and Computational Methods

#### 550.344 Mathematical modeling of one-dimensional non-linear motion in a fluid-saturated porous medium

**Holmurodov A. E. (Каршинский Государственный университет, Узбекистан), Dilmuradov N. D. (Karshi State University)**

doi: 10.18698/2309-3684-2018-1-315

The paper focuses on a mathematical model for propagation of the one-dimensional non-linear waves in fluid-saturated porous media where energy dissipation caused by intercomponent friction takes place. The existence and uniqueness theorem of the classical solution to the porous-elastic media dynamic problem is proved. A difference scheme for solving this problem is submitted. The study gives the results of numerical simulations of seismic wave propagation for a test medium model.

Холмуродов А.Э., Дильмурадов Н. Математическое моделирование одномерного нелинейного движения в насыщенной жидкостью пористой среде. Математическое моделирование и численные методы, 2018, № 1, с. 3-15

#### 539.3 Timoshenko-type asymptotic theory for thin multi-layered plates shells

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

doi: 10.18698/2309-3684-2018-1-1640

The paper presents a new modification of asymptotic theory describing thin multi-layered shells with finite shear rigidity. It is based on asymptotic analysis of general threedimensional equations from the elasticity theory for multi-layered bodies. This modification allows us to derive averaged equations from a Timoshenko-type plate theory. We identified the small geometrical parameter and used it to carry out our asymptotic analysis. We stated local elasticity theory problems which may be solved analytically. We show that when only the dominant terms of asymptotic expansions are taken into account, an asymptotic theory will result in the averaged plate equations of the Kirchhoff — Love type. When taking into account those terms that follow the dominant ones in asymptotic series in a self-similar way as compared to the previous approximation, an asymptotic theory will lead to Timoshenko-type averaged equations. At the same time, theoretical accuracy of the resulting truncated asymptotic solution is as high as that of the solution according to a Kirchhoff — Love type theory. The asymptotic theory modification that we developed makes it possible to use explicit analytical expressions to compute all six stress tensor components for a multi-layered plate with a high degree of accuracy. We used our method to perform a numerical simulation of stresses and displacements in a multi-layered plate subjected to uniform pressure that causes the plate to bend. Numerical computations show that our Timoshenko-type asymptotic theory provides a similarly high accuracy of computing flexural, shear and lateral stresses as compared to a three-dimensional finite element solution over a very fine mesh and a Kirchhoff — Love-type asymptotic theory. A Timoshenko-type theory will provide a better result for computing buckling than a Kirchhoff — Love-type theory, especially for relatively short plates. When the displacement is longitudinal, a Timoshenko-type theory will only provide a good result for elongated plates.

Димитриенко Ю.И., Юрин Ю.В. Асимптотическая теория типа Тимошенко для тонких многослойных пластин. Математическое моделирование и численные методы, 2018, № 1, с. 16-40

#### 519.6 Numerical solution of the problem of electrophysical parameter recovery using results of ac sounding

**Krasnov I. K. (Bauman Moscow State Technical University), Zubarev K. M. (Bauman Moscow State Technical University), Ivanova T. L. (Bauman Moscow State Technical University)**

doi: 10.18698/2309-3684-2018-1-4154

The problem of the electrophysical parameter recovery of layered media, which is the inverse problem of mathematical physics, is solved on the basis of the electromagnetic field measurement results. Various optimization methods for its solution are formulated. The mathematical model is proposed for a horizontally layered medium with specified parameters consistent with real values. The algorithm is developed for solving the direct problem allowing finding an analytical solution for various environmental parameter values. For solving inverse problems the complete enumeration and Hook - Jeeves methods as well as the developed modified method of complete enumeration are used. According to the results of solving the direct problem, the characteristic features of the medium are found for various values of the electrophysical parameters. When solving the inverse problem using various optimization methods, the features of each algorithm are described.

