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The most important achievements
1946 - 2000

The basis of up-to-date non-linear theory of elastic shells were laid (H.M.Mushtari, K.Z.Galimov). The monography of H.M.Mushtari, K.Z.Galimov "The non-linear theory of elastic shells" (1957) was republished in foreign languages and became the classic one in its field of knowledge. Under the guidance of H.M.Mushtari the Kazan school of the theory of shells was formed.
H.M.Mushtari, K.Z.Galimov

Efficient numerical and variation methods of analysis of non- linear behaviour of elastic and elastic-plastic shells, including the composite ones were worked out. The results were widely adopted in aircraft building, rocket production, shipbuilding, chemical engineering industry.
H.M.Mushtari, K.Z.Galimov,M.S.Kornyshin, I.G.Teregulov, I.V.Svirsky, M.S.Ganejeva, H.M.Yakupov and others

Non-linear theory of thin-walled structure elements interaction with working mediums (liquid, gas, soils) was developed. The results are used in mechanical engineering, engine production, pipeline and parachute systems projection.
Equations of dynamics of three-layer plates and shells with structure nonsymmetric in thickness were derived, analysis of static and dynamic stability, forced and parametric oscillations was conducted. A large series of investigations was performed on oscillations of cylindrical shells with a gas and a compressible fluid. Dynamic interaction of the cylindrical and spherical shells, the continuous elastic filler and the gas in the space was studied. Axisymmetrical shapes of oscillations of thin-walled cylindrical tube were studied theoretically and experimentally, generation of waves in the circular direction and catastrophic failure were found. Behaviour of plates, shallow panels, shells and parachutes in a flow of incompressible ideal liquid was studied. Experimental models of wave propellers were created.
M.A.Ilgamov, B.V.Gulin, V.A.Ivanov, Zh.M.Sakhabutdinov, V.V.Ridel, R.G.Yakupov, A.N.Gilmanov, R.G.Zaripov, V.L.Fedyajev, M.V.Taldykin, Z.V.Skvortsova and others

Analytical and numerical methods of oil-content contour determining in working conditions of supercharging and extracting wells were devised.
G.S.Salehov, V.D.Chugunov,V.L.Danilov, V.V.Skvortsov, M.H.Hairulin, A.I.Nikiphorov and others

There were made experimental and theoretical investigations of the shock waves in gas in the closed and open tubes. The processes of moving away gases cleaning by aerosols were examined. By means of analytic-numerical methods there were studied non-linear and chaotic oscillations of cylindrical shell in a stream of gas; of a gas cavity in liquid in sonoluminescence condition; of a tube with liquid; of a superconducting cable. A linear theory on the propagation of waves of different geometry in the polydispersed vapor-gas-droplets suspensions was developed. The nonsteady wave discharge of a boiling liquid from high-pressure pipes during its accidental depressurization was studied.
M.A.Ilgamov, D.A.Gubaidulin, R.G.Zaripov, A.A.Aganin, A.L.Tukmakov and others.

There was developed the theory and methods of calculating stresses, strains and stability of shells of multiplex geometry under intensive thermoforce loading, consideration physical and geometrical nonlinearity, interaction with agressive media. There were suggested the methods of reduction of strains and stresses concentration in dangerous zones of a reservoir for cryogen liquid (M.S.Ganejeva and others). It was made durability prediction of large-scale cooling towers constructions (N.M.Yakupov and others)

It was created the universal procedure of numerical solving the tasks of the viscous gas stream flow about aerodynamic objects (A.N.Gilmanov and others); of gas motion in three-dimensional regions of intricate configuration consideration chemical transmutations and intensive heat supply (Zh.M.Sahabutdinov and others). It was analysed the deceleration of supersonic gas stream in a flat channel. Special features of working processes in the chamber of internal-combustion engine, in a furnace of a spectrometer were studied.

There were worked out special methods of numerical solving the tasks of water flooding the oil pools in complicated physical- geological conditions; of determining the filtering parameters while the nonstationary filtration on the base of incorrect problems theory; of discovering the situation of a source of water-bearing stratum pollution. Variation principles were built for the problem of filtering in the deformated medium of compound reology (M.H.Hairullin, A.I.Nikiforov, P.A.Mazurov and others).

Mathematical models were created, on the basis of which there were studied physical-mechanical processes of electric arc welding and thermo-hardening the hardware;the motion of steam-gas-drop mixture in cooling towers (A.B.Mazo, V.L.Fedyajev and others); the streams of thermo-unbalanced plasma in discharging cameras of plasma generators (F.A.Saljanov).

The method of vector functions by Lyapunov was developed for investigating the stability of non-linear logycal-dynamic systems of control and systems with random structure changes (A.I.Malikov). There were studied the flow of liquid with free surface consideration the contact line of three phases division (F.H.Tazjukov and others); the processes of heat mass transfer while fraction crystallization (P.P.Osipov). There were obtained analytical solutions of the problem of control of mass flow rate of space objects for the future (U.N.Zakirov).


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