and Computational Methods

Rubric: "01.02.00 Mechanics"

doi: 10.18698/2309-3684-2016-2-5568

We suggest classification for dynamical problems of a space station motion near a precessing small planet. This classification is based on three signs. These signs are the model of the asteroid gravitational potential, the method of holding the space station near the small planet, the type of dynamical problem. Within the offered classification we review the results received earlier. In particular, we construct sets of the space station equilibria or stationary orbits if the asteroid gravitational potential is composed by potentials of two real or conjugate complex point masses on real or imaginary distance and if the station coast along the leier or it moves freely. (In our case the leier is a tether with ends fixed in the asteroid poles). Moreover, we establish some facts of stability for the found orbits and equilibria and note some integrable cases of the motion equations along the leier

Rodnikov A. Modeling of a space station dynamics in vicinity of an asteroid. Маthematical Modeling and Coтputational Methods, 2016, №2 (10), pp. 55-68

doi: 10.18698/2309-3684-2015-4-7591

This article deals with the finite-element RKDG method (Runge-Kutta Discontinuous Galerkin) and its application for numerical integration of three-dimensional system of equations of ideal gas on unstructured grids. By means of the described algorithm we solved two test tasks. For each task we conducted the analysis and compared the task solution with well-known analytical solutions or with tabular data. We also give error assessment in the solution.

Dimitrienko Y., Koryakov M., Zakharov A. Application of RKDG method for computational solution of three-dimensional gas-dynamic equations with non-structured grids. Маthematical Modeling and Coтputational Methods, 2015, №4 (8), pp. 75-91

doi: 10.18698/2309-3684-2014-3-2538

The mechanical analog, allowing qualitatively and quantitatively describe the main features of inelastic deformation of the structural material at varying temperatures is presented. Analog is constructed using physical conceptions of polycrystalline structural material microstructures and the micromechanism of deformation process in combination with known provisions of the phenomenological theory of plasticity and creep. In the context of the particular modes of thermal and mechanical impacts on a heat-stressed structure this approach allows choosing a rational option of the structural material model adequately describing the most essential effects specific for the process of inelastic non-isothermal deformation. A variant of such a model under material singleaxis loading is developed and an example of its parameter numerical values selection is presented.

Zarubin V., Kuvyrkin G., Savelyeva I. Mechanical analog modeling of the inelastic non-isothermal deformation processes. Маthematical Modeling and Coтputational Methods, 2014, №3 (3), pp. 25-38

doi: 10.18698/2309-3684-2016-1-316

The article offers the calculation algorithm of deflected mode of an absolutely flexible bar interacting with the external air flow. The algorithm is based on the replacement of the continual mechanical system by the discrete set of rectilinear finite elements and concentrated masses. The authors show differential equations of mass motion with allowance for an aerodynamic load and dissipative forces and integrate them by numerical method. That made it possible to find both the equilibrium position of the flexible bar in the flow, and the critical flow velocity which causes violent bar vibrations in case of its excess.

Sorokin F., Nizametdinov F. Numerical simulation of absolutely flexible bAR motion in the air flow. Маthematical Modeling and Coтputational Methods, 2016, №1 (9), pp. 3-16

doi: 10.18698/2309-3684-2015-2-7386

In the paper we propose an algorithm of parameters (time constants of the turbine) iden-tification using the gradient method with an adaptive model. The adaptive mathematical model has the same structure as the identification object. The identification criterion is based on the loss function, which is the misalignment between the left and right sides of the equation, which describes the adaptive model. Thus it is avoided the need of finding the solution of a nonlinear equation for the adaptive model in an explicit form. In the model the signal observed at the output of the identified object is used instead of the output signal. Since mathematical models are nonlinear, the Newton – Kantorovich linearization and the matrix operator apparatus are applied to solve the problem. The features of gradient vector computation and features of the identification algorithm and its organization are considered. The results of the two time constants identification for the mathematical model of the turbine PT-12/15-35/10M are presented.

Kornyushin Y., Egupov N., Kornyushin P. Identification of parameters of regulator actuators for steam power turbines using matrix operator apparatus. Маthematical Modeling and Coтputational Methods, 2015, №2 (6), pp. 73-86

doi: 10.18698/2309-3684-2014-2-2848

We propose a method for calculating effective viscoelastic properties of composite materials under steady-state cyclical vibrations. The method is based on asymptotic averaging of periodic structures and finite-element solution of local problems of viscoelasticity in periodicity cells of composite materials. We provide examples of numerical simulation of viscoelastic properties for composites with unidirectional reinforcement, and of calculations of complex tensors of stress concentration in a periodicity cell. The paper presents a comparative analysis of dependencies of loss tangent of complex composite elasticity

modulus on vibration frequencies obtained through FEA calculations and rough mixed formulae. We show that rough mixed formulae, often used for calculating dissipative properties of composite materials, can yield appreciable calculation errors.

Dimitrienko Y., Gubareva E., Sborschikov S. Finite element modulation of effective viscoelastic properties of unilateral composite materials. Маthematical Modeling and Coтputational Methods, 2014, №2 (2), pp. 28-48

doi: 10.18698/2309-3684-2016-1-3851

The purpose of this article is to deduce general and approximate equations for the torsional vibration of the viscoelastic round bar rotating around the symmetry axis with the constant angular velocity. Within the research we develop the algorithm allowing to define the bar deflected mode. The received approximate equations enabled to numerically solve the problem of the bar torsional vibrations. Moreover, we carry out a comparative analysis of the results obtained for exponential and weakly singular kernels of the viscoelastic operator. As a result, we estimate the rotation influence on the bar vibrations

Khudoynazarov K., Abdirashidov A., Burkutboyev . Torsional vibrations of the viscoelastic round bar rotating with the constant angular velocity. Маthematical Modeling and Coтputational Methods, 2016, №1 (9), pp. 38-51

doi: 10.18698/2309-3684-2017-1-2231

The study tested a model of a layered hierarchically constructed composite, whose structure has a morphology similar to fractal formation. In our research we developed an algorithm for studying the interaction of an alternating electric field with a fractal composite, as well as a software package that allows simulating fractal characteristics of the composite under study and calculating the electrical parameters of the composite medium. Moreover, we studied the boundaries of the developed model application: the maxand min-dimensions of the composite, at which fractal properties appear. We investigated the frequency dependences of the permittivity of a fractal composite.

The results of the research can be used in designing the materials with predefined electrophysical parameters and characteristics, as well as in developing the elements and devices that possess absorbing and selective properties.

Korchagin S., Terin D., Klinaev Y. Simulating a fractal composite and studying its electrical characteristics. Маthematical Modeling and Coтputational Methods, 2017, №1 (13), pp. 22-31

doi: 10.18698/2309-3684-2017-1-7890

The research examines the planar and three-dimensional problems of an ice cover perturbed by a point pulse source localized in the depth of an infinitely deep liquid. We studied the ice cover of different thickness and carried out numerical study of its perturbations by sources located at different depths. The main attention is paid to the ice cover perturbations that arise directly above the source.

Savin A., Gorlova N., Strunin P. Numerical simulation of the point pulse source impact in a liquid on the ice cover. Маthematical Modeling and Coтputational Methods, 2017, №1 (13), pp. 78-90