and Computational Methods

Rubric: "01.02.00 Mechanics"

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: 10.18698/2309-3684-2016-1-6888

The article examines methods of aircraft motion parameters recovery from the data of their low resolution recordings in the gas-dynamic ejection experimental test. Desired conditions were satisfied by the use of Hermitian piecewise polynomial interpolation. Implementation of Tikhonov regularization provides the most flexible approach to the problem under consideration.

Plyusnin A. Aircraft motion parameters recovery from the data of their discrete registration. Part 1. Methods without use of regularization. Маthematical Modeling and Coтputational Methods, 2016, №1 (9), pp. 68-88

doi: 10.18698/2309-3684-2015-3-316

The article describes the method for calculating the stability of a rod under simultaneous action of axial force and torque, considering changing the torsion of the rod when it’s bent. The method is based on the use of the complete system of equations. The following cases are considered: end clamped rod, rod with a hinged support, the rod in the form of compressed and twisted console. Diagrams of dependence of the critical axial force versus the critical torque are obtained, i.e., the range of rod stability for the case of loading is determined.

Dubrovin V., Butina T. Modeling the stability of compressed and twisted rods in precise problem statement. Маthematical Modeling and Coтputational Methods, 2015, №3 (7), pp. 3-16

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

doi: 10.18698/2309-3684-2015-3-1740

Within the framework of solving the problem of active control of the elastic and damping elements of multi-wheeled vehicle (MWV) suspension brackets investigating the properties of suspension bracket families designed both for different travels and for different loading is of great importance. Their kinematic schemes can be also rather various. It is not feasible to collect the required amount of information for families of vehicles of different design and operating characteristics. Performing a full analytical study to determine the appropriate characteristics is not possible. This problem could be successfully solved only by simulation. A mathematical model of the MWV motion is developed. The characteristic feature of the model is that the vehicle speed is not set forcedly, but it is generated by the interaction of the rotating wheeled propellers with the supporting base. It results in high accuracy in modeling real processes of MWV moving along an uneven road. The developed model can be applied to research various laws of multi-wheeled vehicle suspension bracket control.

Zhileykin M., Sarach E. Mathematical model of movement of the multi-wheeled vehicles with torsional flexible bearing system. Маthematical Modeling and Coтputational Methods, 2015, №3 (7), pp. 17-40

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: 10.18698/2309-3684-2017-1-3254

The article considers the modeling results of incompressible layered composites with finite strains deformation according to the individual layers characteristics. The article proposes an asymptotic averaging method version for layered nonlinearly elastic incompressible composites with finite deformations and periodic structure. We are using a universal representation of the defining relations for incompressible composite layers, proposed by Yu.I. Dimitrienko, which allows us to simulate simultaneously for a complex of various nonlinear elastic media models characterizedby the choice of a pair of energy tensors. We proved that if all composite layers are incompressible, the composite as a whole is also an incompressible, but anisotropic, medium. The article considers the problem of laminated plate uniaxial stretching from incompressible layers with finite deformations. Using the developed method, we calculated the effective deformation diagrams connecting the averaged Piola — Kirchhoff stress tensors components and the strain gradient, as well as the stress distribution in the composite layers.

The developed method for calculating effective deformation diagrams and stresses in composite layers can be used in the design of elastomeric composites with specified properties.

Dimitrienko Y., Gubareva E., Kolzhanova D., Karimov S. Incompressible layered composites with finite deformations on the basis of the asymptotic averaging method. Маthematical Modeling and Coтputational Methods, 2017, №1 (13), pp. 32-54

doi: 10.18698/2309-3684-2015-3-4157

The article describes an analytical solution to the model problem about stratified flow wave action on the underwater pipeline in the case of the circulation flow. Numerical computations of the hydrodynamic reactions for the real sea conditions are performed. The values of the flow parameters at which the wave-making drag and the lift capacity of the pipeline reaches its maximum are determined.

Vladimirov I., Korchagin N., Savin A. Hydrodynamic reactions in the model of circulatory streamlining the pipeline by bottom sea currents. Маthematical Modeling and Coтputational Methods, 2015, №3 (7), pp. 41-57

doi: 10.18698/2309-3684-2016-3-323

The purpose of this research was to develop a multilevel model for multiscale deformation of three-layer (sandwich) structures made of polymeric composite materials such as plates with a foam based filler. We took into account the micromechanical processes of deformation and damageability in the matrix and reinforcing filler and foam, as well as macroscopic defects such as non-impregnation of the composite skins. First, we did a finite element modeling of stress-strain state, damageability and destruction of the sandwich plates with skins made of hybrid carbon fiber composites, with different types of defect such as non-impregnation, under the flexural uniform pressure. Then we found the characteristic features of the deformation and damageability process in this type of composite structures. Finally, we developed a method which can be used to calculate the deformation, damageability and destruction of sandwich plates made of polymer composite materials applied in various industries: shipbuilding, aviation, rocketry.

Dimitrienko Y., Yurin Y., Fedonyuk N. Numerical modeling of deformation and strength of sandwich composite structures with defects. Маthematical Modeling and Coтputational Methods, 2016, №3 (11), pp. 3-23