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Yuan, Xue-gang; Zhang, Wen-zheng; Zhang, Hong-wu; Zhu, Zheng-you

Stability analysis of radial inflation of incompressible composite rubber tubes. (English) Zbl 1213.74059

Appl. Math. Mech., Engl. Ed. 32, No. 3, 301-308 (2011).
Summary: The inflation mechanism is examined for a composite cylindrical tube composed of two incompressible rubber materials, and the inner surface of the tube is subjected to a suddenly applied radial pressure. The mathematical model of the problem is formulated, and the corresponding governing equation is reduced to a second-order ordinary differential equation by means of the incompressible condition of the material, the boundary conditions, and the continuity conditions of the radial displacement and the radial stress of the cylindrical tube. Moreover, the first integral of the equation is obtained. The qualitative analyses of static inflation and dynamic inflation of the tube are presented. Particularly, the effects of material parameters, structure parameters, and the radial pressure on radial inflation and nonlinearly periodic oscillation of the tube are discussed by combining numerical examples.

Cited in 1 Document

MSC:

74B20 Nonlinear elasticity
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\textit{X.-g. Yuan} et al., Appl. Math. Mech., Engl. Ed. 32, No. 3, 301--308 (2011; Zbl 1213.74059)
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References:

[1] Beatty, M. F. Topics in finite elasticity: hyperelasticity of rubber, elastomers, and biological tissues-with examples. Applied Mechanics Review, 40(12), 1699–1733 (1987)
[2] Fu, Y. B. and Ogden, R. W. Nonlinear Elasticity: Theory and Applications, Cambridge University Press, London (2001)
[3] Attard, M. M. Finite strain-isotropic hyperelasticity. International Journal of Solids and Structures, 40(17), 4353–4378 (2003) · Zbl 1054.74524
[4] Haughton, D. M. and Kirkinis, E. A comparison of stability and bifurcation criteria for inflated spherical elastic shells. Math. Mech. Solids, 8(5), 561–572 (2003) · Zbl 1055.74016
[5] Horgan, C. O. and Polignone, D. A. Cavitation in nonlinearly elastic solids: a review. Applied Mechanics Review, 48(7), 471–485 (1995)
[6] Knowles, J. K. Large amplitude oscillations of a tube of incompressible elastic material. Quart. Appl. Math., 18(1), 71–77 (1960) · Zbl 0099.19102
[7] Ren, J. S. Dynamical response of hyper-elastic cylindrical shells under periodic load. Applied Mathematics and Mechanics (English Edition), 29(10), 1319–1327 (2008) DOI 10.1007/s10483-008-1007-x · Zbl 1235.74147
[8] Yuan, X. G., Zhang, R. J., and Zhang, H. W. Controllability conditions of finite oscillations of hyper-elastic cylindrical tubes composed of a class of Ogden material models. Computers, Materials and Continua, 7(3), 155–165 (2008)
[9] Chou-Wang, M. S. and Horgan, C. O. Void nucleation and growth for a class of incompressible nonlinear elastic materials. International Journal of Solids and Structures, 25(11), 1239–1254 (1989) · Zbl 0703.73025
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.