Mechanics

2003, No. 2

S.A. Lychev, E.Y. Elenitskii

TO THE Y. Ed. SENITSKII 70th ANNIVERSARY

Yurii Edwardovich Senitskii is a specialist famous for his works in applied mechanics and mathematics. He is honoured worker of science of Russian Federation, Doctor of Technical Science, Professor, full member of New York Academy of Science. Senitskii much contributed to complicated problem of integrability of differential equations from dynamical nonhomogenious anisotropic elasticity, plates and shells theories, coupled problems describing the interaction of structural members under different physical fields, research of high-speed impact and impuls loading, special and emergency calculations. He introduced vector-matrix finite integral transformations and elaborate structural algorithm of such transformations, designed for solving wide range of the both self-adjoined and non self-adjoined problems of mathematical physics. His original and novice ideas, mathematical culture much affected theoretical aspects of structural engeneering as well as applied problems of durability, stability, vibration and optimisation known from energetical, building-on, petrol-tank industry. Y. E. Senitskii is respected among international scientific community and it is the best evidence of his outstanding accomplishments.

Y.N. Radayev, Y.N. Bakhareva, Y.N. Ryabova

IThe equations of axially-symmetric problem of the mathematical theory of plasticity are considered in the case when a stress state corresponds to an edge of the Tresca prism. The Tresca yield criterion and associated flow rule are used to formulate the basic equations. The hyperbolic equilibrium equations which formally can be treated independently from kinematic equations are represented in the curvi-linear co-ordinate net of the stress principal lines. The system of two ordinary differential equations is then derived by introducing a new variable called as the self-similar variable. The existence of self-similar solutions can be proved when the self-similar variable being a product of power function of isostatic co-ordinates. Supposing special values for parameters involved in self-similar solution, the problem is shown can be reduced to obtaining solution of a non-linear non-autonomous ordinary differential equation. This equation is analyzed numerically in the domain, where its right-hand side is naturally determined.

L.I. Fridman

NON-STATIONARY DYNAMICAL ELASTIC PROBLEM FOR FINITE CYLINDER

In the present work the solution of non-stationary dynamical elastic problem for finite cylinder is given. The descriptive functions are represented by means of convergent series over orthogonal functions.