Skip to main content
SpringerLink
Log in

The Stress State of Composite Cylindrical Shells Based on Refined Theory with Allowance for the Piezoelectric Effect

  • RELIABILITY, STRENGTH, AND WEAR RESISTANCE OF MACHINES AND STRUCTURES
  • Published:
Journal of Machinery Manufacture and Reliability Aims and scope Submit manuscript

Abstract

In this article, we present a refined mathematical model of the stress–strain state of multilayer composite cylindrical shells taking into account the piezoelectric effect. The displacements and the electric potential of the shell are represented as polynomials in the normal coordinates two degrees higher in comparison with the classical Kirchhoff–Love type of theory. A mathematical model of the electromechanical state of composite shells is obtained using the variational Lagrange principle. The formulated electroelasticity boundary value problem is solved by reducing three-dimensional equations to two-dimensional ones. An example of calculating the stress state of the boundary layer type of composite cylindrical shells with symmetric and asymmetric distributions of layers under the action of arbitrary mechanical and electrical loads is treated taking into account the piezoelectric effect.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Fig. 1.
Fig. 2.
Fig. 3.

Similar content being viewed by others

REFERENCES

  1. Baker, A., Dutton, S., and Kelly, D., Composite Materials for Aircraft Structures, 2nd ed., AIAA Educ. Ser., Reston, VA: AIAA, 2004.

  2. Grishanina, T.V. and Shklyarchuk, F.N., Dinamika upravlyaemykh konstruktsii (Dynamics of Controlled Structures), Moscow: Izd-vo MAI, 2007.

  3. Gol’denveizer, A.L., Teoriya uprugikh tonkikh obolochek (Theory of Thin Elastic Shells), Moscow: Nauka, 1976.

  4. Friedrichs, K.O., Kirchhoff’s boundary conditions and the edge effect for elastic plates, Proc. Symp. Appl. Math. Elasticity, 1950, vol. 3, p. 117–124.

  5. Timoshenko, S.P. and Woinowsky-Krieger, S., Theory of Plates and Shells, New York: McGraw-Hill, 1959.

    MATH  Google Scholar 

  6. Firsanov, V.V. and Chan, N.D., Energy-consistent theory of cylindrical shells, J. Mach. Manuf. Reliab., 2011, vol. 40, no. 6, pp. 543–548. https://doi.org/10.3103/S1052618811050098

    Article  Google Scholar 

  7. Firsanov, V.V. and Fam, V.T., Stress-strain state of the spherical shell exposed to an arbitrary load based on a non-classical theory, Prob. Prochn. Plast., 2019, vol. 81, no. 3, pp. 359–368. https://doi.org/10.32326/1814-9146-2019-81-3-359-368

    Article  Google Scholar 

  8. Firsanov, V.V. and Doan, T.N., Investigation of the statics and free vibrations of cylindrical shells on the basis of a nonclassical theory, Compos.: Mech., Comput., Appl.: Int. J., 2015, vol. 6, no. 2, pp. 135–166.  https://doi.org/10.1615/CompMechComputApplIntJ.v6.i2.40

    Article  Google Scholar 

  9. Reddy, J.N., Mechanics of Laminated Composite Plates and Shells: Theory and Analysis, 2nd ed., Boca Raton, Fla.: CRC Press, 2004.

    Book  Google Scholar 

  10. Gol’denveizer, A.L., Derivation of an approximate theory of shells by means of asymptotic integration of the equations of the theory of elasticity, J. Appl. Math. Mech., 1963, vol. 27, no. 4, pp. 903–924. https://doi.org/10.1016/0021-8928(63)90177-1

    Article  MathSciNet  Google Scholar 

  11. Zveryaev, E.M. and Olekhova, L.V., Iteration interpretation of semi-inverse Saint-Venant method in constructing the equations of thin-walled structural elements made of composite material, Tr. Mosk. Aviats. Inst., 2015, no. 79, p. 6.

  12. Ulitko, A.F., Metod sobstvennykh vektornykh funktsii v prostranstvennykh zadachakh teorii uprugosti (Method of Vector Eigenfunctions in Spatial Problems of Theory of Elasticity), Kiev: Naukova Dumka, 1979.

  13. Vasil’ev, V.V. and Lur’e, S.A., To the problem of improvement of the theory of shallow shells, Izv. Akad. Nauk. SSSR, Mekh. Tverd. Tela, 1990, no. 6, p. 139–146.

  14. Wu, X.-H., Chen, Ch., Shen, Ya-P., and Tian, X.-G., A high order theory for functionally graded piezoelectric shells, Int. J. Solids Struct., 2002, vol. 39, no. 20, pp. 5325–5344. https://doi.org/10.1016/S0020-7683(02)00418-3

    Article  MATH  Google Scholar 

  15. Parton, V.Z. and Kudryavtsev, B.A., Elektromagnitouprugost’ p’ezoelektricheskikh i elektroprovodnykh tel (Electromagnetoelasticity of Piezoelectric and Electroconductive Bodies), Moscow: Nauka, 1998.

  16. Tzou, H.S., Piezoelectric Shells: Distributed Sensing and Control of Continua, Dordrecht: Kluwer, 1993.

    Book  Google Scholar 

  17. Dimitrienko, Yu.I., Morozov, A.N., Sokolov, A.P., and Nichegovskii, E.S., Modeling efficient piezoelectric composite materials, Vestn. MGTU N. E. Baumana, Ser. Estestv. Nauki, 2010, no. 3, pp. 86–96.

  18. Ambartsumyan, S.A., Teoriya anizotropnykh plastin (Theory of Anisotropic Plates), Moscow: Nauka, 1967.

  19. Grinchenko, V.T., Ulitko, A.F., and Shul’ga, N.A., Mekhanika of svyazannykh polei v elementakh konstruktsii, vol. 5: Elektrouprugost’ (Mechanics of Coupled Fields in Structural Elements, vol. 5: Electroelasticity), Kiev: Naukova dumka, 1989.

  20. Vlasov, V.Z., Izbrannye trudy, vol. 1: Obshchaya teoriya obolochek (Selected Writings, vol. 1: General Theory of Shells), Moscow: Akad. Nauk SSSR, 1962.

Download references

Author information

Authors and Affiliations

  1. Moscow Aviation Institute, Moscow, Russia

    V. V. Firsanov & L. H. Nguyen

  2. Le Quy Don State Technical University, Hanoi, Socialist Republic of Vietnam

    L. H. Nguyen

Authors
  1. V. V. Firsanov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. L. H. Nguyen
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to L. H. Nguyen.

Ethics declarations

The authors declare that they have no conflict of interest.

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Firsanov, V.V., Nguyen, L.H. The Stress State of Composite Cylindrical Shells Based on Refined Theory with Allowance for the Piezoelectric Effect. J. Mach. Manuf. Reliab. 50, 312–318 (2021). https://doi.org/10.3103/S1052618821040038

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.3103/S1052618821040038

Keywords:

Search

Navigation