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Three-Layer Cylindrical Shell with Nonlinear Deformation

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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.

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REFERENCES

  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.

  2. Ustarkhanov, O.M., Muselemov, H.M., and Akaev, N.K., Sandwich structures, Russ. Eng. Res., 2016, vol. 36, no. 10, pp. 815–818.

    Article  Google Scholar 

  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.

    Article  Google Scholar 

  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.

  5. Vasil’kov, G.V., Iterative methods to solve nonlinear problems in constructional mechanics, Doctoral (Eng.) Dissertation, Moscow: Russ. Transp. Univ, MIIT, 1989.

  6. Adkins, J.E. and Green, A.E., Large Elastic Deformations, Oxford: Clarendon, 1960.

    MATH  Google Scholar 

  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.

  8. Sukhinin, S.N., Prikladnye zadachi ustoichivosti mnogosloinykh kompozitnykh obolochek (Applied Tasks in Stability of Multilayered Composite Shells), Moscow: Fizmatlit, 2010.

  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.

  10. Chulkov, P.P., Oscillation equations for elastic layered shells, Din. Sploshnoi Sredy, 1970, no. 7, pp. 55–60.

  11. Prusakov, A.P., Finite deflections of multilayered shells, Izv. Akad. Nauk SSSR, Mekh. Tverd. Tela, 1971, no. 3, pp. 119–125.

  12. Prusakov, A.P., The nonlinear bending equations of gently sloping multilayer shells, Sov. Appl. Mech., 1971, vol. 7, no. 3, pp. 235–239.

    Article  Google Scholar 

  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.

  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.

    Article  MATH  Google Scholar 

  15. Singh, B. and Nanda, B.K., Dynamic analysis of damping in layered and welded beams, Eng. Struct., 2013, vol. 48, pp. 10–20.

    Article  Google Scholar 

  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.

  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.

  18. Panin, V.F. and Gladkov, Yu.A., Konstruktsii s zapolnitelem: Spravochnik (Constructions with a Filler: Handbook), Moscow: Mashinostroenie, 1991.

  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.

  20. Prokhorov, B.F. and Kobelev, V.N., Trekhsloinye konstruktsii v sudostroenii (Three-Layer Constructions in Ship Building), Leningrad: Sudostroenie, 1972.

  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.

  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.

    Article  Google Scholar 

  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.

  24. Demidovich, B.P. and Maron, I.A., Computational Mathematics, Moscow: Mir, 1981.

  25. Egorov, A.I., Obyknovennye differentsial’nye uravneniya s prilozheniyami (Common Differential Equations with Applications), Moscow: Fizmatlit, 2005, 2nd ed.

  26. Piskunov, N.P., Differentsial’noe i integral’noe ischisleniya (Differential and Integral Estimates), Moscow: Nauka, 1985.

  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. 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.

    MathSciNet  Google Scholar 

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ACKNOWLEDGMENTS

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

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Correspondence to O. M. Ustarkhanov.

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Translated by Bernard Gilbert

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Ustarkhanov, O.M., Yusupov, A.K., Muselemov, K.M. et al. Three-Layer Cylindrical Shell with Nonlinear Deformation. Russ. Engin. Res. 39, 95–101 (2019). https://doi.org/10.3103/S1068798X19020266

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  • DOI: https://doi.org/10.3103/S1068798X19020266

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