Skip to main content
SpringerLink
Log in

Concentrated contact interactions in cuspidate prismatic shell-like bodies

  • Original
  • Published:
Archive of Applied Mechanics Aims and scope Submit manuscript

Abstract

This paper deals with a class of linearly elastic material bodies of a special shape, namely the cuspidate prismatic shell-like bodies introduced by I. Vekua, studied in the framework of Vekua’s 0-order approximation theory. It is shown per exempla that when such bodies are subject to concentrated boundary loads, concentrated internal contact interactions may arise. This fact helps to motivate the quest for a generalization of the standard theory, which covers only diffuse internal contact interactions.

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

Similar content being viewed by others

References

  1. Chinchaladze N., Gilbert R.P., Jaiani G., Kharibegashvili S., Natroshvili D.: Existence and uniqueness theorems for cusped prismatic shells in the N-th hierarchical model. Math. Methods Appl. Sci. 31(11), 1345–1367 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  2. Jaiani G.: A cusped prismatic shell-like body under the action of concentrated moments. Z. Angew. Math. Phys. 59, 518–536 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  3. Jaiani G.: On a nonlocal boundary value problem for a system of singular differential equations. Appl. Anal. 87(1), 83–97 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  4. Jaiani G.: A cusped prismatic shell-like body with the angular projection under the action of a concentrated force. Rend. Accad. Naz. Sci. XL Mem. Mat. Appl. 1240 Vol: XXX, fasc. 1, 65–82 (2006)

    MathSciNet  Google Scholar 

  5. Jaiani G.: Elastic bodies with non-smooth boundaries—cusped plates and shells. ZAMM Z. Angew. Math. Mech. 76(Suppl. 2), 117–120 (1996)

    MATH  Google Scholar 

  6. Jaiani, G.: Solution of Some Problems for a Degenerate Elliptic Equation of Higher Order and Their Application to Prismatic Shells. Tbilisi University Press, Tbilisi, 178 (1982) (in Russian; Georgian and English summaries)

  7. Jaiani G., Kharibegashvili S., Natroshvili D., Wendland W.L.: Two-dimensional hierarchical models for prismatic shells with thickness vanishing at the boundary. J. Elast. 77(2), 95–122 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  8. Podio-Guidugli P.: Examples of concentrated contact interactions in simple bodies. J. Elast. 75, 167–186 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  9. Podio-Guidugli P.: On concentrated contact interactions. Birkhäuser of Prog. Nonlinear Differ. Equ. Appl. 68, 137–147 (2006)

    Article  MathSciNet  Google Scholar 

  10. Podio-Guidugli, P., Schuricht, F.: Concentrated actions on cuspidate bodies. J. Elast. (2010). doi:10.1007/s10659-010-9295-0

  11. Schuricht F.: A new mathematical foundation for contact interactions in continuum physics. Arch. Rat. Mech. Anal. 184, 495–551 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  12. Schuricht, F.: Interactions in continuum physics. In: Šilhavý, M. (ed.) Mathematical Modeling of Bodies with Complicated Bulk and Boundary Behavior, Quaderni di Matematica 20, 169–196 (2007)

  13. Timoshenko S.P., Goodier J.N.: Theory of Elasticity, pp. 567. McGraw-Hill, NY (1970)

    MATH  Google Scholar 

  14. Vekua, I.: Shell Theory: General Methods of Construction. Pitman Advanced Publishing Program, Boston-London-Melburn, pp. 287 (1985)

Download references

Author information

Authors and Affiliations

  1. I. Vekua Institute of Applied Mathematics, Iv. Javakhishvili Tbilisi State University, 2 University Str., 0186, Tbilisi, Georgia

    N. Chinchaladze, G. Jaiani & B. Maistrenko

  2. Department of Civil Engineering, University of Rome TorVergata, Viale Politecnico 1, 00133, Rome, Italy

    P. Podio-Guidugli

Authors
  1. N. Chinchaladze
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. G. Jaiani
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. B. Maistrenko
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. P. Podio-Guidugli
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to G. Jaiani.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Chinchaladze, N., Jaiani, G., Maistrenko, B. et al. Concentrated contact interactions in cuspidate prismatic shell-like bodies. Arch Appl Mech 81, 1487–1505 (2011). https://doi.org/10.1007/s00419-010-0496-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00419-010-0496-6

Keywords

Search

Navigation