, Volume 48, Issue 7, pp 1791–1804 | Cite as

On the numerical solution of some two-dimensional boundary-contact delocalization problems

  • N. Zirakashvili


The elastic equilibrium of a multi-layer confocal elliptic ring is studied. The ring consists of steel, rubber and celluloid layers which differ in thickness and in the order in which they are placed relative to one another. Using the solutions of the considered problems, the following delocalization problem is solved: for a three-layer elliptic body, the external elliptic boundary of which is loaded by normal point force and the internal boundary is stress-free and the layers of which are in rigid or sliding contact with one another, by an appropriate choice of layer thickness and arrangement of the layers relative to one another we can obtain a sufficiently uniform distribution of normal displacements on the internal elliptic boundary. Numerical solutions are obtained by the boundary element method and the related graphs are constructed. For the two-layer ellipse, exact and approximate solutions of the same problem are obtained respectively by the method of separation of variables and by the boundary element method. The results obtained by both methods are compared and the conclusion as to the reliability of the numerical boundary element method is made.


Boundary-contact problem Boundary element method Fictitious load Method of separation variables 


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Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  1. 1.I. Vekua Institute of Applied Mathematics of Iv. JavakhisviliTbilisi State UniversityTbilisiGeorgia
  2. 2.University of GeorgiaTbilisiGeorgia

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