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Galina A. Starushenko

Galina A. Starushenko
Dnipropetrovsk Regional Institute of State Management of National Academy of State Management at the President of Ukraine, Ukraine, Dnipropetrovsk · Information technologies and information systems

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53
Publications
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274
Citations
Citations since 2017
17 Research Items
152 Citations
20172018201920202021202220230102030
20172018201920202021202220230102030
20172018201920202021202220230102030
20172018201920202021202220230102030

Publications

Publications (53)
Article
Paper is devoted to the effective stationary heat conductivity for the fibre composite materials. We are aimed on getting on analytical expression for effective thermal conductivity coefficient. Asymptotic homogenization approach, based on the multiple scale perturbation method, is used. This allows to reduce the original boundary value problem in...
Article
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Unsteady heat conduction in fibre composite materials is studied. 2D composite media consist of a matrix with circular inclusions in hexagonal lattice structures. Perfect contact between different materials is assumed on the boundary of the fibres. The temperature field is modelled by a heat equation. Laplace transform and asymptotic homogenization...
Article
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In the first part of our review paper, we consider the problem of approximating the Green’s function of the Lagrange chain by continuous analogs. It is shown that the use of continuous equations based on the two-point Padé approximants gives good results. In the second part of the paper, the problem of singularities arising in the classical theory...
Article
In general, asymptotic homogenization methods (AHMs) are based on the hypothesis of perfect scale separation. In practice, this is not always the case. The problem arises of improving the solution in such a way that it becomes applicable if the inhomogeneity parameter is not small. Our study focuses on the higher order asymptotic homogenization for...
Article
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This paper is devoted to comparing the asymptotics of a solution, describing the wave motion of a discrete lattice and its continuous approximations. The transition from a discrete medium to a continuous one changes the symmetry of the system. The influence of this change on the asymptotic behavior of waves is of great interest. For the discrete ca...
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The effective properties of the fiber-reinforced composite materials with fibers of circular cross section are investigated. The novel estimation for the effective coefficient of thermal conductivity refining the classical Maxwell formula is derived. The method of asymptotic homogenization is used. For analytical solution of the periodically repeat...
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The effective properties of the fiber-reinforced composite materials with fibers of circle cross section are investigated. The novel estimation for the effective coefficient of thermal conductivity refining the classical Maxwell formula is derived. The method of asymptotic homogenization is used. For an analytical solution of the periodically repea...
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In this paper, we study various variants of Verhulst-like ordinary differential equations (ODE) and ordinary difference equations (O Δ E). Usually Verhulst ODE serves as an example of a deterministic system and discrete logistic equation is a classic example of a simple system with very complicated (chaotic) behavior. In our paper we present exampl...
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The objective of the article is constructing of the two-factor model on the basis of the statistical material of the Webometric Rating of Universities, which analytically describes the status of Ukrainian higher educational institutions in terms of Webometrics indicators, provides an opportunity for its quantitative and qualitative analysis and for...
Article
The effective properties of the fiber-reinforced composite materials with fibers of square cross-section are investigated. The novel formula for the effective coefficient of thermal conductivity refining the classical Maxwell formula (MF) is derived. The methods of asymptotic homogenization, boundary shape perturbation and Schwarz alternating proce...
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Self-consistent approximation and Padé approximants are used for calculation of percolation threshold for elasticity problem.
Article
Досліджено підхід з оцінювання державної політики України у сфері вищої освіти з використанням даних міжнародного рейтингу університетів Webometrics. Продемонстровано важливість аналізу даних Webometrics під час оцінювання науково-дослідницької складової діяльності українських вищих навчальних закладів. Розроблено комплексний статистичний алгоритм...
Article
Homogenisation theory and lubrication approach are adopted to study transport problems for systems of densely packed, high-contrast fibre composites. The effective conductivity properties of composites with inclusions of various shapes are derived. Contact conditions are analysed for boundaries between the composite phases. In addition, asymptotic...
Article
This paper is a continuation of the investigations reported in the Part I. Based on the asymptotic approach and the lubrication theory, the composite with rhombic inclusions are studied. Models of composites with curvilinear rhombic inclusions and thin interfaces on phase boundaries are constructed with the help of non-smooth argument substitution...
Article
Free vibrations of a composite membrane with a hexagonal lattice circular inclusion are investigated. We aim at a study of the lower frequency spectrum, i.e. it is assumed that the minimum space period of the eigenform is essentially larger than the characteristic dimension of the cell periodicity of the analyzed structure. This implies a possibili...
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Effective conductivity of a 2D composite corresponding to the regular hexagonal arrangement of superconducting disks is expressed in the form of a long series in the volume fraction of ideally conducting disks. According to our calculations based on various resummation techniques, both the threshold and critical index are obtained in good agree...
Article
The fiber-reinforced composite materials with periodic cylindrical inclusions of a circular cross-section arranged in a hexagonal array are analyzed. The governing analytical relations of the thermal conductivity problem for such composites are obtained using the asymptotic homogenization method. The lubrication theory is applied for the asymptotic...
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One of the major advantages of homogenization is a possibility of the generalization of the obtained results. Namely, if a solution to the local problem is found, then without principal problems one may solve not only the analyzed problem, by also a series of related static and dynamic problems, including: linear, quasi-linear, the eigenvalue probl...
Article
Full-text available
