Shota Rustaveli National Science Foundation of GeorgiaStart Date: 2012-12-20 End Date: 2014-12-19
Cusped plates and beam s, on the one hand, are very important details from the practical point of view, such plates and beam s
are often encountered in spatial structures with partly fixed edges, e.g., stadium ceilings, aircraft wings, submarine wings etc., in
machine-tool design, as in cutting-machines, planning-machines, in astronautics, turbines, and in m any other areas of
engineering (e.g., dam s); on the other hand, their theoretical analysis and calculation are mathematically connected with the
study of very difficult problem s for degenerate partial differential equations which are not covered by the general theory for
degenerate partial differential equations. Som e satisfactory results are achieved in this direction in the case of Lipschitz domains
but in the case of non-Lipschitz domains there are a lot of open problem s. This is a one part of the objectives of the present
project. To this end there will be used function-analytic, approximate and special methods (suitable to problem s peculiarities).
As results, boundary value problem s in the zero and first approximation for hierarchical models of cusped plates and beams in
case of 3-D non-Lipschitz domains will be investigated.
The objective of the present project is separation and investigation of such classes of problem s, which can be studied applying
dimensional reduction and decom position methods. The methods and approaches already created by participants for
investigation of hierarchical models for elastic prismatic shells, for investigation of peculiarities of formulation of boundary
conditions for cusped prismatic shells caused by cusped geometry will be used and modified.
It should be noted that the two models from four which will be considered in the project have not been investigated so far, and
one is in initial stage of investigation.
In the project both the senior and the young (six of them are under the ages 38, three among them under the ages 28)
generation will be participated. In spite of the different age of participants most of them are highly qualified scientists with the
good experience of joint scientific collaboration, that is confirmed by their participation in the international scientific projects and
scientific meetings and their publications in internationally highly ranked journals , in particular, with impact factor.