Краснов И.К., Зубарев К.М., Иванова Т.Л. Численное решение задачи восстановления электрофизических параметров по результатам зондирования переменным током. Математическое моделирование и численные методы, 2018, № 1, с. 41-54

#### 51-74 Numerical simulation of thermal conditions of the Russian instrument complex ACS, integrated into European ExoMars spacecraft

**Semena N. P. (Институт космических исследований РАН)**

doi: 10.18698/2309-3684-2018-1-5569

The article describes the problems and results of the numerical simulations of the thermal conditions of the Russian instrument complex ACS (Atmospheric Chemistry Suite) in the course of its integration into the European ExoMars spacecraft. The main problem was to make consistent the mathematical models of the ACS and spacecraft. This problem has been solved using the ACS nodal mathematical model. The algorithm for generating an ACS mathematical model, the details of its integration into the European spacecraft general model, its capabilities and limitations are described, as well as the results of numerical simulation of the ACS thermal conditions and their comparison with the flight telemetry.

Семена Н.П. Численное моделирование тепловых режимов российского приборного комплекса АЦС, интегрированного в европейский космический аппарат ExoMars. Математическое моделирование и численные методы, 2018, № 1, с. 55-69

#### 539.3 Simulation of the interaction process of a high-speed projectile with a three-layer spaced combined barrier

**Dobritsa B. T. (Bauman Moscow State Technical University), Pashkov S. V. (Томский государственный университет), Dobritsa D. B. (АО "НПО им. С.А. Лавочкина")**

doi: 10.18698/2309-3684-2018-1-7089

The article describes the numerical study of the process of a high-speed projectile interaction with the spaced combined barrier including mesh bumpers which was carried out using the author's numerical realization in a Lagrangian 3D formulation on tetrahedral cells. There was used the deformation fracture criterion for equivalent plastic deformation to calculate contact interactions, the Johnson method and the method of bifurcation on nodes of a computational grid to describe cracks. The boundary condition of ideal sliding on a tangent and impermeability on a normal was used for fragments and contact surfaces. The protective properties of a three-layer spaced barrier with two layers of mesh protection were evaluated in a wide range of impact velocities simulating the effects of micrometeorites and fragments of orbital debris on the structures of spacecraft meteoric protection. High performance of protective mesh bumpers and their advantage in comparison with bulk bumpers are shown. A technique for simulating high-speed impact on the spaced barriers allowing reducing the calculation time for long distances between layers is described.

Добрица Б.Т., Добрица Д.Б., Пашков С.В. Моделирование процесса взаимодействия высокоскоростного ударника с трехслойной разнесенной комбинированной преградой. Математическое моделирование и численные методы, 2018, № 2, с. 70-89.

#### 519.8 Probability model of meeting an attack of different types of weapon

**Chuev V. U. (Bauman Moscow State Technical University), Dubogray I. V. (Bauman Moscow State Technical University), Anisova T. L. (Bauman Moscow State Technical University)**

doi: 10.18698/2309-3684-2018-1-9097

On the basis of the continuous Markov processes theory we have developed a probabilistic model of the two-way battle of one combat unit against two enemy units of different types. The authors have obtained calculation formulas for computing current and final states under various firing tactics of the unit. We have determined the applicability areas for different combat tactics of the unit. The study shows that the right choice of the firing tactics can considerably increase the probability of the victory in the battle. The developed model of the two-way battle may be used for estimating the combat effectiveness of the multipurpose weaponry units.

Чуев В.Ю., Дубограй И.В., Анисова Т.Л. Вероятностная модель отражения атаки разнотипных средств. Математическое моделирование и численные методы, 2018, № 1, с. 90-97

#### 519.248 Methods for solving the problem of non-parametric testing of Lehmann's hypotheses when testing parallel systems

**Timonin V. I. (Bauman Moscow State Technical University), Tyannikova N. D. (Bauman Moscow State Technical University)**

doi: 10.18698/2309-3684-2018-1-98112

The article considers the problem of testing the Lehmann power hypothesis for two censored samples. The Kolmogorov — Smirnov type criterion based on a comparison of the Kaplan — Meier type estimates of the distribution functions for each censored sample is developed to test the power hypothesis. A method for calculating the exact statistics distributions is described on the basis of the model of particle random walk over an integer lattice. The probability values are calculated for a wide range of possible sample sizes. The convergence of this statistics distribution to the standard Kolmogorov — Smirnov distribution is proved provided that the hypothesis being tested is valid. The properties of a power parameter estimate obtained by minimizing statistics are investigated by statistical modeling methods.

Тимонин В.И., Тянникова Н.Д. Методы решения задачи непараметрической проверки гипотез Лемана при испытаниях параллельных систем. Математическое моделирование и численные методы, 2018, № 1, с. 98-112