plane elasticity problems, the elastic plate with holes, conservation laws, exact solutions of the theory of elasticity.

Elastic state of a rectangular plate with free-form holes was studied; the plate was exposed to loads directed to the sides along the normal lines. On the outlines of the holes zero values of the stress component are maintained. With such boundary conditions an exact solution of the problem was built in the form of quadratures on the outer boundary and the boundaries of the holes’ outlines. For this purpose an infinite system of laws of equation conservation of the theory of elasticity was found and used that is dependant on the stress component in a linear fashion. For simplicity the case of just one hole was studied in detail in the article. For a certain number of holes the problem shall be solved in much the same way.

Senashov Sergei Ivanovich

e-mail: sen@sibsau.ru, Dr. Sci. Phys. & Math., Professor, M. Reshetnev Siberian State Aerospace University, Krasnoyarsk, Russia.

Savostyanova Irina Leonidovna

e-mail: savostyanova@sibsau.ru, Ph.D. in Pedagogy, M. Reshetnev Siberian State Aerospace University, Krasnoyarsk, Russia.