Skip to main content
SpringerLink
Log in

Deformation of an Elastoplastic Three-Layer Circular Plate in a Temperature Field

  • Published:
Mechanics of Composite Materials Aims and scope

A boundary-value problem on axisymmetric deformation of a circular elastoplastic plate, asymmetric across its thickness, in a temperature field is formulated. The physical equations of state used correspond to the theory of small elasticoplastic strains. The effect of a temperature field on the stress-strain state of the plate is considered. The intensity of thermal flow is constant. To describe the kinematics of the plate package, the hypotheses of a broken line are accepted: in the thin load-bearing layers, the Kirchhoff hypotheses are valid; in the rigid core, incompressible across it thickness, the Tymoshenko hypothesis is valid. The work of core in the tangential direction is taken into account. The equilibrium equations are derived by the variational method. An analytical solution of the boundary-value problem is obtained by the method of elastic solutions. A numerical analysis of the stress-strain state of a plate with a hinged contour is carried out.

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.
Fig. 4.

Similar content being viewed by others

References

  1. V. V. Bolotin and Yu. N. Novichkov, Mechanics of Multilayered Structures [in Russian], Mashinostroenie, Moscow (1980).

    Google Scholar 

  2. E. I. Starovoitov, D. V. Leonenko, and A. V. Yarovaya, “Vibrations of round three-layer plates under the action of various types of surface loads,” Strength of Mater., 35, No. 4, 346−352 (2003).

    Article  Google Scholar 

  3. E. I. Starovoitov, V. D. Kubenko, and D. V. Tarlakovskii, “Vibrations of circular sandwich plates connected with an elastic foundation,” Russian Aeronautics, 52, No. 2, 151–157 (2009).

    Article  Google Scholar 

  4. E. I. Starovoitov, D. V. Leonenko, and D. V. Tarlakovsky, “Resonance vibrations of circular composite plates on an elastic foundation,” Mech. Compos. Mater., 51, No. 5, 561–570 (2015).

    Article  Google Scholar 

  5. E. I. Starovoitov and D. V. Leonenko, “Impact of thermal and ionizing radiation on a circular sandwich plate on an elastic foundation,” Int. Appl. Mech., 47, No. 5, 580−589 (2011).

    Article  Google Scholar 

  6. D. V. Leonenko and E. I. Starovoitov, “Thermal impact on a circular sandwich plate on an elastic foundation,” Mech. of Solids, 47, No. 1, 111–118 (2012).

    Article  Google Scholar 

  7. I. Ivañez, M. M. Moure, S. K. Garcia-Castillo, and S. Sanchez-Saez, “The oblique impact response of composite sandwich plates,” Compos. Structures, No. 133, 1127–1136 (2015).

  8. V. S. Deshpande and N. A. Fleck, “Dynamic response of a clamped circular sandwich plate subject to shock loading,” J. Appl. Mech., 71, No. 5, 637–645 (2004).

    Article  Google Scholar 

  9. V. N. Paimushin and R. K. Gazizullin, “Static and monoharmonic acoustic impact on a laminated plate,” Mech. Compos. Mater., 53, No. 3, 283–304 (2017).

    Article  Google Scholar 

  10. V. N. Paimushin, V. A. Firsov, and V. M. Shishkin, “Modeling the dynamic response of a carbon-fiber-reinforced plate at resonante vibrations considering the internal friction in the material and the external aerodynamic damping,” Mech. Compos. Mater., 53, No. 4, 425–440 (2017).

    Article  Google Scholar 

  11. V. N. Paimushin, “Theory of moderately large deflectıons of sandwıch shells having a transversely soft core and reinforced along their contour,” Mech. Compos. Mater., 53, No. 1, 1–16 (2017).

    Article  Google Scholar 

  12. T. P. Romanova, “Modeling the dynamic bending of rigid-plastic hybrid composite elliptical plates with a rigid insert,” Mech. Compos. Mater., 53, No. 5, 563–578 (2017).

    Article  Google Scholar 

  13. K. T. Takele, “Interfacial strain energy continuity assumption-based analysis of an orthotropic sandwich plate using a refined layer-by-layer theory,” Mech. Compos. Mater., 54, No. 3, 419–444 (2018).

    Article  Google Scholar 

  14. L. Škec and G. Jelenić, “Analysis of a geometrically exact multi-layer beam with a rigid interlayer connection,” Acta Mechanica, 225, No. 2, 523–541 (2004).

