Distinctive features of moment shells theory using for calculation of hyperelastic cylindrical shells inflation

Capa

Citar

Texto integral

Acesso aberto Acesso aberto
Acesso é fechado Acesso está concedido
Acesso é fechado Acesso é pago ou somente para assinantes

Resumo

The paper concerns investigation of nonlinear moment shells theories equations application to solution of axisymmetric hyperelastic cylindrical shell static inflation problems. Elasticity equations used for calculation of shells deforming at arbitrary displacements and rotations and relations are obtained on the basis of a modified Kirchhoff–Love model. Results of calculations of linear elastic and neo-Hookean cylindrical shell based on moment theories relations and traditionally used for considered problems solution momentless theory are compared. Shell thickness is considered to be both constant and variable. It is shown that moment theories equations are suitable only when stress-strain state rapidly varying along a meridian. These equations possess a well-posedeness in comparison to equations of shells theory based on the modified Kirchhoff–Love model.

Sobre autores

E. Korovaytseva

Lomonosov Moscow State University, Institute of Mechanics

Autor responsável pela correspondência
Email: katrell@mail.ru
Moscow, Russia

Bibliografia

  1. Usyukin V.I. Structural mechanics of space technique structures. Moscow: Mashinostroenie, 1988. 392 p. (in Russian)
  2. Kylytchanov K.M. Some problems of soft shells statics at large strains [Nekotorye zadachi statiki myagkikh obolochek pri bol’shikh deformatsiyakh]. Ph.-m. sciences candidate thesis, Leningrad: 1984. 133 p. (in Russian)
  3. Druz’ B.I. et al. Statement and numerical solution of soft shells dynamics and equilibrium problems // In: Sbornik DVIIMU “Issledovaniya po sudovym myagkim i gibkim konstruktsiyam”. 1982. P. 113–130. (in Russian)
  4. Kolpak E.P. Stability and subsritical statements of momentless shells at large strains [Ustoichivost’ i zakriticheskie sostoyaniya bezmomentnykh obolochek pri bol’shikh deformatsiyakh]. Ph.-m. sciences doctor thesis, Saint-Petersburg: 2000. 334 p. (in Russian)
  5. Kolesnikov A.M. Large deformations of hyperelastic shells [Bol’shie deformatsii vysokoelastichnykh obolochek]. Ph.-m. sciences candidate thesis, Rostov-na-Donu: 2006. 115 p. (in Russian)
  6. Gimadiev R.Sh., Gimadieva T.Z., Paimushin V.N. On dynamic process of elastomeric thin shells inflation under the influence of overload pressure // Applied Mathematics and Mechanics, 2014, vol. 78. iss. 2, pp. 236–248. (in Russian). https://doi.org/10.1016/j.jappmathmech.2014.07.009
  7. Usyukin V.I. Technical theory of soft shells [Tekhnicheskaya teoriya myagkikh obolochek]. Ph.-m. sciences doctor thesis, Moscow: 1971. 361 p. (in Russian)
  8. Usyukin V.I. On equations of soft shells large deformations theory. Proceedings of the Academy of Sciences of the USSR, Mechanics of Solids, 1976, no. 1, pp. 70–75. (in Russian)
  9. Healey T.J., Li Q., Cheng R.B. Wrinkling Behavior of Highly Stretched Rectangular Elastic Films via Parametric Global Bifurcation // J Nonlinear Sci 23, 777–805 (2013). https://doi.org/10.1007/s00332-013-9168-3
  10. Li Q., Healey T. Stability boundaries for wrinkling in highly stretched elastic sheets // Journal of the Mechanics and Physics of Solids, 2016, vol. 97, pp. 260–274. https://doi.org/10.1016/j.jmps.2015.12.001
  11. Fu C., Wang T., Xu F., Huo Y., Potier-Ferry M. A modeling and resolution framework for wrinkling in hyperelastic sheets at fnite membrane strain // Journal of the Mechanics and Physics of Solids, 2018, vol. 124, pp. 446–470. https://doi.org/10.1016/j.jmps.2018.11.005
  12. He L., Lou J., Dong Y. et al. Variational modeling of plane-strain hyperelastic thin beams with thickness-stretching effect // Acta Mechanica, 2018, vol. 229, pp. 4845–4861. https://doi.org/10.1007/s00707-018-2258-4
  13. Wang Y., Zhu W. Nonlinear transverse vibration of a hyperelastic beam under harmonically axial loading in the subcritical buckling regime // Applied Mathematical Modelling, 2021, vol. 94, pp. 597–618. https://doi.org/10.1016/j.apm.2021.01.030
  14. Khaniki H.B., Ghayesh M.H., Chin R. et al. Nonlinear continuum mechanics of thick hyperelastic sandwich beams using various shear deformable beam theories // Continuum Mechanics and Thermodynamics, 2022, vol. 34, pp. 781–827. https://doi.org/10.1007/s00161-022-01090-y
  15. Steigmann D.J. Thin-plate theory for large elastic deformations // International Journal of Non-Linear Mechanics, 2007, vol. 42 (2), pp. 233–240. https://doi.org/10.1016/j.ijnonlinmec.2006.10.004
  16. Amabili M., Balasubramanian P., Breslavsky I.D. et al. Experimental and numerical study on vibrations and static deflection of a thin hyperelastic plate // Journal of Sound and Vibration, 2016, vol. 385, pp. 81–92. https://doi.org/10.1016/j.jsv.2016.09.015
  17. Breslavsky I.D., Amabili M., Legrand M. Static and Dynamic Behavior of Circular Cylindrical Shell Made of Hyperelastic Arterial Material // Journal of Applied Mechanics, 2016, vol. 83 (5), 9 p. https://doi.org/10.1115/1.4032549
  18. Amabili M., Breslavsky I.D., Reddy J.N. Nonlinear higher-order shell theory for incompressible biological hyperelastic materials // Computer Methods in Applied Mechanics and Engineering, 2019, vol. 346, pp. 841–861. https://doi.org/10.1016/j.cma.2018.09.023
  19. Zhang J., Xu J., Yuan X. et al. Nonlinear Vibration Analyses of Cylindrical Shells Composed of Hyperelastic Materials // Acta Mechanica Solida Sinica, 2019, vol. 32, pp. 463–482. https://doi.org/10.1007/s10338-019-00114-6
  20. Paimushin V.N. A theory of thin shells with finite displacements and deformations based on a modified Kirchhoff–Love model // Journal of Applied Mathematics and Mechanics, 2011, vol. 75, iss. 5, pp. 568–579. https://doi.org/10.1016/J.JAPPMATHMECH.2011.11.011
  21. Korovaytseva E.A. Mixed equations of soft shells theory // Trudy MAI. 2019. № 108. (in Russian). https://doi.org/10.34759/trd-2019-108-1
  22. Shapovalov L.A. Elastica equations of thin shells at axisymmetric deformation // Proceedings of the Academy of Sciences of the USSR, Mechanics of Solids, 1976, no. 3, pp. 62–72. (in Russian).
  23. Korovaytseva E.A. Modeling of processes of hyperelastic thin-walled shells of revolution deforming. [Ph.-m. sciences doctor thesis], Moscow: 2024. 290 p. (In Russian).

Arquivos suplementares

Arquivos suplementares
Ação
1. JATS XML
Baixar

Declaração de direitos autorais © Russian Academy of Sciences, 2025