Mechanics

Double Layer of Polymer Melts in Channels of Dies

Authors: Snigerev B. A., Tazyukov F. K.

Numerical simulation of double-layer nonlinear viscous flow in channels of dies was performed. The fluid motion is described by equations conservation of mass and momentum, supplemented by the rheological equation of state of nonlinear viscous fluid on the Carreau model. The technique of numerical solve the problem based on the finite element method is described. Results the field of velocities, pressure, stresses, position the interface boundary of two-layer flow depending on rheological properties of liquid and flow regimes are presented.

Using Galerkin Method for Solving Linear Optimal Control Problems

Authors: Pankratov I. A.

The linear optimal control problem is considered. Duration of the controlled process is fixed. It is necessary to minimize the functional, that characterizes the energy consumption. A method of constructing an approximate solution based on the Galerkin method is proposed. Examples of numerical solutions of the problem are given.

Simulation of Incompressible Nonviscoussevere Fluid on a Regular Grid in Three-dimensional Space

Authors: Liverovskiy D. I., Shevirev S. P.

This study focuses on modification of the method of Davydov (large particles) in the case of incompressible liquid. We consider the simulation of a heavy incompressible nonviscous fluid by Davydov's modified method in a three-dimensional case. Besides, comparison of the received results with a two-dimensional case is carried out. Formulas of modified Davydovs's method for the case of three spatial dimensions are lead out including difference analogue of the three-dimensional Poisson equation for the pressure. The criterion of stability is generalized.

About the Specifics of Identification Thermomechanical Characteristics of Functionally Graded Materials

Authors: Vatulyan A. O., Nesterov S. A.

Functionally graded materials are widely used in engineering fields with large thermo-mechanical loads. Efficiency of application of these materials depends on accurate knowledge of the laws of heterogeneity. Earlier, the authors have proposed an approach for the identification of smooth laws of heterogeneity for thermoelastic rod. To do this, were received operator equation linking activities and measurable functions for the solution of inverse problem and carried out computational experiments.

Investigation of Harmonic Waves in the Viscoelastic Layer

Authors: Anofrikova N. S., Sergeeva N. V.

The paper deals with the study of harmonic waves in the viscoelastic layer. The properties of the material are described by the constitutive equations in the integral form. The fractional exponential function of Rabotnov is chosen as a kernel of integral operator. Two cases are considered: symmetric stress-strain state (SSS) and asymmetric SSS. The properties of modes which change in time harmonically are investigated for the purpose of studying of the free vibrations. Dispersion equations for both cases are derived. The numerical solutions of dispersion equations are obtained.