    Article  Google Scholar 

  15. H. V. Zadeh and M. Tahani, “Analytical bending analysis of a circular sandwich plate under distributed load,” Int. J. of Recent Advances in Mech. Eng., 6, No. 1. (2017). DOI: https://doi.org/10.14810/ijmech.2017.6101.

  16. L. Yang, O. Harrysson, H. West, and D. A. Cormier, “Comparison of bending properties for cellular core sandwich panels,” Mater. Sci. Appl., 4, No. 8, 471−477 (2013).

    Google Scholar 

  17. C. R. Lee, S. J. Sun, and Т. Y. Каm, “System parameters evaluation of flexibly supported laminated composite sandwich plates,” AIAA J., 45, No. 9 (2007).

  18. J. Dallot, K. Sab “Limit analysis of multi-layered plates. Pt. I: The homogenized Love–Kirchhoff model,” J. Mech. and Phys. Solids., 56, No. 2, 561–580 (2008).

    Article  CAS  Google Scholar 

  19. Z. Xie, “An approximate solution to the plastic indentation of circular sandwich panels,” Mech. Compos. Mater., 54, No. 2, 243–250 (2018).

    Article  Google Scholar 

  20. Zh. Wang, G. Lu, F. Zhu, and L. Zhao, “Load-carrying capacity of circular sandwich plates at large deflection,” J. Eng. Mech., 143, No. 9 (2017). DOI: https://doi.org/10.1061/(ASCE)EM.1943-7889.0001243.

  21. A. Kudin, M. A. V. Al-Omari, B. G. M. Al-Athamneh, and H. K. M. Al-Athamneh, “Bending and buckling of circular sandwich plates with the nonlinear elastic core material,” Int. J. Mech. Eng. and Information Techn., 3, No. 8, 1487–1493 (2015). DOI: https://doi.org/10.18535/ijmeit/v2i8.02

    Article  Google Scholar 

  22. A. P. Yankovskii, “Refined modeling of flexural deformation of layered plates with a regular structure made from nonlinear hereditary materials,” Mech. Compos. Mater., 53, No. 6, 705–724 (2017).

    Article  Google Scholar 

  23. J. Belinha and L. M. Dints, “Nonlinear analysis of plates and laminates using the element free Galerkin method,” Compos. Struct., 78, No. 3, 337–350 (2007).

    Article  Google Scholar 

  24. A. M. Zenkour, “A Comprehensive analysis of functionally graded sandwich plates. Pt 1: Deflection and stresses,” Int. J. Solids Struct., 42, No. 18/19, 5224–5242 (2005).

    Article  Google Scholar 

  25. A. M. Zenkour and N. A. Alghamdi, “Thermomechanical bending response of functionally graded nonsymmetric sandwich plates,” J. Sandwich Struct. Mater., 12, No. 1, 7–46 (2009).

    Article  Google Scholar 

  26. E. I. Starovoitov, D. V. Leonenko, and D.V. Tarlakovskii, “Thermoelastic deformation of a circular sandwich plate by local loads,” Mech. Compos. Mater., 54, No. 3, 299–312 (2018).

    Article  Google Scholar 

  27. A. A. Il’yushin, Plasticity [in Russian], Gostekhizdat, Moscow-Leningrad (1948).

    Google Scholar 

  28. E. I. Starovoitov, “Description of the thermomechanical properties of some structural materials,” Strength of Mater., 20, No. 4, 426–431 (1988).

    Article  Google Scholar 

Download references

Acknowledgements

This work was financially supported by the Belarusian Republican Foundation for Fundamental Research (Project No. T18P-090).

Author information

Authors and Affiliations

  1. Belarusian State University of Transport, Gomel, Belarus

    E. I. Starovoitov & D. V. Leonenko

Authors
  1. E. I. Starovoitov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. D. V. Leonenko
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to E. I. Starovoitov.

Additional information

Translated from Mekhanika Kompozitnykh Materialov, Vol. 55, No. 4, pp. 727-740, July-August, 2019.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Starovoitov, E.I., Leonenko, D.V. Deformation of an Elastoplastic Three-Layer Circular Plate in a Temperature Field. Mech Compos Mater 55, 503–512 (2019). https://doi.org/10.1007/s11029-019-09829-6

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11029-019-09829-6

Keywords

Search

Navigation