and Computational Methods

#### 519.6 Influence of point defects in the structure of a cellular-automaton calculator on the solution of a 2D scalar wave equation

**Matyushkin I. V. (Институт проблем проектирования в микроэлектронике РАН), Zapletina M. A. (Институт проблем проектирования в микроэлектронике РАН)**

doi: 10.18698/2309-3684-2017-3-319

The study analyzed the influence of artificially introduced local inhomogeneities (defects) on the dynamics of the cellular-automaton solution of the scalar wave equation. We used a cellular-automaton scheme, which is taken from the Crank-Nicolson mesh scheme. To estimate the relationship between the perturbed and unperturbed solutions, we introduced an integral characteristic of the “energy” of the cellular automaton field. The computational experiment showed that, despite the oscillation phase drift, the average “energy” and its deviation are conserved, and the solution is not destroyed. Findings of the research show that the “energy” deviation is proportional to the total distance of the defects to the symmetry center.

Matyushkin I.V., Zapletina M.A. Influence of point defects in the structure of a cellular-automaton calculator on the solution of a 2D scalar wave equation.Маthematical Modeling and Computational Methods, 2017, №3 (15), pp. 3–19.

#### 539.374 Model of non-isothermal elastoplastic deformation of structural materials under complex loading

**Temis Y. M. (Центральный институт авиационного моторостроения им. П.И. Баранова), Hudyakova A. D. (Центральный институт авиационного моторостроения им. П.И. Баранова/Bauman Moscow State Technical University)**

doi: 10.18698/2309-3684-2017-3-2035

The study introduces a model of elastoplastic deformation of structural alloys under conditions of complex nonisothermal loading. The model is based on the plastic flow theory. Within the research we derived the relations that made it possible to determine the parameters of the model using the results of sample tests according to the program of rigid symmetric cyclic deformation. Moreover, we developed an algorithm for determining the plasticity parameters from a limited set of experimental data. Based on the algorithm developed, we obtained the plasticity parameters for the nickel alloy IN738LC over a wide temperature range.

Temis Yu.M., Khudyakova A.D., Model of non-isothermal elastoplastic deformation of structural materials under complex loading.Маthematical Modeling and Computational Methods, 2017, №3 (15), pp. 20–37

#### 539.376 Modeling of load-bearing capacity of a smooth cylindrical shell under conditions of material creep

**Dubrovin V. M. (Bauman Moscow State Technical University), Semyonov K. S. (Bauman Moscow State Technical University/RSC Energia)**

doi: 10.18698/2309-3684-2017-3-3848

The study introduces a method for calculating the load-bearing capacity of a smooth cylindrical shell, which has been under the action of axial and transverse loads for a long time. We assume that with prolonged loading, the shell material is subject to the phenomenon of creep, which in turn affects the load-bearing capacity of the shell. As a result, we obtained relations that made it possible to estimate this influence.

Dubrovin V.M., Semenov K.S. Modeling of load-bearing capacity of a smooth cylindrical shell under conditions of material creep .Маthematical Modeling and Computational Methods, 2017, №3 (15), pp. 38-48

#### 539.3 Finite element modeling of damageability and durability of composite structures with local delaminations

**Dimitrienko Y. I. (Bauman Moscow State Technical University), Yurin Y. V. (Bauman Moscow State Technical University)**

doi: 10.18698/2309-3684-2017-3-4970

The study centers around a technique developed for modeling damageability of laminated composite structures with defects of the delamination type under cyclic loading. The procedure consists of 3 stages iteratively repeated in time: finite element simulation of a macroscopic stress-strain state of the structure with defects; simulation of the microscopic stress-strain state near the defects; modeling the damage accumulation in the matrix, which connects the layers of reinforcing fibers near the defect. The model takes into account the curvilinear anisotropy of the composite material in the structure of complex geometric shapes. The study gives an example of a numerical calculation of a fragment of a composite structure of a helicopter carrier blade, taking into consideration the defect of the delamination type. The results suggest that there is a possibility of using the developed technique for damageability modeling in complex composite structures. The finite-element solution of the macroscopic problem is found by means of the SMCM software platform developed at the Scientific and Educational Center for Supercomputer Engineering Modeling and Software Development (SEC “SIMPLEX”) of Bauman Moscow State Technical University.

