C. J. Benham [Biopolymers 18, 609–623 (1979)] and independently by M. Le Bret [Biopolymers 23, 1835-1867 (1984)] in elastic models for DNA; unstable rings have since become an important example of elastic instabilities in rods both for the development of new methods and in applications. The purpose of this note is to show that the problem had been completely solved by John Henry Michell in 1889 in a rather elegant manner and to reflect on its history and modern developments.
MSC:
| 74K10 | Rods (beams, columns, shafts, arches, rings, etc.) |
| 74G60 | Bifurcation and buckling |
| 74-03 | History of mechanics of deformable solids |
| 74A60 | Micromechanical theories |
| 01A60 | History of mathematics in the 20th century |
| 01A55 | History of mathematics in the 19th century |
Citations:
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