and Computational Methods

#### 539.3 Computational modeling of conjugated gasdynamic and thermomechanical processes in composite structures of high speed aircraft

**Dimitrienko Y. I. (Bauman Moscow State Technical University), Koryakov M. N. (Bauman Moscow State Technical University), Zakharov A. A. (Bauman Moscow State Technical University), Stroganov A. S. (Bauman Moscow State Technical University)**

doi: 10.18698/2309-3684-2014-3-324

In the article we propose an algorithm for the numerical simulation of conjugate gasdynamic and thermomechanical processes in composite structures of high-speed aircraft. The algorithm allows calculating all parameters of the three-dimensional gasdynamic flow near the surface of the aircraft, heat exchange on the surface, heat and mass transfer processes in the internal structure of thermodestructive polymer composite, as well as processes of composite construction thermodeformation, including the effects of changes in the elastic characteristics of the composite, variable thermal deformation, shrinkage caused by thermal degradation, building up interstitial gas pressure in the composite. An example of numerical simulation of conjugated processes in a model composite construction of high-speed aircraft illustrates the possibilities of the proposed algorithm.

Dimitrienko Y., Koryakov M., Zakharov A., Stroganov A. Computational modeling of conjugated gasdynamic and thermomechanical processes in composite structures of high speed aircraft. Маthematical Modeling and Coтputational Methods, 2014, №3 (3), pp. 3-24

#### 517.1:539.434 Mechanical analog modeling of the inelastic non-isothermal deformation processes

**Zarubin V. S. (Bauman Moscow State Technical University), Kuvyrkin G. N. (Bauman Moscow State Technical University), Savelyeva I. Y. (Bauman Moscow State Technical University)**

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

#### 539.3 Modeling polyurethane viscoelasticity at moderately high strain rates

**Belkin A. E. (Bauman Moscow State Technical University), Dashtiev I. Z. (TSNIISM), Lonkin B. V. (Bauman Moscow State Technical University)**

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

#### 629.762 Calculation of aircraft gas-dynamic ejection systems with due consideration of the secondary combustion effects

**Plyusnin A. V. (JSC MIC NPO Mashinostroyenia)**

doi: 10.18698/2309-3684-2014-3-5573

The article presents a method of accounting for secondary combustion effects when solid propellant power device is used for the gas-dynamic ejection of lifting vehicles. The method is based on thermo chemistry calculations. The suggested method can be easily applied to engineering calculations of aircraft gas-dynamic ejection systems as well as to the analysis of experimental data involving secondary combustion effects.

Plyusnin A. Calculation of aircraft gas-dynamic ejection systems with due consideration of the secondary combustion effects. Маthematical Modeling and Coтputational Methods, 2014, №3 (3), pp. 55-73

#### 629.735.33.016+621.45.015 Simulating atmospheric conditions influence on flight program optimization for a subsonic passenger aircraft

**Mozzhorina T. Y. (Bauman Moscow State Technical University), Gubareva E. A. (Bauman Moscow State Technical University)**

doi: 10.18698/2309-3684-2014-3-7488

We examined effects of typical for different climatic zones atmospheric conditions on flight program optimization for a subsonic long-haul passenger aircraft. Simulation of flight and power plant performance was based on current traditional approaches used in solving problems of this kind. The acceleration-climb flight segment has been optimized by minimizing fuel consumption at this flight segment. The cruising flight segment has been optimized considering operating limitations accepted for civil aviation. The in-built model of bypass turbojet engine was used for simulating the flight. This model allows calculating power plant performances under any flight conditions. The flight of subsonic aircraft has been examined in one vertical plane. Calculations have been performed for 6 standard air temperature variations with altitude (depending on climatic zone). Atmospheric pressure variation near Earth surface was considered and effects of atmospheric conditions on flight program optimization were estimated.

Mozzhorina T., Gubareva E. Simulating atmospheric conditions influence on flight program optimization for a subsonic passenger aircraft. Маthematical Modeling and Coтputational Methods, 2014, №3 (3), pp. 74-88

#### 519.6 Two-dimensional self-organized critical Мanna model

**Podlazov A. V. (Keldysh Institute of Applied Mathematics of the Russian Academy of Scienсes)**

doi: 10.18698/2309-3684-2014-3-89110

We propose a full solution for Manna model, two-dimensional conservative sand pile model with isotropic rules of grains redistribution on average. We determined the general properties indices of avalanches distribution (size, area, perimeter, duration, the multiplicity of topplings) for the model both analytically and numerically. The solution is based on spatio-temporal decomposition of avalanches described in terms of toppling layers and waves and on division of the motion of grains into directed and undirected types. The former of the two is treated as the dynamics of active particles with some physical properties described.

Podlazov A. Two-dimensional self-organized critical Мanna model. Маthematical Modeling and Coтputational Methods, 2014, №3 (3), pp. 89-110

#### 517.9:519.6 Analysis of bifurcations in double-mode approximation for Kuramoto — Tsuzuki system

**Malinetsky G. G. (Keldysh Institute of Applied Mathematics of the Russian Academy of Scienсes), Faller D. S. (Keldysh Institute of Applied Mathematics of the Russian Academy of Scienсes)**

doi: 10.18698/2309-3684-2014-3-111125

The article discusses emergence of chaotic attractors in the system of three ordinary differential equations arising in the theory of reaction–diffusion models. We studied the dynamics of the corresponding one- and two-dimensional maps and Lyapunov exponents of such attractors. We have shown that chaos is emerging in an unconventional pattern with chaotic regimes emerging and disappearing repeatedly. We had already studied this unconventional pattern for one-dimensional maps with a sharp apex and a quadratic minimum. We applied numerical analysis to study characteristic properties of the system, such as bistability and hyperbolicity zones, crisis of chaotic attractors.

Malinetsky G., Faller D. Analysis of bifurcations in double-mode approximation for Kuramoto — Tsuzuki system. Маthematical Modeling and Coтputational Methods, 2014, №3 (3), pp. 111-125