Advertisement

Russian Engineering Research

, Volume 39, Issue 2, pp 95–101 | Cite as

Three-Layer Cylindrical Shell with Nonlinear Deformation

  • O. M. UstarkhanovEmail author
  • A. K. Yusupov
  • Kh. M. Muselemov
  • T. O. Ustarkhanov
  • G. G. Irzaev
Article

Abstract

A mathematical model is proposed for the stress–strain state of a three-layer (sandwich) structure, taking account of nonlinear deformation of the supporting layers. Nonlinear deformation of a symmetric three-layer cylindrical shell under the action of transverse loads is considered, for different boundary conditions.

Keywords:

cylindrical shell three-layer structures sandwich structures nonlinear deformation stress–strain state supporting layer equilibrium equation boundary conditions transverse loads 

Notes

ACKNOWLEDGMENTS

Financial support was provided by the Russian President (grant MK-6112.2018.8).

REFERENCES

  1. 1.
    Mikeladze, M.Sh., Vvedenie v tekhnicheskuyu teoriyu ideal’no-plastinchatykh tonkikh obolochek (Introduction to the Technical Theory of Ideally Plate Thin Shells), Tbilisi: Metsniereba, 1969.Google Scholar
  2. 2.
    Ustarkhanov, O.M., Muselemov, H.M., and Akaev, N.K., Sandwich structures, Russ. Eng. Res., 2016, vol. 36, no. 10, pp. 815–818.CrossRefGoogle Scholar
  3. 3.
    Buyakov, I.A., Nonlinear equations of a Timoshenko-type theory of laminated anisotropic shells, Mech. Compos. Mater., 1979, vol. 15, no. 3, pp. 292–296.CrossRefGoogle Scholar
  4. 4.
    Buyakov, I.A., Deformation in the direction of the normal in a non-linear Tymoshenko shell, Mekh. Kompoz. Mater., 1980, no. 2, pp. 358–359.Google Scholar
  5. 5.
    Vasil’kov, G.V., Iterative methods to solve nonlinear problems in constructional mechanics, Doctoral (Eng.) Dissertation, Moscow: Russ. Transp. Univ, MIIT, 1989.Google Scholar
  6. 6.
    Adkins, J.E. and Green, A.E., Large Elastic Deformations, Oxford: Clarendon, 1960.zbMATHGoogle Scholar
  7. 7.
    Solomonov, Yu.S., Georgievskii, V.P., Nedbai, A.Ya., et al., Metody rascheta tsilindricheskikh obolochek iz komopiztsionnykh materialov (Calculation Methods of Cylindrical Shells from Composite Materials), Moscow: Fizmatlit, 2009.Google Scholar
  8. 8.
    Sukhinin, S.N., Prikladnye zadachi ustoichivosti mnogosloinykh kompozitnykh obolochek (Applied Tasks in Stability of Multilayered Composite Shells), Moscow: Fizmatlit, 2010.Google Scholar
  9. 9.
    Sukhinin, S.N., Simulation of stability of three-layer composite shells in their axial compression, Kosmonavtika Raketostr., 2015, no. 3 (82), pp. 52–58.Google Scholar
  10. 10.
    Chulkov, P.P., Oscillation equations for elastic layered shells, Din. Sploshnoi Sredy, 1970, no. 7, pp. 55–60.Google Scholar
  11. 11.
    Prusakov, A.P., Finite deflections of multilayered shells, Izv. Akad. Nauk SSSR, Mekh. Tverd. Tela, 1971, no. 3, pp. 119–125.Google Scholar
  12. 12.
    Prusakov, A.P., The nonlinear bending equations of gently sloping multilayer shells, Sov. Appl. Mech., 1971, vol. 7, no. 3, pp. 235–239.CrossRefGoogle Scholar
  13. 13.
    Piskunov, V.G. and Verizhenko, V.E., Lineinye i nelineinye zadachi rascheta sloistykh konstruktsii (Linear and Nonlinear Problems of Calculation of Layered Constructions), Kiev: Budivel’nik, 1986.Google Scholar
  14. 14.
    Alibeigloo, A., Free vibration analysis of nano-plate using three-dimensional theory of elasticity, Acta Mech., 2011, vol. 222, no. 11, pp. 149–159.CrossRefzbMATHGoogle Scholar
