Instability of Toroidal Membrane with Large Tensile Deformation

Shang Xin-chun; Cheng Chang-jun

Volume 12 Issue 6

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Article Navigation > Applied Mathematics and Mechanics > 1991 > 12(6): 523-530

Shang Xin-chun, Cheng Chang-jun. Instability of Toroidal Membrane with Large Tensile Deformation[J]. Applied Mathematics and Mechanics, 1991, 12(6): 523-530.

Citation:

Shang Xin-chun, Cheng Chang-jun. Instability of Toroidal Membrane with Large Tensile Deformation[J]. Applied Mathematics and Mechanics, 1991, 12(6): 523-530.

Citation:

Shang Xin-chun, Cheng Chang-jun. Instability of Toroidal Membrane with Large Tensile Deformation[J]. Applied Mathematics and Mechanics, 1991, 12(6): 523-530.

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Instability of Toroidal Membrane with Large Tensile Deformation

Department of Mechanics, Lanzhou University, Lanzhou

Received Date: 1990-09-22
Publish Date: 1991-06-15

Abstract

Abstract

In this paper, the problem of large axisymmetric deformation of hyperelastic membrane is reformulated on the basis of the general theory of finite elasticity. From the fundamental equations derived here, the tensile instability of toroidal rubberlike membrane with Mooney-Rivlin's model constitutive relation is solved by using the shooting method. The upper and lower limit loads and the response curve of the displacement to the load are given.
- hyperelasticity,
- large deformation,
- fundamental equation,
- shooting method,
- tensile instability

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References(8)

References

[1]	Green,A.E.and J.E.Adkins,Large Elastic Deformations and Non-Linear ContinuumMechanics,Chap.4,Clarendon Press(1960).
[2]	Eringen,A.C,Non-Linear Theory of Continuous Media,Chap.6,McCraw-Hill BookCompany,Inc.(1962).
[3]	Kydoniefs,A.D.and A.J.M.Spencer,The finite inflation of an elastic toroidal membrane ofcircular cross section,Int.J.Engng.Sci.,5(1967),367-391.
[4]	Hill,J.M.,The finite inflation of thick-walled elastic torus,Q.J.Mech Appl.Math.,33(1980),471-490.
[5]	Hill,J.M.,Finite deformation of thick-walled inner tubes and tyres under inflation androtation,D.E.Carlson and R.T.Shield,Eds.,Finite Elasticity,Proc.IUTAM Symp.,Lehigh Univ.,Martimus Nijhoff Pubs.(1982),211-236.
[6]	Yang,W.H.and W.W.Feng,On axisymmetrical deformations of non-linear membranes,Trans.ASME,J.Appl.Mech.,92(1970),1002-1011.
[7]	朱正佑、程昌钧,《分支问题的数值计算方法》,第三章,兰州大学出版社(1989).
[8]	Hart-Smith,L.J.,Elasticity parameters for finite deformations of rubber-like materials,ZAMP,17(1966),608-626．

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