Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



Plane deformations of membranes and networks with circular cords

Author: Jingyu Shi
Journal: Quart. Appl. Math. 51 (1993), 69-79
MSC: Primary 73G05; Secondary 73K10
DOI: https://doi.org/10.1090/qam/1205937
MathSciNet review: MR1205937
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Abstract: Deformations of membranes and networks formed with two families of highly elastic cords are considered. The cords are along the radial and circumferential directions of concentric circles and are perfectly joined together at their intersection points so that there is no slip relative to each other. The deformations studied include: (1) symmetric deformation of circular arcs or annuli, (2) straightening of circular arcs and (3) inverse bending of circular arcs. It is found that the second is a universal deformation, which satisfies the equilibrium equations for any constitutive relations of the material of the cords.

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DOI: https://doi.org/10.1090/qam/1205937
Article copyright: © Copyright 1993 American Mathematical Society

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