Skip to main content
Log in

Dynamic deformation of rigid-plastic curvilinear plates of variable thickness

  • Published:
Journal of Applied Mechanics and Technical Physics Aims and scope

Abstract

A general solution is obtained for the problem of dynamic bending of an ideal rigid-plastic plate of variable thickness with a simply supported or clamped curvilinear contour under the action of a short-time high-intensity explosive-type load uniformly distributed over the surface. Several mechanisms of plate deformation are demonstrated to exist. For each mechanism, equations of dynamic deformation are derived and conditions of mechanism implementation are analyzed. Examples of numerical solutions are given.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. K. L. Komarov and Yu. V. Nemirovsky, Dynamics of Rigid-Plastic Structural Elements [in Russian], Nauka, Novosibirsk (1984).

    Google Scholar 

  2. Yu. V. Nemirovsky and T. P. Romanova, “Dynamics of plastic deformation of curvilinear plates,” Int. Appl. Mech., 37, No. 12, 1568–1578 (2001).

    Article  Google Scholar 

  3. Yu. V. Nemirovsky and T. P. Romanova, “Plastic deformation of doubly connected plates with a curvilinear contour under dynamic loads,” in: Urgent Problems of Dynamics and Strength in Theoretical and Applied Mechanics [in Russian], Tekhnoprint, Minsk (2001), pp. 515–525.

    Google Scholar 

  4. Yu. V. Nemirovsky and T. P. Romanova, “Dynamic plastic damage of simply and doubly connected elliptic plates,” J. Appl. Mech. Tech. Phys., 43, No. 2, 291–301 (2002).

    Article  Google Scholar 

  5. Yu. V. Nemirovsky and T. P. Romanova, “Modeling and analysis of forging of thin-walled structures with smooth convex contours,” in: Mechanics of Shells and Plates, Proc. of the 20th Int. Conf. on the Theory of Shells and Plates (Nizhnii Novgorod, September 17–19, 2002), Izd. Nizhegor. Univ., Nizhnii Novgorod (2002), pp. 231–239.

    Google Scholar 

  6. Yu. V. Nemirovsky and T. P. Romanova, “Damage of plane targets with non-concave contours under explosive loading,” Nauch. Vestn. Novosib. Gos. Tekh. Univ., No. 2, 77–85 (2002).

  7. Yu. V. Nemirovsky and T. P. Romanova, “Dynamics of plastic plates in the form of irregular ovals,” in: Urgent Problems of Mechanics and Applied Mathematics [in Russian], Proc. Int. Workshop (Voronezh, June 4–8, 2002), Part 1, Voronezh State University, Voronezh (2003), pp. 182–196.

    Google Scholar 

  8. Yu. V. Nemirovsky and T. P. Romanova, “Dynamic behavior of rigid-plastic sector plates,” Int. Appl. Mech., 40, No. 4, 440–447 (2004).

    Article  Google Scholar 

  9. Yu. V. Nemirovsky and T. P. Romanova, “Damage of rigid-plastic doubly connected curvilinear plates in a viscous medium under explosive loads,” in: Science. Industry. Defence, Proc. 7th All-Russia Conf. (Novosibirsk, April 19–21, 2006), Novosibirsk State Tech. Univ., Novosibirsk (2006), pp. 317–323.

    Google Scholar 

  10. M. I. Reitman and G. S. Shapiro, Methods of Optimal Design of Deformable Solids [in Russian], Nauka, Moscow (1976).

    Google Scholar 

  11. Yu. V. Nemirovsky and V. N. Mazalov (eds.), Optimal Design: Bibliographic Index [in Russian], Vol. 1 and 2, Inst. Hydrodynamics, Sib. Div., Acad. of Sci. of the USSR, Novosibirsk (1975).

    Google Scholar 

  12. H. Yakimawa, “Design of optimal dynamically loaded structures,” in: Novel Directions in Structural Design [Russian translation], Stroiizdat, Moscow (1989), pp. 245–262.

    Google Scholar 

  13. Yu. V. Nemirovsky, “Optimal design of homogeneous and layered plastic beams under dynamic loading,” in: Proc. 5th All-Russia Workshop (Novosibirsk, April 7–8, 2005), Novosibirsk State University of Architecture and Civil Engineering, Novosibirsk (2005), pp. 261–267.

    Google Scholar 

  14. B. A. Lyukshin and V. A. Kovalev, “Calculation of elastoplastic shells of revolution of variable thickness under dynamic loading,” in: T. M. Platova (ed.), Mechanics of Continuous Media (collected scientific papers) [in Russian], Izd. Tomsk. Univ., Tomsk (1983), pp. 10–17.

    Google Scholar 

  15. M. I. Erkhov, Theory of Ideal Plastic Solids and Structures [in Russian], Nauka, Moscow (1978).

    Google Scholar 

  16. Yu. V. Nemirovsky and T. P. Romanova, “Dynamic deformation of a curved plate with a rigid insert,” J. Appl. Mech. Tech. Phys., 47, No. 2, 254–265 (2006).

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

__________

Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 5, pp. 108–120, September–October, 2007.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Nemirovsky, Y.V., Romanova, T.P. Dynamic deformation of rigid-plastic curvilinear plates of variable thickness. J Appl Mech Tech Phys 48, 712–722 (2007). https://doi.org/10.1007/s10808-007-0092-x

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10808-007-0092-x

Key words

Navigation