On Cusped Shell-like Structures

  • George JaianiEmail author
Part of the Advanced Structured Materials book series (STRUCTMAT, volume 15)


This paper is updated concise survey of results concerning elastic cusped shells, plates, and beams and cusped prismatic shell-fluid interaction problems.


Cusped beams Cusped plates Cusped prismatic shells Mathematical modeling Linear elasticity 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Vekua, I.N.: On one method of calculating of prismatic shells. Trudy Tbilis. Mat. Inst. 21, 191–259 (1955) (in Russian).Google Scholar
  2. 2.
    Vekua, I.N.: Shell Theory: General Methods of Construction. Pitman, Boston (1985).Google Scholar
  3. 3.
    Jaiani, G.: On a mathematical model of bars with variable rectangular cross-sections. ZAMM Z. Angew. Math. Mech. 81(3), 147–173 (2001)CrossRefGoogle Scholar
  4. 4.
    Jaiani, G.V.: Theory of Cusped Euler-Bernoulli Beams and Kirchoff-Love Plates. Lect. Notes TICMI, 3 (2002).Google Scholar
  5. 5.
    Mikhlin, S.G.: Variational Methods in Mathematical Physics. Nauka, Moscow (1970).Google Scholar
  6. 6.
    Jaiani, G., Schulze, B.-.W.: Some Degenerate Elliptic Systems and Applications to Cusped Plates. Mathematische Nachrichten 280(4), 407 (2007)CrossRefGoogle Scholar
  7. 7.
    Avalishvili, M., Gordeziani, D.: Investigation of two-dimensional models of elastic prismatic shell. Georgian Math. J. 10(1), 36 (2003)Google Scholar
  8. 8.
    Schwab, C.: A-posteriori modelling error estimation for hierarchic Plate Models. Numer. Math. 74, 221–259 (1996)CrossRefGoogle Scholar
  9. 9.
    Jaiani, G., Kharibegashvili, S., Natroshvili, D., Wendland, W.L.: Two-dimensional Hierarchical Models for Prismatic Shells with Thickness Vanishing at the Boundary. J. Elasticity 77(2), 95–122 (2004)CrossRefGoogle Scholar
  10. 10.
    Chinchaladze, N., Gilbert, R., 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)CrossRefGoogle Scholar
  11. 11.
    Chinchaladze, N., Jaiani, G., Maistrenko, B., Podio-Guidugli, P.: Concentrated contact interactions in cuspidate prismatic shell-like bodies. Arch. Appl. Mech. DOI: 10.1007/s00419-010-0496-6Google Scholar
  12. 12.
    Chinchaladze, N., Gilbert, R., Jaiani, G., Kharibegashvili, S., Natroshvili, D.: Cusped elastic beams under the action of stresses and concentrated forces. Appl. Anal. 89(5), 757–774 (2010)CrossRefGoogle Scholar
  13. 13.
    Jaiani, G.: On Physical and Mathematical Moments and the Setting of Boundary Conditions for Cusped Prismatic Shells and Beams. Proceedings of the IUTAM Symposium on Relation of Shell, plate, Beam, and 3D Models, IUTAM Bookseries, 9: 133–146, Springer (2008).Google Scholar
  14. 14.
    Jaiani, G.V.: Elastic bodies with non-smooth boundaries–cusped plates and shells. Z. Angew. Math. Mech. 76(Suppl. 2), 117–120 (1996)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  1. 1.I. Vekua Institute of Applied Mathematics of Iv. Javakhishvili Tbilisi State UniversityTbilisiGeorgia

Personalised recommendations