Skip to main content
Log in

Nonlinear Deformation of a Piecewise Homogeneous Cylinder Under the Action of Rotation

  • Published:
Mechanics of Composite Materials Aims and scope

Deformation of a piecewise cylinder under the action of rotation is investigated. The cylinder consists of an elastic matrix with circular fibers of square cross section made of a more rigid elastic material and arranged doubly periodically in the cylinder. Behavior of the cylinder under large displacements and deformations is examined using the equations of a nonlinear elasticity theory for cylinder constituents. The problem posed is solved by the finite-difference method using the method of continuation with respect to the rotational speed of the cylinder.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1.
Fig. 2.
Fig. 3.
Fig. 4.
Fig. 5.
Fig. 6.
Fig. 7.
Fig. 8.
Fig. 9.

Similar content being viewed by others

References

  1. К. Loffer, Die berechnung von Rotierenden Scheiben und Schalen, Göttingen, Springer, Verlag OHG (1961).

    Book  Google Scholar 

  2. Composite materials: Handbook, eds. V. V. Vasil’ev and Yu. M. Tarnopolskii [in Russian], Mashinostroenie (1990).

  3. М. Tervonen and A. Pramila, “Stresses in a hollow rotating cylindrically orthotropic tube,” Mech. Compos. Mater., 32, No. 6, P. 577-581 (1996).

    Article  Google Scholar 

  4. G. G. Portnov and Ch. E. Bakis, “Estimation of limit strains in disk-type flywheels made of compliant elastomeric matrix composite undergoing radial creep,” Mech. Compos. Mater., 36, No. 1, 87-94 (2000).

    Article  Google Scholar 

  5. G. Portnov, A. N. Uthe, I. Cruz, R. P. Fiffe, and F. Arias, “Design of steel-composite multirim cylindrical flywheels manufactured by winding with high tensioning and in situ curing. 1. Basic relations,” Mech. Compos. Mater., 41, No. 2, 139-152 (2005).

    Article  Google Scholar 

  6. G. Portnov, A. N. Uthe, I. Cruz, R. P. Fiffe, and F. Arias, “Design of steel-composite multirim cylindrical flywheels manufactured by winding with high tensioning and in situ curing. 2. Numerical analysis,” Mech. Compos. Mater., 41, No. 3, 241-254 (2005).

    Article  Google Scholar 

  7. U. Johnson and P. Mellor, Plasticity Theory for Engineers [Russian translation], M., Mashinostroenie (1979).

  8. G. S. Pisarenko and N. S. Mozharovskii, Equations and Boundary-Value Problems of the Theory of Plasticity and Creep. Handbook [in Russian], Kiev, Nauk. Dumka (1981).

  9. V. V. Sokolovsky, Plasticity Theory [in Russian], M., Vysh. Shkola (1969).

  10. Thermal Strength of Mashine Parts, eds, I. A. Birger and B. F. Shora [in Russian], M., Mashnostroenie (1975).

  11. V. M. Akhundov and T. A. Skripochka, “Large deformations of homogeneous and fiber-reinforced cylinders under the action of centrifugal forces,” Mech. Compos. Mater., 45, No. 3, 235-248 (2009).

    Article  Google Scholar 

  12. V. M. Akhundov and T. A. Skripochka, “Axisymmetric deformation of revolving cylinders made of homogeneous and fiber-reinforced elastic materials,” Mech. Compos. Mater., 47, No. 2, 211-220 (2011).

    Article  Google Scholar 

  13. V. M. Akhundov, “Modeling large deformations of fibrous bodies of revolution based on applied and carcass theories. 3. Rotational motion,” Mech. Compos. Mater., 50, No. 6, 809-816 (2014).

    Article  Google Scholar 

  14. V. M. Akhundov, “Applied theory of composites with low fiber fillings at large deformations,” Mekh. Kompos. Mater. Konstr., 7, No. 1, 3-15 (2001).

    Google Scholar 

  15. V. M. Akhundov, “Carcass theory of fibrous media with uncurved and locally curved fibers at large deformations,” Mech. Compos. Mater., 51, No. 6, 683-694 (2015).

    Article  Google Scholar 

  16. A. I. Lurye, Nonlinear Elasticity Theory [in Russian], M., Nauka (1980).

  17. A. K. Malmeister, V. P., Tamuzh, and G. A. Teters, Strength of Polymer and Composite Materials [in Russian], Riga, Zinatne (1980).

  18. Introduction into the Mechanics of Continuous Media, ed. K. F. Chernykh [in Russian], L., Izd. Leningr. Univ. (1984).

  19. V. M. Akhundov, “Analysis of elastomeric composites based on fiber reinforced systems. 1. Development of design methods for composite materials,” Mech. Compos. Mater., 34, No. 6, 515-524 (1998).

    Article  Google Scholar 

  20. G. A. Korn and T. M. Korn Mathematical Handbook for Scientists and Engineers: Definitions, Theorems and Formulas for Reference and Review, N.Y.: General Publ. Company (2000).

  21. Dzh. Ortega and V. Reinboldt, Itegration Methods for Solving of Nonlinear Systems of Equations with Many Unknowns [Russian translation], M., Mir (1975).

  22. K. F. Chernykh, Nonlinear Elasticity Theory in Machine-Building Calculations [in Russian], L., Mashinostroenie (1986).

  23. V. Z. Parton, P. I. Perlin, Method of Mathematical Elasticity Theory[in Russian], M., Nauka (1981).

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to V. M. Akhundov.

Additional information

Translated from Mekhanika Kompozitnykh Materialov, Vol. 54, No. 2, pp. 345-360 , March-April, 2018.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Akhundov, V.M., Kostrovа, M.M. Nonlinear Deformation of a Piecewise Homogeneous Cylinder Under the Action of Rotation. Mech Compos Mater 54, 231–242 (2018). https://doi.org/10.1007/s11029-018-9734-8

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11029-018-9734-8

Keywords

Navigation