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.
- S. M. Genensky and R. S. Rivlin, Infinitesimal plane strain in a network of elastic cords, Arch. Rational Mech. Anal. 4 (1959), 30–44 (1959). MR 108925, DOI https://doi.org/10.1007/BF00281377
- W. A. Green and J. Shi, Plane deformations of membranes formed with elastic cords, Quart. J. Mech. Appl. Math. 43 (1990), no. 3, 317–333. MR 1070959, DOI https://doi.org/10.1093/qjmam/43.3.317
- W. A. Green and Jingyu Shi, Degenerate deformations and uniqueness in highly elastic networks, Quart. Appl. Math. 50 (1992), no. 3, 501–516. MR 1178430, DOI https://doi.org/10.1090/qam/1178430
- W. A. Green and Jingyu Shi, Deformations of discrete elastic networks, IMA J. Appl. Math. 45 (1990), no. 2, 99–113. MR 1080840, DOI https://doi.org/10.1093/imamat/45.2.99
- Jingyu Shi, Plane deformations of shear-resisting membranes formed of elastic cords, J. Engrg. Math. 26 (1992), no. 3, 379–393. MR 1177961, DOI https://doi.org/10.1007/BF00042741
---, Elastic networks and membranes, Ph.D. thesis, Nottingham University, U.K., 1988
- A. J. M. Spencer, Continuum mechanics, Longman, London-New York, 1980. Longman Mathematical Texts. MR 597343
- N. W. McLachlan, Ordinary Non-Linear Differential Equations in Engineering and Physical Sciences, Oxford, at the Clarendon Press, 1950. MR 0039135
---, Bessel Functions for Engineers, Oxford Press, Oxford, 1946
S. M. Genensky and R. S. Rivlin, Infinitesimal plane strain in a network of elastic cords, Arch. Rational Mech. Anal. 4, 30–44 (1959–60)
W. A. Green and Jingyu Shi, Plane deformations of membranes formed with elastic cords, Quart. J. Mech. Appl. Math. 43, 317–333 (1990)
---, Degenerate deformations and uniqueness in highly elastic networks, Quart. Appl. Math. 50, 501–516 (1992)
---, Deformations of discrete elastic networks, IMA J. Appl. Math. 45, 99–113 (1990)
J. Shi, Plane deformations of shear-resistant membranes formed of elastic cords, J. Engrg. Math., to appear
---, Elastic networks and membranes, Ph.D. thesis, Nottingham University, U.K., 1988
A. J. M. Spencer, Continuum Mechanics, Longman, New York, 1980
N. W. Mclachlan, Ordinary Non-Linear Differential Equations in Engineering and Physical Sciences, Oxford Press, Oxford, 1950
---, Bessel Functions for Engineers, Oxford Press, Oxford, 1946
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Article copyright:
© Copyright 1993
American Mathematical Society