  15. 15.
    Singh, B. and Nanda, B.K., Dynamic analysis of damping in layered and welded beams, Eng. Struct., 2013, vol. 48, pp. 10–20.CrossRefGoogle Scholar
  16. 16.
    Ustarkhanov, O.M., Durability of three-layer constructions with regular discrete filler, Doctoral (Eng.) Dissertation, Rostov-on-Don: Rostov State Univ. Civil Eng., 2000.Google Scholar
  17. 17.
    Kobelev, V.N., Destruction mechanics of a filler of three-layer constructions, Izv. Vyssh. Uchebn. Zaved., Aviats. Tekh., 1987, no. 3, pp. 15–16.Google Scholar
  18. 18.
    Panin, V.F. and Gladkov, Yu.A., Konstruktsii s zapolnitelem: Spravochnik (Constructions with a Filler: Handbook), Moscow: Mashinostroenie, 1991.Google Scholar
  19. 19.
    Prokhorov, B.F. and Deryushchev, V.V., The effect of technological defects on the carrying capacity of three-layer constructions, Tekhnol. Sudostr., 1981, no. 10, pp. 25–29.Google Scholar
  20. 20.
    Prokhorov, B.F. and Kobelev, V.N., Trekhsloinye konstruktsii v sudostroenii (Three-Layer Constructions in Ship Building), Leningrad: Sudostroenie, 1972.Google Scholar
  21. 21.
    Ustarkhanov, O.M., Kobelev, V.N., Kobelev, V.V., and Abrosimov, N.A., Experimental study of three-layer beams with metal honeycomb filler and composite layers, Materialy mezhdunarodnoi nauchno-tekhnicheskoi konferentsii “Sovremennye nauchno-tekhnicheskie problemy grazhdanskoi aviatsii” (Proc. Int. Sci.-Tech. Conf. “Modern Scientific-Technical Problems in Civil Aviation”), Moscow: Mosk. Gos. Tekh. Univ. Grazhd. Aviats., 1999, pp. 32–33.Google Scholar
  22. 22.
    Liew, K.M., Jiang, L., Lim, M.K., and Low, S.C., Experimental detection of disbonds and delaminalion in honeycomb structures, Eng. Fract. Mech., 1994, vol. 47, no. 5, pp. 723–741.CrossRefGoogle Scholar
  23. 23.
    Kobelev, V.N., Ustarkhanov, O.M., and Batdalov, M.M., Including the nonlinearity of the deformation of the bearing layers in calculation of cylindrical shells, Materialy nauchno-tekhnicheskoi konferentsii “Nekotorye problemy sozdaniya progressivnoi tekhniki i tekhnologii proizvodstva” (Proc. Sci.-Tech. Conf. “Creation of Advanced Industrial Equipment and Technologies”), Makhachkala: Dagest. Gos. Tekh. Univ., 1998, pp. 65–67.Google Scholar
  24. 24.
    Demidovich, B.P. and Maron, I.A., Computational Mathematics, Moscow: Mir, 1981.Google Scholar
  25. 25.
    Egorov, A.I., Obyknovennye differentsial’nye uravneniya s prilozheniyami (Common Differential Equations with Applications), Moscow: Fizmatlit, 2005, 2nd ed.Google Scholar
  26. 26.
    Piskunov, N.P., Differentsial’noe i integral’noe ischisleniya (Differential and Integral Estimates), Moscow: Nauka, 1985.Google Scholar
  27. 27.
    Petrovskii, I.G., Lektsii po teorii obyknovennykh diferentsial’nykh uravnenii (Lectures on the Theory of Common Differential Equations), Myshkis, A.D. and Oleinik, O.A., Eds., Moscow: Mosk. Gos. Univ., 1984.Google Scholar
  28. 28.
    Prusakov, A.P., General equations of bending and stability of three-layer plates with light filler, Prikl. Matem. Mekh., 1951, vol. 15, pp. 48–52.MathSciNetGoogle Scholar

Copyright information

© Allerton Press, Inc. 2019

Authors and Affiliations

  • O. M. Ustarkhanov
    • 1
    Email author
  • A. K. Yusupov
    • 1
  • Kh. M. Muselemov
    • 1
  • T. O. Ustarkhanov
    • 1
  • G. G. Irzaev
    • 1
  1. 1.Dagestan National Research UniversityMakhachkalaRussia

Personalised recommendations