and Computational Methods

Rubric: "01.02.00 Mechanics"

doi: 10.18698/2309-3684-2015-2-2345

The article describes a class of promising anisogrid structures representing mesh shell of unidirectional carbon. A brief analysis of existing approaches to modeling deformation of grid structures is presented. New mathematical and numerical models are proposed for reliable description of complex behavior of anisogrid structures under different kinds of loads. A high degree of accuracy and stability of the numerical model based on the expansions of unknown functions in Chebyshev polynomials and Fourier series is caused by the lack of saturation of such approximations. Efficiency of the proposed models and techniques is demonstrated on the example of solving test boundary-value problems and a problem of axial compression of anisogrid cylindrical shell.

Golushko S., Semisalov B. Numerical modeling of anisogrid structures deformation using schemes of high accuracy without saturation. Маthematical Modeling and Coтputational Methods, 2015, №2 (6), pp. 23-45

doi: 10.18698/2309-3684-2014-4-317

On the basis of mathematical model of thermal interaction between inclusion and the matrix we estimated influence of inclusions deviations from spherical shape on the effective thermal conductivity coefficient of the composite and associated with such deviation a possible occurrence of the anisotropy of the composite with respect to the property of thermal conductivity. Using the dual variational formulation of the stationary problem of heat conduction in an inhomogeneous body we built bilateral estimates of effective thermal conductivity.

Zarubin V., Kuvyrkin G., Savelyeva I. Effective thermal conductivity of a composite in case of inclusions shape deviations from spherical ones. Маthematical Modeling and Coтputational Methods, 2014, №4 (4), pp. 3-17

doi: 10.18698/2309-3684-2015-2-4657

The article describes a method for calculating the dynamic stability of cylindrical shell under axial compressive time-varying load. The case of linearly varying load was con-sidered as an example.

Dubrovin V., Butina T. Modeling of the dynamic stability of a cylindrical shell under the axial compressive load. Маthematical Modeling and Coтputational Methods, 2015, №2 (6), pp. 46-57

doi: 10.18698/2309-3684-2016-2-323

The purpose of this article is to propose a model of deformation of elastic-plastic composite materials with periodic structures with an allowance for fault probability of the composite phases. The model is based on a variant of the deformation theory of plasticity with the active loading. To simulate the effective characteristics of elastic-plastic composites, we applied the method of asymptotic homogenization of periodic structures. For numerical solution of linearized problems on the periodicity cell we offered the finite elements method using SMCM software medium developed at the Scientific-Educational Center of Supercomputer Engineering Modeling and Program Software Development of the Bauman Moscow State Technical University. We provide the research with the examples of numerical computations for dispersion-reinforced metal composites (aluminum matrix filled with SiC particles). Finally, we present the results of numerical modeling of deformation processes, damage accumulation and metal-composite destruction.

Dimitrienko Y., Gubareva E., Sborschikov S. Multiscale modeling of elastic-plastic composites with an allowance for fault probability. Маthematical Modeling and Coтputational Methods, 2016, №2 (10), pp. 3-23

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: 10.18698/2309-3684-2014-1-3656

The theory of thin constructive-orthotropic plates with a two-periodic structure was suggested. Examples of such structures are honeycomb sandwich panels and backed plates. The theory is based on equations of a three-dimensional elasticity theory with the help of asymptotic expansions in terms of a small parameter being the ratio of a plate thickness and a characteristic length without introducing any hypotheses on a distribution character for displacements and stresses through the thickness. Local problems were formulated for finding stresses in all structural elements of a plate. It was shown that the global (averaged by the certain rules) equations of the plate theory are similar to equations of the

Dimitrienko Y., Gubareva E., Sborschikov S. Asymptotic theory of constructive-orthotropic plates with two-periodic structures. Маthematical Modeling and Coтputational Methods, 2014, №1 (1), pp. 36-56

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: 10.18698/2309-3684-2014-2-115126

During the last decades we are witnessing climate changes. Scientists assume global warming to be the result of man-generated increase of green house gases in the atmosphere, the most important one being СО2. The article deals with the problem and describes cutting-edge solutions for stabilising climate. The research makes use of a seasonal global combined threedimensional hydrodynamic model of climate. This model of climate includes model of the World Ocean with real depths and configuration of continents, model of evolution of sea ice and energy — moisture balance model of the atmosphere. The first stage covers estimation of climate change through 2100 following IPCC A2 СО2 increase scenario. The calculations yield rise of average annual surface temperature of the atmosphere by 3,5 С. A number of calculations have been made to estimate possibility of stabilising climate at the level of 2010 by means of controlled release of sulphate aerosol into stratosphere. The aerosol will reflect and disperse a part of the coming solar radiation. We have calculated concentration (albedo) of the aerosol from 2010 to 2100 which will enable us to stabilise the average annual temperature of the surface layer of atmosphere. We have shown that by this way it is impossible to achieve the seasonal uniform approximation to the existing climate, although it is possible to significantly reduce the greenhouse warming effect. Provided that the aerosol is distributed evenly in space in stratosphere, we can stabilize the average annual temperature of the atmosphere, herewith in middle and low latitudes the climate will be colder by 0,1…0,2 С and in high latitudes it will be warmer by 0,2…1,2 С. Besides, these differences are essentially seasonal in nature, they increase in winter. If we stop releasing the aerosol in 2080 the average annual global temperature of the atmosphere will rise, reaching the former value without the aerosol by the year 2100.

Parkhomenko V. Modelling global climate stabilisation by controlled emission of stratospheric aerosol. Маthematical Modeling and Coтputational Methods, 2014, №2 (2), pp. 115-126

doi: 10.18698/2309-3684-2014-3-3954

The article presents a mathematical model of the viscoelastic behavior of polyurethane SKU-PFL-100 for strain range of 0...30 % and moderately high strain rates up to 10–1. To determine the viscous component of the deformation Bergstrom – Boyce rheological model has been applied. Relationship between stress and the elastic component of deformation is described by an Arruda – Boyce potential. We determined the model parameters using experimental compression diagrams of polyurethane obtained from Instron Electropuls 1000 machine at different strain rates. The model parameter values obtained by minimizing a function of the calculated value deviations from the experimental results are given. It is shown that in the considered range of deformations and strain rates model allows describing the polyurethane behavior with sufficient accuracy for practical purposes. The model is designed for calculating polyurethane shock-absorber parts, cushions, buffers and other structures subjected to dynamic loading.

Belkin A., Dashtiev I., Lonkin B. Modeling polyurethane viscoelasticity at moderately high strain rates. Маthematical Modeling and Coтputational Methods, 2014, №3 (3), pp. 39-54