and Computational Methods

#### 539.3 Asymptotic theory of constructive-orthotropic plates with two-periodic structures

**Dimitrienko Y. I. (Bauman Moscow State Technical University), Gubareva E. A. (Bauman Moscow State Technical University), Sborschikov S. V. (Bauman Moscow State Technical University)**

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

#### 001.92 Disadvantages of citation index and Hirsch and using other scientometrics

**Polyanin A. D. (Bauman Moscow State Technical University/Ishlinsky Institute for Problems in Mechanics/MEPhI)**

doi: 10.18698/2309-3684-2014-1-131144

The paper deals with the citation index and h-index, which are the main scientometric indices, currently used for evaluating the performance of scientists and university professors. The author indicates their main disadvantages and considers a number of illustra-tive examples. The study shows that the normalized citation index (taking into account the presence of co-authors) has a number of important advantages in comparison with other scientometric indices. The author proposes new indices — the maximum citation indices, which can be easily calculated, have a simple and clear interpretation and have a number of distinct advantages in comparison with the h-index.

Polyanin A. Disadvantages of citation index and Hirsch and using other scientometrics. Маthematical Modeling and Coтputational Methods, 2014, №1 (1), pp. 131-144

#### 539.3:621.01 Numerical simulation of nonlinear deformation of thin elastic shells

**Gavryushin S. S. (Bauman Moscow State Technical University)**

doi: 10.18698/2309-3684-2014-1-115130

The article shows theoretical bases of the methods and algorithms developed to analyze the stability and supercritical behavior of thin elastic shells. The author deals with the problem of numerical analysis of nonlinear deformation of the spherical dome loaded with uniform external pressure. An algorithm for the numerical analysis method based on the parameter continuation method combined with the method of the subspace change of control parameters. The author illustrates the effectiveness of the proposed algorithm by sample calculations.

Gavryushin S. Numerical simulation of nonlinear deformation of thin elastic shells. Маthematical Modeling and Coтputational Methods, 2014, №1 (1), pp. 115-130

#### 51-71:74 Long-period oscillations of aircraft at hypersonic speeds

**Sidnyaev N. I. (Bauman Moscow State Technical University), Glushkov P. A. (Bauman Moscow State Technical University)**

doi: 10.18698/2309-3684-2014-1-99114

The article presents the theoretical analysis of the long-period (phugoid) aircraft oscillations, which has a lifting force and performs a flight at hypersonic speeds in any atmosphere. Oscillations are caused by mutual transition of kinetic energy into potential energy during the flight along the path having an oscillatory character and being determined primarily by controlled longitudinal zero momentum in steady flight. The study shows that with the speed approximating to the first cosmic speed, the decrease in gravity at height dominates the decrease in density of the atmosphere, so that with increasing speed the period of phugoid oscillations tends asymptotically to the corresponding period of the satellite. During the research there were obtained analytical expressions for the short-period oscillations or vibrations at the angle of attack. The study demonstrates that these expressions, as well as the expressions for the long-period oscillations are in good agreement with numerical solutions.

Sidnyaev N., Glushkov P. Long-period oscillations of aircraft at hypersonic speeds. Маthematical Modeling and Coтputational Methods, 2014, №1 (1), pp. 99-114

#### 519.63:532.5 Numerical-analytical method of solving two-dimensional problems of natural convection in a closed cavity

**Basarab M. A. (Bauman Moscow State Technical University)**

doi: 10.18698/2309-3684-2014-1-1835

The author offers a method (PGRM) of numerical-analytical solving the equation system in partial derivatives describing the natural thermal convection in the complicated-shaped dimensional cavity with arbitrary boundary conditions. The new approach is based on a combination of Petrov – Galerkin method and R-functions (Rvachev functions) and makes it possible to obtain temperature, vortex and current functions satisfying the boundary condi-tions in the form of expansions in certain bases. The coordinated choice of bases provides a natural way to approximate the boundary conditions for the flow function. Unsteady convec-tion problems are solved by combining PGRM and Rothe method.