Effective conductivity of a 2D composite corresponding to the regular hexagonal arrangement of superconducting disks is expressed in the form of a long series in the volume fraction of ideally conducting disks. According to our calculations based on various re-summation techniques, both the threshold and critical index are obtained in good agreemen...
Article
In this paper, a two-phase computational model of a composite (TwPM) with cylindrical inclusion of square cross-sections and small sizes is proposed. The applied asymptotic techniques devoted to the analysis of the constructed TwPM are validated through a comparison of the results reported by others. A simple analytical formula of the reduced heat...
Article
The problem of determining the effective thermal conductivity of a composite material with periodic cylindrical inclusions of a circular cross-section arranged in a square grid is analyzed. Defining mathematical relationships are derived on the basis of a three-phase composite model, asymptotic homogenization technique and application of the bounda...
Article
The solution of the Three-phase composite model (coinciding with the Maxwell Garnett formula) is transformed using the Padé approximants. The obtained Padé approximants fundamentally expand the applicability limits of the Maxwell Garnett solution. The explicit analytical formulae for the effective coefficient of thermal conductivity of the composit...
Article
Thermal conductivity of composite materials with periodically distributed cylindrical inclusions of square cross-section is investigated. Analytical interpolation formula for the effective thermal conductivity in transversal direction valid in the entire range of volume fraction of inclusions and value of their thermal conductivity is derived. The...
Article
The fiber-reinforced composite materials with cylindrical inclusions of a square cross-section are analyzed using three-phase composite model combined with the asymptotic homogenization. The problem of thermal conductivity of such composite structure is solved in the zero- and first-order approximations using the boundary shape perturbation method....
Article
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A modified three-phase composite model yielding reliable effective characteristics of composite structures has been proposed. In particular, the problem of effective heat transfer coefficient of the composite structure with periodically located inclusions of circular cross-sections located on a square net is solved. Advantages of the proposed model...
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Article
This paper is devoted to the numerical analysis of the various continuum models of a 1D discrete media. Namely, we consider intermediate, quasi-continuum, and improved quasi-continuum models. The analysis of various receptions of continualization in a linear case is carried out. For this purpose, we consider the solution in the form of a traveling...
Article
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This paper considers the problem of thin interface in a fibre reinforced composite material. Using the singular asymptotic procedure, the authors obtain simplified relations known as spring model. Phenomenon of edge effect is also studied using the Papkovich-Fadle approach. The singularities of the limit problem are analysed.
Conference Paper
A variety approaches for continuous approximation of a discrete medium are studied using an example of 1D chain of linear oscillators.
Article
Full-text available
An asymptotic approach is proposed to describe the strongly anisotropic solids. We simplified the input boundary value problem using ratios of the elastic constants as small parameters. The obtained results can be used for the investigation of the composite materials.
Article
The analytical method of wave and oscillation theory differential equations periodic solution building on the so-called saw-tooth argument transformation base has been used in the paper series [V.N. Pilipchuk, in: International Congress of Mathematicians, Zurich, 3–11 August 1994, Short Communications, 1994, p. 202; V.N. Pilipchuk, G.A. Starusenko,...
Article
Pade approximants approach is proposed for estimating the thermal behaviour of nonlinear composite materials with periodic microstructures, the effective conductivities of which depend on the temperature. The central idea is to restate the homogenization problem for a nonlinear composite in terms of the corresponding problem for the linear one. Suc...
Article
Full-text available
An analytical solution, describing the effective heat conductivity of composite materials with a periodic array of cylindrica inclusions with square cross–section, has been obtained by asymptotic methods and Padé approximants for any values of th concentration of inclusions and conductivity.
Article
Solutions of differential equations of motion for mechanical systems with periodic impulsive excitation are represented in a special form which contains a standard pair of non-smooth periodic functions and possesses the structure of an algebra without division. This form is also suitable in the case of excitation with a periodic series of discontin...
Article
An approximate solution of the problem of the determination of the effective thermal conductivity of a pile field during construction on permafrost is prosed on the basis of asymptotic approaches.
Article
An analytical solution, describing homogenized coefficients for composite materials with periodic cylindrical inclusions of square section domain, has been obtained by asymptotic methods and Pade approximants for any size of inclusions and its conductivity.
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The analytical method of saw-tooth argument transformation, which can be considered as the argument representation by two non-smooth functions of the special form, is known in the wave oscillation theory. In the present paper saw-tooth transformation technique has developed applicably to the elasticity theory periodic tasks.
Article
The method described in [1] of introducing a non-smooth argument by means of special identities is shown to provide an additional means of analysing one-dimensional systems with a periodic structure. A modification of the transformation is constructed which greatly extends the possible applications.
Article
The fundamental inequalities for two-point Padé approximants corresponding to two asymptotic expansions of the effective transport coefficients λ e (x)/λ 1 , x=λ 2 /λ 1 -1 have been derived, where λ 1 and λ 2 denote the transport moduli of the composite components. The inequalities achieved constitute the new bounds on the values of λ e (x)/λ 1 – t...
Article
A dynamical problem for a perforated membrane with free holes is considered. A solution is obtained with the help of the averaging method and the use of two-scaling decompositions. To solve local problems, we apply the variational Bubnov-Galerkin method. The first correction to the frequency is determined from the averaging equation of order ?1and...
Article
We consider transverse oscillations of a membrane with a square network of perforations whose contour is clamped and whose aperture edges are free. We apply the method of averaging in conjunction with variational methods for solving cell problems. The eigenfunctions and characteristic frequencies of oscillation are represented as asymptotic series...

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