and Computational Methods

#### 539.3 Numerical modeling of deformation and strength of sandwich composite structures with defects

**Dimitrienko Y. I. (Bauman Moscow State Technical University), Yurin Y. V. (Bauman Moscow State Technical University), Fedonyuk N. N. (Krylov State Research Centre, St. Petersburg)**

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

#### 539.3 Simulation of dynamic stability of a cylindrical shell under cyclic axial impact

**Dubrovin V. M. (Bauman Moscow State Technical University), Butina T. A. (Bauman Moscow State Technical University)**

doi: 10.18698/2309-3684-2016-3-2432

In this article we suggest a method for calculating the dynamic stability of a cylindrical shell with its axial compressive time-varying load, and cyclic axial load, which varies according to a certain law. As an example, we consider the axial load, changing linearly and the cyclic load, which varies according to the harmonic law. To show the cyclic load, we use Ince — Strutt diagram, defining the stable and unstable regions of the shell fluctuations.

Dubrovin V., Butina T. Simulation of dynamic stability of a cylindrical shell under cyclic axial impact. Маthematical Modeling and Coтputational Methods, 2016, №3 (11), pp. 24-32

#### 533.6.011.5 Modification of Pohlhausen method for calculating heat transfer on blunt bodies

**Kotenev V. P. (Bauman Moscow State Technical University), Bulgakov V. N. (Bauman Moscow State Technical University), Ozhgibisova Y. S. (Bauman Moscow State Technical University)**

doi: 10.18698/2309-3684-2016-3-3352

Modification of Pohlhausen method is developed. It allows for quick and effective heat transfer distribution over the blunt body surfaces. Calculations were done. Their results are described in comparison with the numerical solution of a problem within the framework of Navier — Stokes equations.

Kotenev V., Bulgakov V., Ozhgibisova Y. Modification of Pohlhausen method for calculating heat transfer on blunt bodies. Маthematical Modeling and Coтputational Methods, 2016, №3 (11), pp. 33-52

#### 629.762 Pressurization parameters simulation of container empty space during aircraft gas dynamic ejection considering real gas properties

**Plyusnin A. V. (Bauman Moscow State Technical University)**

doi: 10.18698/2309-3684-2016-3-5378

The article considers the pressurization process of a container empty space with the help of a high-pressure cylinder, which antecedes the gas dynamic ejection of an aircraft. Comparative calculations of this process were done in the quasi-stationary approximation using equations of state for both ideal and real gases. The article shows the necessity of accounting deviations in thermodynamic properties of the operating medium from the ideal-gas behavior in order to estimate correctly both gas reserves in the cylinder and temperature variations in the pressurized volumes.

Plyusnin A. Pressurization parameters simulation of container empty space during aircraft gas dynamic ejection considering real gas properties. Маthematical Modeling and Coтputational Methods, 2016, №3 (11), pp. 53-78

#### 551.048 Modelling influence of outflow into the Kara-Bogaz-Gol Bay on probability density of the Caspian Sea level fluctuations

**Frolov A. V. (Water Problems Institute of the Russian Academy of Sciences)**

doi: 10.18698/2309-3684-2016-3-7992

The paper considers long-term fluctuations of the Caspian Sea level as a nonlinear system output with positive and negative feedbacks. The Caspian Sea model with due consideration of an outflow into the Kara-Bogaz-Gol Bay is designed. Density distribution of the sea level is obtained as a solution to the corresponding Fokker — Planck — Kolmogorov equation. The bimodal probability density of the sea level distribution, which meets the endorheic Caspian Sea (if you cut off the Kara-Bogaz-Gol Bay), is shown to turn into the single-mode probability density in case of simultaneous influence of evaporation and seawater outflow into the Kara-Bogaz-Gol Bay on the sea level.

Frolov A. Modelling influence of outflow into the Kara-Bogaz-Gol Bay on probability density of the Caspian Sea level fluctuations. Маthematical Modeling and Coтputational Methods, 2016, №3 (11), pp. 79-92

#### 551.513 Algorithm for computational performance improvement and processor load balancing to simulate the general atmosphere circulation

**Parkhomenko V. P. (ФИЦ ИУ РАН/Bauman Moscow State Technical University)**

doi: 10.18698/2309-3684-2016-3-93109

The paper analyzes some factors affecting the parallel implementation performance of the atmospheric general circulation model designed on a cluster type multiprocessor computer. It considers several modifications of the initial parallel code of this model in order to improve both its computational efficiency and processor load balancing. The numerical scheme is modified according to the time of the atmospheric general circulation model for parallel computing of dynamics and physics blocks. The proposed procedure is used along with the procedures of paralleling the dynamics and physics blocks based on decomposition of the computational domain. It allows both optimizing the processor load balancing and increasing the paralleling efficiency. The data obtained while using the scheme for the physics block load balancing allow for complication of the physics block without increasing the total computational time. The results of numerical experiments are given.

Parkhomenko V. Algorithm for computational performance improvement and processor load balancing to simulate the general atmosphere circulation. Маthematical Modeling and Coтputational Methods, 2016, №3 (11), pp. 93-109

#### 531.36:521.1 Modelling the search for stationary space station orbits in the vicinity of an oblate-shaped asteroid

**Rodnikov A. V. (Bauman Moscow State Technical University)**

doi: 10.18698/2309-3684-2016-3-110118

We suggest a numerical and analytical algorithm of searching for stationary space station orbits in the vicinity of an oblate asteroid, when these orbits correspond to relative equilibrium positions of the space station on the plane defined by the asteroid precession and proper rotation axes, in the case of the asteroid being represented by a solid body of an approximately dynamically symmetric shape, compressed along the axis of dynamic symmetry. The algorithm is based on representing the asteroid gravitational potential by a composition of two complex conjugate point masses and consists of sequential variable substitution steps, reducing the problem to solving algebraic equations analytically and numerically. We supply a number of facts concerning evolution of stationary orbits in cases of changes in precession angular velocity.

Rodnikov A. Modelling the search for stationary space station orbits in the vicinity of an oblate-shaped asteroid. Маthematical Modeling and Coтputational Methods, 2016, №3 (11), pp. 110-118