I.Vekua Institute of Applied Mathematics Tbilisi I. Javakhishvili  State University

Department of Shell Theory

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Institute of Applied Mathematics-professor Tengiz Meunargia

The department of the shell theory at the Institute was founded by Academician I. Vekua who dedicated many research works to the problems of the refined theory of shells. This investigations load the foundation for the work of the department where both the classical theory, based on the Kirchoff-Love hypothesis and refined theory of shells (E.Reissner, Friedrichs-Goldenweizer, A. Green, W. Koiter, D. Nagdi, P. Ciarlet, I. Vekua, I. Vorovich etc.) are represented. The analytical and numerical methods for the solution of the three-dimensional as well as two-dimensional problems are worked out.
Among the basic results, obtained by the members of the department, the following are of most importance:
1. By means of the method of I. Vekua, who had constructed the linear theory of thin and shallow shells, the system of differential equations was obtained for geometrically and physically non-linear and non-shallow shells. By means of the method of a small parameter their solution has been reduced to the system of plane theory of elasticity and Reissner type equations. (T. Meunargia)
The same method had been used for solving the problems of stress concentration for some elastic bodies and the obtained results were compared to the well-known results (M. Mosia).
For shell-type bodies the system of geometrical non-linear equations of elastic mixtures is obtained and the problems of stress concentration for sperical shells and plates have been solved (R. Janjgava).
For I. Vekua approximations (N=0, N=1, N=2) some well-known problems of stretch-press and bending of a plate are solved (M. Narmania).
2. The three-dimensional problems of the thermo elasticity are effectively solved at the orthogonal curvilinear coordinate. The circulation of blood has been investigated (N. Khomasuridze).
The analytical and numerical solutions of some boundary value problems of the theory of elasticity for elliptic bodies are obtained and the programme prouct for obtaining their numerical solutions is worked out (N. Zirakashvili).
For certain classes of boundary value problems of the transtropic, non-homogeneous parallelepiped, to which belong the axi-symmetric state, plane deformation state, twisting and shear, the exact solution has been found (Z. Siradze).
3. The packet of applied programmes ,,Enguri’’ has been mode that enobles to find the solutions of the problems of stress concentration for various forms of opening holes (A. Gogia).
The numerical solutions of some characteristic equations of the plane theory of elasticity are found and numerical calculation is done for spherical shells (Ts. Intskirveli, L. Gurgenidze).

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