Shota Rustaveli National Science Foundation of GeorgiaStart Date: 2013-01-20 End Date: 2013-04-20
Studies with pupils participation
“On approximate solution of one class of singular integral equations”
It is Georgian scientists owe very much to offer a great value of scientific heritage of the Academician Nikoloz Muskhelishvili to pupils. My willing is to perform some work with youth which in future will give a great stimulus on the scientific research way. Study of boundary value problems for the composite bodies weakened by cracks has a great practical significance. By the project proposal is planed (considered) to study value problems of the anti-plane elasticity theory for orthotropic (in particular case, isotropic) plane. Very interesting cases when cracks intersect an interface or penetrate it at rectangular angle will be studied. Intended by the project proposal the question of the approached decision of one system (pair) of the singular integral equations when cracks intersect an interface (task-1) or penetrate it at zero angle (task-2) for finding the tangent stress jumps will be studied by numerical experiments. In my researches have been studied the problem of above mentioned questions in the neighborhood of the crack endpoints and at the parting line. With collaboration of pupils at first will be proposed new algorithms based on the collocation, spectral and asymptotic methods. For the approximate solution above mentioned tasks will be created new algorithms and a complex of program system using one of the modern C++ operation program systems.