Skip to main content
SpringerLink
Log in

Modeling the Dynamic Behavior of Rigid-Plastic Thin Reinforced Curvilinear Plates with a Hole on a Viscous Foundation

  • Published:
Mechanics of Composite Materials Aims and scope

A mathematical model is developed for the dynamic behavior of rigid-plastic thin reinforced layered curvilinear, hinge-supported or clamped, plates with an arbitrary free hole. The plates are on a viscous foundation and are subjected to the action of a dynamic load of explosive type uniformly distributed on its surface. The plates are hybrid, multilayered, and fibrous, with their layers distributed symmetrically with respect to the middle surface. In each layer, the reinforcing fibers are located parallel or normal to the external contour of plate. The structural model of a reinforced layer is used. Depending on intensity of the load, various dynamic deformation modes of the plates are possible. From the principle of virtual power, with account of d’Alembert’s principle, the equations of dynamic behavior of the plates are obtained and the conditions for their implementation are determined for each of the modes. Analytical expressions for estimation of their limit loads are obtained. The variant of quasi-isotropic reinforcement is considered. Numerical examples for a reinforced elliptic plate with a circular hole are given.

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.

Institutional subscriptions

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. C. W. Lim, S. Kitipornchai, and K. M. Liew, “Free vibration analysis of doubly connected super elliptical laminated composite plates,” Compos. Sci. Technol., 58, 435-445 (1998). https://doi.org/10.1016/S0266-3538 (97) 00167-X

  2. E. Altunsaray, “Static deflections of symmetrically laminated quasi-isotropic super-elliptical thin plates,” Ocean Engineering, 141, 337-350 (2017). https://doi.org/10.1016/j.oceaneng.2017.06.032

    Article  Google Scholar 

  3. A. P. Yankovskii, “Viscoplastic dynamics of metallic composite shells of layered-fibrous structure under the action of loads of explosive type. I. Statement of the problem and method for solution,” J. Mathematical Sci., 192, No. 6, 623-633 (2013). https://doi.org/10.1007/s10958-013-1421-7

    Article  Google Scholar 

  4. A. P. Yankovskii, “Employing the time-explicit method of central differences for numerically modeling the dynamic behavior elastoplastic flexible reinforced plates,” Wychislit. Mekh. Splosh. Sred, 9, No. 3, 279-297 (2016). https://doi.org/10.7242/1999-6691/2016.9.3.24.

    Google Scholar 

  5. O. N. Popov, A. P. Malinovskii, M. O. Moiseenko, and T. A. Тreputneva, “On the problem of calculation of inhomogeneous structural beyond the limit of elasticity,” Vest. TGASU, Вест. ТГАСУ, No. 4, 127-142 (2013).

  6. N. A. Abrosimov, A.V. Elesin, and N. A. Novosel’tsev, “Numerical analysis of the effect of reinforcement structure on the dynamic behavior and ultimate deformability of composite shells of revolution,” Mech. Compos. Mater., 50, No. 2, 313-326 (2014). https://doi.org/10.1007/s11029-014-9409-z

    Article  Google Scholar 

  7. F. D. Morinière, R. C. Alderliesten, and R. Benedictus, “Modelling of impact damage and dynamics in fibre-metal laminates. A review,” Int. J. Impact Eng., 67, 27-38 (2014). https://doi.org/10.1016/j.ijimpeng.2014.01.004

    Article  Google Scholar 

  8. H. Arora, P. Del Linz, and J. P. Dear, “Damage and deformation in composite sandwich panels exposed to multiple and single explosive blasts,” Int. J. Impact Eng., 104, 95-106 (2017).

    Article  Google Scholar 

  9. N. Jones, “Some recent developments in the dynamic inelastic behavior of structures,” Ships and Offshore Structures, 1, No. 1, 37-44 (2006).

    Article  Google Scholar 

  10. Z. Wang, G. Lu, F. Zhu, and L. Zhao, “Load-carrying capacity of circular sandwich plates at large deflection,” J. Eng. Mech., 143, No. 9, 04017057-1-12 (2017).

    Google Scholar 

  11. Yu. V. Nemirovskii and T. P. Romanova, “Dinamic Resistance of Plane Plastic Barriers [in Russian], Novosibirsk: Izd. GEO, (2009).

    Google Scholar 

  12. Yu. V. Nemirovskii, “On a condition of plasticity (strength) for a reinforced layer,” Prikl. Mekh. Tekhn. Fiz., 10, No. 5, 81-88 (1969).

    Google Scholar 

  13. Yu. V. Nemirovskii and B. S. Resnikoff, “On limit equilibrium of reinforced slabs and effectiveness of their reinforcement,” Archiwum Inzynierii Ladowej, XXI, No. 1, 57-67 (1975).

    Google Scholar 

  14. A. R. Rzhanitsyn, Limit Equilibrium of Plates and Shells [in Russian], M.: Nauka (1983).

  15. N. A. Abrosimov and V. G. Bazhenov, “Nonlinear Problems of the Dynamics of Composite Structures [in Russian], N. Novgorod, Izd. NNGU (2002).

  16. Yu. V. Nemirovskii and N. A. Fedorova, Mathematical Modeling of Plane Structures of Reinforced Fibrous Materials [in Russian], Krasnoyarsk, Izd. SFU (2010).

    Google Scholar 

  17. S. A. Аmbartsumyan, Theory of Anisotropic Plates: Strength, Stability, and Vibrations [in Russian], M., Nauka (1987).

