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Mathematical Modeling of the Thermal Shell State of the Cylindrical Cryogenic Tank During Filling and Emptying
Mathematics and Mathematical Modelling # 06, December 2015
DOI: 10.7463/mathm.0615.0829350
pp. 44-60
Local Temperature Distribution on the Spacecraft Surface under Uneven Solar Radiation
Aerospace Scientific Journal # 05, September 2015
DOI: 10.7463/aersp.0515.0820883
pp. 49-63
Dielectric Permeability of Anisotropic Fiber Mesh-Reinforced Composite
Radiooptics # 06, November 2015
DOI: 10.7463/rdopt.0615.0816600
pp. 88-104
Mathematical Modeling of Dielectric Characteristics of the Metallic Band Inclusion Composite
Mathematics and Mathematical Modelling # 05, October 2015
DOI: 10.7463/mathm.0515.0815604
pp, 64-82
Permittivity of Composite with Metallic Inclusions as an Ellipsoid of the Rotation
Radiooptics # 04, July 2015
DOI: 10.7463/rdopt.0415.0811296
Mechanically Interacting Bimetallic Shell Walls of the Liquid Rocket Engine Chamber Under Diffusion Soldering
Aerospace Scientific Journal # 04, July 2015
DOI: 10.7463/aersp.0415.0800092
pp. 51-63
Mathematical Modeling of Electrical Conductivity of Dielectric with Dispersed Metallic Inclusions
Mathematics and Mathematical Modelling # 03, June 2015
DOI: 10.7463/mathm.0315.0793596
pp. 59–72
Temperature State of Noncooled Nozzle Adjutage of Liquid Rocket Engine
Aerospace Scientific Journal # 03, May 2015
DOI: 10.7463/aersp.0315.0793049
pp. 6-16
A Variational Approach to the Estimate of the Permittivity of a Composite with Dispersed Inclusions
Mathematics and Mathematical Modelling # 02, April 2015
DOI: 10.7463/mathm.0215.0769483
pp. 37-49
Estimate of permittivity of anisotropic composites with lamellar inclusions by the self-assessment method
Mathematics and Mathematical Modelling # 01, February 2015
DOI: 10.7463/mathm.0115.0776021
pp. 36-48

Engineering Education # 08, August 2014
DOI: 10.7463/0814.0720691
pp.237-255
Mathematical simulation of heat transfer in unidirectional fiber composite
Engineering Education # 01, January 2014
DOI: 10.7463/0114.0657262
In order to justify a reliable application domain for the calculation dependence which allows one to determine the effective heat conductivity coefficient of transversely isotropic unidirectional fiber composite in the plane perpendicular to the fibers; a mathematical model of heat transfer in representative elements of this composite’s structure was created. An ordered arrangement of parallel fibers was considered for the case when their centers coincide with the nodes of cross sectional plane grid with square cells or cells in the form of equilateral triangles. Quantitative analysis of developed mathematical model was performed using the finite element method with controlled integrated computational error. Presented results are important for assessing the temperature condition and efficiency of heat-stressed structures made of unidirectional fiber composite.
Evaluation of effective thermal conductivity of unidirectional fiber composites by the method of self-consistency
Engineering Education # 11, November 2013
DOI: 10.7463/1113.0622927
The self-consistency method was used to estimate the components of a thermal conductivity tensor of unidirectional fiber composite, which is transversally isotropic with respect to an axis arranged parallel to the fibers. In this method it is possible to estimate effective values of parameters for the composite as a whole by averaging the perturbed distributions of the parameters over the elements of the composite structure and equating averaged results to zero. A perturbed temperature field and heat flux density distribution over the fibers and composite matrix were calculated on the basis of the developed mathematical models of heat interaction between these elements of the structure and a transversely isotropic homogeneous material which has required coefficients of thermal conductivity. For validation of the final calculated dependences, bilateral estimates based on dual variation formulation of the stationary problem of heat conduction in an inhomogeneous solid body were used. The calculated dependencies can be used for forecasting effective thermal conductivity of unidirectional fiber composites.
