Abstract
Finite axisymmetric deformation of a thin toroidal shell under action of internal pressure is studied. The shell is reinforced by two systems of threads located along parallels and meridians and is considered as anisotropic membrane. The nonlinear theory of membranes is used. To find membrane deformations and displacements the system of ordinary differential equations of the fourth order is delivered. The method of asymptotic integration in the case when the meridian radius is much smaller than the parallel one is elaborated. Asymptotic and numerical results are compared.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Eriksson, A., Nordmark, A.: Instability of thin hyper-elastic space membranes under pressure loads. Comput. Methods Appl. Mech. Eng. 237–240, 118–129 (2012)
Filippov, SB.: Finite post-critical deformation of an inflatable anisotropic toroidal membrane. In: 6th European Congress on Computational Methods in Applied Sciences and Engineering, Book of Abstracts, Vienna, p. 124 (2012)
Filippov, SB.: Finite axisymmetric deformation of an inflatable anisotropic toroidal membrane made of Neo-Hookean material. In: Shell and Membrane Theories in Mechanics and Biology: From Macro- to Nanoscale Structures, Proceedings of the International Scientific Conference, Minsk, pp. 22–24 (2013)
Jacques, N., Potier-Ferry, M.: On mode localisation in tensile plate buckling. C. R. Mecanique 333, 804–809 (2005)
Kolesnikov, A.M., Zubov, L.M.: Large bending deformations of a cylindrical membrane with internal pressure. Z. Angew. Math. Mech. 89, 288–305 (2009)
Kydoniefs, A.D., Spencer, A.J.M.: The finite inflating of an elastic toroidal membrane of circular cross section. Int. J. Eng. Sci. 5, 367–391 (1967)
Li, X., Steigmann, D.J.: Finite deformation of a pressurized toroidal membrane. Int. J. NonLinear Mech. 30, 583–595 (1995)
Libai, A., Simmonds, J.G.: The Nonlinear Theory of Elastic Shells, 2nd edn. Cambridge University Press, Cambridge (1998)
Ng, B.S., Reid, W.H.: An initial-value method for eigenvalue problems using compound matrices. J. Comp. Phys. 30, 125–136 (1979)
Oñate, E., Kröplin, B. (eds.): Textile Composites and Inflatable Structures II, Computational Methods in Applied Sciences, vol. 8. Springer, Dordrecht (2008)
Pietraszkiewicz, W.: Geometrically nonlinear theories of thin elastic shells. Adv. Mech. 12, 51–130 (1989)
Tamadapu, G., DasGupta, A.: In-plane surface modes of an elastic toroidal membrane. Int. J. Eng. Sci. 60, 25–36 (2012)
Tamadapu, G., DasGupta, A.: Finite inflation analysis of a hyperelastic toroidal membrane of initially circular cross-section. J. Nonlinear Mech. 49, 31–39 (2013)
Acknowledgments
This work was supported by RFBR (grant 13-01-00523) which is gratefully acknowledged.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Filippov, S.B., Tovstik, P.E. (2015). Finite Axisymmetric Deformation of an Inflatable Anisotropic Toroidal Membrane. In: Altenbach, H., Mikhasev, G. (eds) Shell and Membrane Theories in Mechanics and Biology. Advanced Structured Materials, vol 45. Springer, Cham. https://doi.org/10.1007/978-3-319-02535-3_10
Download citation
DOI: https://doi.org/10.1007/978-3-319-02535-3_10
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-02534-6
Online ISBN: 978-3-319-02535-3
eBook Packages: EngineeringEngineering (R0)