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Archive of Applied Mechanics

, Volume 81, Issue 10, pp 1487–1505 | Cite as

Concentrated contact interactions in cuspidate prismatic shell-like bodies

  • N. Chinchaladze
  • G. Jaiani
  • B. Maistrenko
  • P. Podio-Guidugli
Original

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.

Keywords

Cuspidated (cusped) Vekua’s shells Cuspidated (cusped) plates Cuspidated (cusped) prismatic shell-like bodies Concentrated contact interactions Concentrated boundary loads 

References

  1. 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)MathSciNetMATHCrossRefGoogle Scholar
  2. 2.
    Jaiani G.: A cusped prismatic shell-like body under the action of concentrated moments. Z. Angew. Math. Phys. 59, 518–536 (2008)MathSciNetMATHCrossRefGoogle Scholar
  3. 3.
    Jaiani G.: On a nonlocal boundary value problem for a system of singular differential equations. Appl. Anal. 87(1), 83–97 (2008)MathSciNetMATHCrossRefGoogle Scholar
  4. 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)MathSciNetGoogle Scholar
  5. 5.
    Jaiani G.: Elastic bodies with non-smooth boundaries—cusped plates and shells. ZAMM Z. Angew. Math. Mech. 76(Suppl. 2), 117–120 (1996)MATHGoogle Scholar
  6. 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)Google Scholar
  7. 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)MathSciNetMATHCrossRefGoogle Scholar
  8. 8.
    Podio-Guidugli P.: Examples of concentrated contact interactions in simple bodies. J. Elast. 75, 167–186 (2004)MathSciNetMATHCrossRefGoogle Scholar
  9. 9.
    Podio-Guidugli P.: On concentrated contact interactions. Birkhäuser of Prog. Nonlinear Differ. Equ. Appl. 68, 137–147 (2006)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Podio-Guidugli, P., Schuricht, F.: Concentrated actions on cuspidate bodies. J. Elast. (2010). doi: 10.1007/s10659-010-9295-0
  11. 11.
    Schuricht F.: A new mathematical foundation for contact interactions in continuum physics. Arch. Rat. Mech. Anal. 184, 495–551 (2007)MathSciNetMATHCrossRefGoogle Scholar
  12. 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)Google Scholar
  13. 13.
    Timoshenko S.P., Goodier J.N.: Theory of Elasticity, pp. 567. McGraw-Hill, NY (1970)MATHGoogle Scholar
  14. 14.
    Vekua, I.: Shell Theory: General Methods of Construction. Pitman Advanced Publishing Program, Boston-London-Melburn, pp. 287 (1985)Google Scholar

Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  • N. Chinchaladze
    • 1
  • G. Jaiani
    • 1
  • B. Maistrenko
    • 1
  • P. Podio-Guidugli
    • 2
  1. 1.I. Vekua Institute of Applied MathematicsIv. Javakhishvili Tbilisi State UniversityTbilisiGeorgia
  2. 2.Department of Civil EngineeringUniversity of Rome TorVergataRomeItaly

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