Mechanics

Numerical Study of Stress-Strain State of a Thin Anisotropic Rectangular Plate

Authors: Nedorezov P. F.

Static bending of a thin rectangular anisotropic plate is considered in the framework of Kirchhoff hypotheses. At each point of the plate there is one plane of elastic symmetry parallel to the middle plane of the plate. It is assumed that the type of boundary conditions does not change along each of the straight sides. By applying of a modified method of spline collocation the twodimensional boundary value problem for the determination of deflection is reduced to a boundary value problem for the system of ordinary differential equations, which is solved numerically.

One-Demential Automodel Problem about Impact of Rigid Body with Elastoplastic Half-Space

Authors: Mantsybora A. A., Semenov K. T.

The one-demential automodel problem about impact of rigid body with elastoplastic half-space is considered. In the case of plastic deformation is accumulated inside Riman simple wave is presented. The solution with a possible wave picture, when perturbation in the environment propagate by means of two elastic waves and one plastic simple wave, is shown. 

The Equivalent Stresses at Calculation of Creep Rupture of Metals Under Complex Stress State (Review)

Authors: Lokoshchenko A. M.

The criteria of creep rupture of metals under complex stress state are based on conception of equivalent stress σe. The basic attention is gived to determination of dependence of equivalent stress from the main stresses σ1, σ2, σ3 and to determination of dependence of rupture time from value σe. The detailed review of dependencies σe(σ1, σ2, σ3) is described, which were proposed by domestic and foreign scientists. The equivalent stresses σe, which are depended only on main stresses, and σe, which are depended also on the additional constants, are considered separately.

Coupled Dynamic Problems of Hyperbolic Thermoelasticity

Authors: Kovalev V. A., Radaev Y. N., Semenov D. A.

In the present paper in the framework of the linear non-dissipative coupled thermoelasticity (GNII, hyperbolic thermoelasticity), treating the heat transport as propagation with finite speed of undamped waves of second sound, harmonic coupled thermoelastic waves propagating in an infinite free from tractions thermoisolated cylinder are studied. Dispersionrelation is derived for this type of thermoelastic waves for an arbitrary azimuthal order. Numerical results for wave numbers depending on frequency are obtained.

Mathematical Models and Contemporary Theories of Physical Fields

Authors: Kovalev V. A., Radaev Y. N.

Elements of the classical field theory based on a variational formulation of the Hamilton type are discussed and corresponding 4- dimensional Lagrange formalism is presented both as the variational and the group theoretical script. Variational symmetries (geometric and generalized) of field equations and the Noether theorem providing a regular way of obtaining a conservation law for every given variational symmetry are revisited in the study in order to give a complete version of the contemporary field theory. All developments are presented in the non-linear frame (i.e.

About Oblique Impact by Perfectly Rigid Body with Plane Boundary on the Nonlinear Elastic Half-Space

Authors: Dudko O. V., Potyanikhin D. A.

In this paper the impact interaction of perfectly rigid body and nonlinear elastic solid, which have plane boundaries, are investigated. Suppose that the moving rigid body has constant velocity, resulting in self-similar formulation of the problem. Possible variants of wave combinations, arising from such interaction, are discussed. The existence condition for evolutionary shock waves and the thermodynamic discontinuities compatibility condition serve as criterions for choosing the wave pattern.

On Some Problems of Reconstruction of Inhomogeneous Pre-Stressed State in Elastic Solids

Authors: Vatulyan A. O., Dudarev V. V.

Presents a general approach to the problem of reconstruction of the inhomogeneous pre-stressed state in an elastic body on its amplitude-frequency response, measured in part of its border. Based on the previously defined generalized reciprocity is the ratio of the sequence of linear ill-posed problems, allowing for refinement of the procedure for pre-stress tensor component. As an example, presented a series of computational experiments on the restoration of monotone functions of the distribution of pre-stressed state the problem of bending vibrations of a rod. 

The Evolutionary Equation for Wave Processes of the Shift Deformation

Authors: Burenin A. A., Ragozina V. E., Ivanova Y. E.

One-dimensional process of formation and the subsequent motion of a flat cross shock wave is studied on the basis of solutions of the corresponding nonlinear evolutionary equation. This equation defines behaviour of the solution in front area of wave process and follows from interior lines of a method of matched asymptotic expansions. Comparative transient analysis of strains of a deformation and volume will be carried out and their basic differences are specified.

Multimodulus Behevior of the Grained Composites on the Base of Unsaturated Polyetheres

Authors: Bessonov D. E., Zezin Y. P., Lomakin E. V.

The results of the investigation of elastic properties of grained composite based on the unsaturated polyetheres were presented. This material was designed to substitute natural rocks in civil and mechanical engineering. The experimental values of elastic modulus and the Poisson‘s ratio under the tension and compression were obtained. It was shown that the investigated composite exhibits the dependence of elastic properties on the type of the stress state.

The Contact Problems for the Elastic Foundation with the Functionally Graded Coatings of the Complicated Structure

Authors: Aizikovich S. M., Krenev L. I., Trubchik I. S.

The contact problemfor the impression of axisymmetrical indenter into a functional graded elastic half-space is considered. Analytical methods for solving this problem have been developed. It is assumed that the indenter has a parabolic shape and contact between the indenter and the coating is smooth. The used method make it possible to find the analytical asymptotically exact problem solution.