Evaluation of effective thermal conductivity of composites with ball inclusions by the method of self-consistency
Engineering Education # 09, September 2013
DOI: 10.7463/0913.0601512
The method of self-consistency was applied to obtaining an estimate of the effective value of thermal conductivity of a composite with ball inclusions. This method was based on averaging of parameters of a perturbed temperature field in elements of a composite structure. The perturbed temperature field in inclusions and ball particles of the composite matrix was found by solving the steady-state heat conduction problem formulated on the basis of a constructed mathematical model of thermal interaction of these elements with a homogeneous material with an unknown coefficient of thermal conductivity. Quantitative analysis of the derived calculated relation was carried out to a sufficiently wide range of the defining parameters to verify reliability of the obtained estimate. The calculation results with respect to this relation are located within the interval between the lower and upper estimates which could be obtained from both a singular approximation of the theory of random functions and the dual variation principle of Hashin - Shtrikman.
Thermal conductivity of the textured composite with anisotropic inclusions in the form of ellipsoids of rotation
Engineering Education # 06, June 2013
DOI: 10.7463/0613.0569312
On the basis of a developed mathematical model of heat transfer in composite with anisotropic inclusions of ellipsoidal shape, a procedure for calculating components of an effective heat-conduction tensor of the textured composite was proposed. A variant of inclusions in the form of ellipsoids of rotation was considered. The main axes of the heat-conduction tensor of such inclusions coincide with symmetric axes of an ellipsoid. In case of conic texture of a composite its possible dispersion was taken into account. The obtained results could be used for estimating effective thermal conductivity of composites modified with nanostructured elements (including carbon nanotubes). Due to electrothermal analogy these results are applicable when consideringcharacteristics of electrical conductivity and dielectric capacitance of textured composites.
Comparative analysis of estimations of heat conduction of a composite with ball inclusions
Engineering Education # 07, July 2013
DOI: 10.7463/0713.0569319
УДК: 541.124
The authors consider different mathematical models of thermal interaction of ball inclusions and the matrix of a composite, used for estimating the effective heat conduction coefficient of this kind of composite. Application of a dual formulation of the variation problem of stationary thermal conductivity in a nonhomogeneous solid body allowed to get double-sided estimations of possible values of the coefficient. It was determined that transition from ball inclusions to cubic ones influenced slightly the effective heat conduction coefficient of a composite. The authors derived an evaluation formula that allowed to obtain a reliable estimation of this coefficient within the whole range of possible variations of the volume concentration of inclusions. Due to the electrothermal analogy it was possible to apply the obtained results in order to estimate characteristics of electrical conductivity and of dielectric capacitance of composites modified with ball inclusions (considering nanostructured elements).
Comparative analysis of estimations of polycrystalline material’s effective thermal conductivity coefficient
Engineering Education # 03, March 2013
DOI: 10.7463/0313.0541029
The authors carried out a comparative quantitative analysis of mathematical models for estimating effective thermal conductivity coefficient of polycrystalline material which consists of chaotically oriented anisotropic crystal grains with identical crystal grid. Along with well-known methods for generating mathematical models, approaches which allowed to obtain new calculating dependences were also considered. The upper and lower bounds for accepted values of this coefficient were obtained with the use of a dual variational formulation of a stationary thermal conductivity problem for a non-homogeneous solid body. Formulas for calculating best-attested estimations were recommended. These formulas could be used for estimating electric conductivity of polycrystalline materials due to electro thermal analogy.
Effective thermal conductivity coefficients of composite with anisotropic ellipsoidal inclusions
Engineering Education # 04, April 2013
DOI: 10.7463/0413.0541050
УДК: 536.2
A mathematical model of heat transfer in a composite material with identically oriented anisotropic ellipsoidal inclusions was created. Formulae for calculating effective thermal conductivity of composite materials, which are anisotropic with respect to the property of thermal conductivity, were obtained on the basis of a developed mathematical model. To estimate the possible error of the results, a dual formulation of the variational problem of stationary heat conduction in a heterogeneous solid body was applied. These results can be used to predict effective thermal conductivity of composite materials with ellipsoidal inclusions, which are among other nanostructured elements (including carbon nanotubes). The obtained formulas can be used for estimating electric conductivity of composite materials with identically oriented anisotropic ellipsoidal inclusions due to electro thermal analogy.
 
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