Basarab M. Numerical-analytical method of solving two-dimensional problems of natural convection in a closed cavity. Маthematical Modeling and Coтputational Methods, 2014, №1 (1), pp. 18-35

#### 62.192 Additive damage accumulation approach to calculation and estimation of objects’ life feartures

**Sadykhov G. S. (Bauman Moscow State Technical University), Krapotkin V. G. (Bauman Moscow State Technical University), Kazakova O. I. (Bauman Moscow State Technical University)**

doi: 10.18698/2309-3684-2014-1-8298

In this paper we prove constitutive equations for calculation and estimation of life’s features of the objects working in normal mode through life’s features of objects working in another self-similar mode where life consumption is modeled according to the law of the additive damage accumulation.

Sadykhov G., Krapotkin V., Kazakova O. Additive damage accumulation approach to calculation and estimation of objects’ life feartures. Маthematical Modeling and Coтputational Methods, 2014, №1 (1), pp. 82-98

#### 539.3 Near-resonant modes of the moving load in the plane problem of elasticity theory for a half-space with a thin coating

**Kaplunov J. D. (Keele University), Oblakova T. V. (Bauman Moscow State Technical University), Prikazchikov D. A. (Bauman Moscow State Technical University)**

doi: 10.18698/2309-3684-2014-1-5767

The study deals with the plane stationary problem of elasticity theory on the motion of a vertical concentrated load along the surface of an elastic half-space with a thin coating. The authors investigated modes in the surface layer at speeds close to the resonant speed of the surface wave. The research was done within the long-wave asymptotic model for the Rayleigh wave in the case of an elastic coated half-space. The modes are classified according to the ratio between the velocity of the load and the resonance speed and to the dispersion coefficient of linear coverage. The study discovers the modes having radiation from the source. The results obtained can be generalized to more complex physical properties of the coating material, including the effects of anisotropy, viscosity and prestraining.

Kaplunov J., Oblakova T., Prikazchikov D. Near-resonant modes of the moving load in the plane problem of elasticity theory for a half-space with a thin coating. Маthematical Modeling and Coтputational Methods, 2014, №1 (1), pp. 57-67

#### 517.1 Special features of mathematical modeling of technical instruments

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

doi: 10.18698/2309-3684-2014-1-517

The paper gives grounds for applying mathematical modeling in the development and improvement of modern technical instruments and systems. It also shows typical stages of mathematical modeling and the sequence of their execution. The authors describe special features and basic methods in quantitative analysis of mathematical models of systems with distributed parameters (in continuous systems).

Zarubin V., Kuvyrkin G. Special features of mathematical modeling of technical instruments. Маthematical Modeling and Coтputational Methods, 2014, №1 (1), pp. 5-17

#### 533.6.011.31.5:532.582.33 Analytical formula with improved accuracy for calculating pressure distribution on the surface of convex, blunt rotation bodies of arbitrary shape

**Kotenev V. P. (Bauman Moscow State Technical University/JSC MIC NPO Mashinostroyenia), Sysenko V. A. (JSC MIC NPO Mashinostroyenia)**

doi: 10.18698/2309-3684-2014-1-6881

The authors developed the analytical formula for fast and accurate calculation of pressure on the surface of rotation bodies with arbitrary shape, which were flown by supersonic gas. The paper provides examples of applying the method for three-dimensional flows of gas.

Kotenev V., Sysenko V. Analytical formula with improved accuracy for calculating pressure distribution on the surface of convex, blunt rotation bodies of arbitrary shape. Маthematical Modeling and Coтputational Methods, 2014, №1 (1), pp. 68-81

#### 5 Математическое и компьютерное моделирование — основа современных инженерных наук

**Aleksandrov A. A. (Bauman Moscow State Technical University), Dimitrienko Y. I. (Bauman Moscow State Technical University)**

doi: 10.18698/2309-3684-2014-1-None

Aleksandrov A., Dimitrienko Y. Математическое и компьютерное моделирование — основа современных инженерных наук. Маthematical Modeling and Coтputational Methods, 2014, №1 (1), pp. 3-4