  18. S. G. Lekhnitskii, Anizotropic Plates [in Russian], M., GITTL (1957).

  19. Yu. V. Nemirovskii and B. S. Reznikov, Stregth of Structural Members of Composite Materials [in Russian], Novosibirsk, Nauka, Sib. Otdelenie (1986).

    Google Scholar 

  20. V. N. Mazalow and Yu. V. Nemirovsky, “Dynamic bending of rigid-plastic annular plates,” Int. J. Non-Linear Mechanics, 11, No. 1, 25-40 (1976).

    Article  Google Scholar 

  21. N. Jones, “Finite deflections of rigid-viscoplastic strain-hardening annular plate loaded impulsively,” Trans. ASME, J. Appl. Mech., 35, No. 2, 349-356 (1968).

    Article  Google Scholar 

  22. N. Jones, “Finite deflections of a simply supported rigid-plastic annular plate loaded dynamically,” Int. J. Solids and Struct., 5, No. 6, 593-603 (1968).

    Article  Google Scholar 

  23. J. Lellep and K. Torn, “Dynamic plastic behavior of annular plates with transverse shear effects,” Int. J. Impact Eng., 34, No. 6, 1061-1080 (2007).

    Article  Google Scholar 

  24. H. R. Aggarwal and C. M. Ablow, “Plastic bending of an annular plate by uniform impulse,” Int. J. Non-Linear Mechanics, 6, No. 1, 69-80 (1971).

    Article  Google Scholar 

  25. Yu. V. Nemirovskii and T. P. Romanova, “Dynamics of a rigid-plastic regular polygonal plate with a hole under the action of explosive loadings,” Boundary-value problems and mathematical modeling: Sb. St. 9 Vseros. Nauch. Konf., November 28-29, 2008, Novokuznetsk. In 3 vol. 1. / NFI GOU <KemGU>; under ed. V. O. Kaledin, Novokuznetsk, 93-97 (2008).

  26. Yu. V. Nemirovskii and T. P. Romanova, “Mechanics of the dynamic behavior of rigid-plastic curvilinear plate with an arbitrary free hole,” Teor. Prikl. Mekh., Mezhdunar. Nauch. Tekhn. Sb., Minsk, BNTU, No. 23, 26-34 (2007).

  27. T. P. Romanova and Yu. V. Nemirovsky, “Dynamic rigid-plastic deformation of arbitrarily shaped plates,” J. Mechanics of Materials and Structures, 3, No. 2, 313-334 (2008). https://doi.org/10.2140/jomms.2008.3.313

    Article  Google Scholar 

  28. Yu. V. Nemirovskii and T. P. Romanova, “Dynamics of rigid-platic curvilinear plate of variable thickness with an arbitrary internal hole,” Prikl. Mekh., 46, No. 3, 70-82 (2010). https://doi.org/10.1007/s10778-010-0311-7.

    Google Scholar 

  29. Yu. V. Nemirovskii and T. P. Romanova, “Dynamics of a round rigid-plastic plate with an arbitrary free internal hole,” Nauka. Promyshl. Oborona (NPO-2008) Trudy 9 Vseros. Nauch. Tekhn. Konf., Novosibirsk, April, 23-25, 2008. Novosibirsk: NGTU, 262-274 (2008).

  30. T. P. Romanova, “Modeling the dynamic bending rigid-plastic reinforced layered round plates with an arbitrary hole on a viscous foundation at explosive loadings,” Probl. Prochn. Plastichn., Iss. 79, No. 3, 267-284 (2017).

  31. T. P. Romanova, “Modeling of dynamic bending of rigid-plastic reinforced layered curvilinear plate with supported circular hole under explosive loads,” PNRPU Mechanics Bulletin, No. 3, 167-187 (2017). https://doi.org/10.15593/perm.mech/2017.3.10.

  32. T. P. Romanova, “Modeling the dynamic bending of rigid-plastic hybrid composite elliptical plates with a rigid insert,” Mech. Compos. Mater., 53, No. 5, 809-828 (2017). https://doi.org/10.1007/s11029-017-9687-3

    Article  Google Scholar 

  33. A. A. Savelov, Plane Curves [in Russian], M., Gos. izd. fiz.-mat. liter. (1960)

  34. M. I. Erkhov, Theory of Ideally Plastic Bodies and Structures [in Russian], M., Nauka (1978).

  35. A. H. Keil, Problems of plasticity in naval structures: explosive and impact loadings,” Mekhanika (collection of translations), No. 2, 197-223 (1961).

  36. L.V. Kantorovich and G. P. Аkilov, Functional Analysis [in Russian], M., Nauka (1984).

  37. T. P. Romanova, “Carrying capacity and optimization of three-layer reinforced concrete annular plate, supported on the internal contour,” PNRPU Mechanics Bulletin, No. 3, 114-132 (2015).

Download references

Author information

Authors and Affiliations

  1. S. A. Hristianovich Institute of Theoretical and Applied Mechanics of Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russia

    T. P. Romanova

Authors
  1. T. P. Romanova
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to T. P. Romanova.

Additional information

Translated from Mekhanika Kompozitnykh Materialov, Vol. 55, No. 3, pp. 425-450, May-June, 2019.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Romanova, T.P. Modeling the Dynamic Behavior of Rigid-Plastic Thin Reinforced Curvilinear Plates with a Hole on a Viscous Foundation. Mech Compos Mater 55, 297–314 (2019). https://doi.org/10.1007/s11029-019-09813-0

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11029-019-09813-0

Keywords

Search

Navigation