Dimitrienko Yu.I. ,Yurin Yu.V. Finite element modeling of damageability and durability of composite structures with local delaminations .Маthematical Modeling and Computational Methods, 2017, №3 (15), pp. 49–70

#### 519.688 Numerical statistical simulation of the process of rarefied gas flow over an aircraft

**Krasnov I. K. (Bauman Moscow State Technical University), Mozzhorina T. Y. (Bauman Moscow State Technical University), Dzhus D. V. (Bauman Moscow State Technical University)**

doi: 10.18698/2309-3684-2017-3-7182

The article considers the application of the direct statistical simulation method to the problems of gas dynamics in a rarefied region. An analytical method for assignment and taking into account complex boundary conditions associated with the geometry of the body located in the computational domain is proposed. An algorithm for the rational description of a body streamlined by a gas is developed.

Krasnov I.K.,Mozzhorina T.Yu., Dzhus D.V. Numerical statistical simulation of the process of rarefied gas flow over an aircraft .Маthematical Modeling and Computational Methods, 2017, №3 (15), pp. 71–82

#### 533.6.011.5:004.622:004.855.5 A method for classifying aircraft surface elements for the numerical-analytical solution of aerodynamic problems

**Kotenev V. P. (Bauman Moscow State Technical University), Raclav R. A. (-), Sapozhnikov D. A. (МГТУ им.Н.Э.Баумана), Chernyshev I. V. (-)**

doi: 10.18698/2309-3684-2017-3-83104

The study introduces an algorithm for classifying the aircraft surface elements based on a binary decision tree with threshold predicates. According to the initial description of the objects, we developed derived characteristics allowing for the classes to be separated with minimal losses. Moreover, we trained and verified the predicates on synthetic data and described an algorithm of obtaining the data for training. Low values of classification errors and ease of implementation make it possible to apply the algorithm for solving aerodynamic applied problems.

Kotenov V.P. ,Ratslav R.A. ,Sapozhnikov D.A. ,Chernyshev I.V. , A method for classifying aircraft surface elements for the numerical-analytical solution of aerodynamic problems .Маthematical Modeling and Computational Methods, 2017, №3 (15), pp. 83–104

#### 551.513 Modeling the process of transition from paleoclimate to the current one as a result of a strong change in conditions

**Parkhomenko V. P. (Bauman Moscow State Technical University/Computing Centre of RAS)**

doi: 10.18698/2309-3684-2017-3-105118

The paper gives the results of numerical calculations on the description of the Earth's climate with the displacement of its axis of rotation, the possibility of which is proven by some geological, archaeological and historical data. The study assumes that the axis inclination angle to the ecliptic plane is maintained. We carried out some calculations on modeling the process of transition from paleoclimate to the current one as a result of displacement of the Earth's rotation axis into the present position. The calculations are based on the hydrodynamic three-dimensional global climate model. As a result, we introduced an approach to calculating the wind speed in the energy-and-water balance atmospheric model. Finally, we developed a method for forming and using the necessary maps and connections between them at the rotation of the Earth's axis.

Parkhomenko V.P.Modeling the process of transition from paleoclimate to the current one as a result of a strong change in conditions .Маthematical Modeling and Computational Methods, 2017, №3 (15), pp. 105–118

#### 519.25 Stochastic coding models and recognition of structural and statistical characteristics of coding sequences

**Kutyrkin V. A. (-), Chaley M. B. (-)**

doi: 10.18698/2309-3684-2017-3-119138

The paper introduces stochastic models explaining real characteristic regularities of coding regions from genomes of various organisms. Due to the growing volume of data on sequenced genomes, there arises a problem of its computer-aided analysis. By using these models, we developed methods for recognizing the structural and statistical properties of genomic DNA sequences, which can be used to find algorithms and computer programs for the automated processing of large amounts of data. The properties of the proposed stochastic coding models are demonstrated in numerical experiments with binary recoded paragraphs of literary works in English and Italian.

Kutyrkin V.A. ,Chaley M.B.Stochastic coding models and recognition of structural and statistical characteristics of coding sequences.Маthematical Modeling and Computational Methods, 2017, №3 (15), pp. 119–138