125 results on '"Thin inclusion"'
Search Results
2. Thin inclusion at the junction of two elastic bodies: non-coercive case.
- Author
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Khludnev, A. M.
- Subjects
- *
BOUNDARY value problems , *CELLULAR inclusions , *EQUILIBRIUM - Abstract
This article addresses an analysis of the non-coercive boundary value problem describing an equilibrium state of two contacting elastic bodies connected by a thin elastic inclusion. Nonlinear conditions of inequality type are imposed at the joint boundary of the bodies providing a mutual non-penetration. As for conditions at the external boundary, they are Neumann type and imply the non-coercivity of the problem. Assuming that external forces satisfy suitable conditions, a solution existence of the problem analysed is proved. Passages to limits are justified as the rigidity parameters of the inclusion and the elastic body tend to infinity. This article is part of the theme issue 'Non-smooth variational problems with applications in mechanics'. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
3. Elastic Equilibrium of Anisotropic Bimaterial Bodies with Thin Elastic Anisotropic Inclusions Under Longitudinal Shear.
- Author
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Vasil'ev, K. V. and Sulym, H. T.
- Subjects
- *
FOURIER integrals , *INTEGRAL transforms , *ELASTIC modulus , *FOURIER transforms , *SEPARATION of variables , *STRESS intensity factors (Fracture mechanics) - Abstract
By using the method of integral Fourier transforms, the method of jump functions, and the method of conjugation of continua of different dimensions, we construct the solution of the basic problem of longitudinal shear of an anisotropic bimaterial containing a system of thin internal ribbon anisotropic inhomogeneities in each half space. By analyzing an example of reducing the problem of longitudinal shear of an anisotropic two-layer structure with thin inhomogeneities to the basic problem, we approve the previously developed method of direct cutting-out. We also investigate the influence of elastic moduli and specific geometric parameters of the problem on the generalized stress intensity factors. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
4. Elasticity Problem with a Cusp between Thin Inclusion and Boundary.
- Author
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Khludnev, Alexander
- Subjects
- *
ELASTICITY , *COHESION , *CUSP forms (Mathematics) , *RIGID bodies - Abstract
This paper concerns an equilibrium problem for an an elastic body with a thin rigid inclusion crossing an external boundary of the body at zero angle. The inclusion is assumed to be exfoliated from the surrounding elastic material that provides an interfacial crack. To avoid nonphysical interpenetration of the opposite crack faces, we impose inequality type constraints. Moreover, boundary conditions at the crack faces depend on a positive parameter describing a cohesion. A solution existence of the problem with different conditions on the external boundary is proved. Passages to the limit are analyzed as the damage parameter tends to infinity and to zero. Finally, an optimal control problem with a suitable cost functional is investigated. In this case, a part of the rigid inclusion is located outside of the elastic body, and a control function is a shape of the inclusion. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
5. Asymptotic modeling of steady vibrations of thin inclusions in a thermoelastic composite.
- Author
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Furtsev, Alexey I., Fankina, Irina V., Rodionov, Alexander A., and Ponomarev, Dmitri A.
- Subjects
- *
ADHESIVES , *DIFFERENTIAL inclusions , *COMPOSITE materials - Abstract
The paper addresses the mathematical justification of a model describing steady vibrations for a planar thermoelastic body with an incorporated thin inclusion. The body is composed of three parts: two adherents and an adhesive layer between them, and we begin with a general mathematical formulation of a problem. By means of the modern methods of asymptotic analysis, we rigorously investigate the behavior of solutions as the thickness of the adhesive tends to zero. As a result, we construct the model that corresponds to the limit case. It turned out that the adhesive is reduced to the inclusion, which is thin (of zero thickness) and relatively hard (compared to the rigidity of the surrounding body). Furthermore, we supplement the obtained results with numerical experiments demonstrating the consistency of the theoretical conclusions. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
6. Elastic body with thin nonhomogeneous inclusion in non-coercive case.
- Author
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Khludnev, Alexander M and Rodionov, Alexander A
- Subjects
- *
ELASTICITY (Economics) , *INVERSE problems , *COERCIVE fields (Electronics) , *DISPLACEMENT (Mechanics) - Abstract
The paper addresses analysis of equilibrium state of an elastic body with a thin nonhomogeneous inclusion in a non-coercive case. We assume that a part of the inclusion is located outside the elastic body, and the traction free boundary condition at the external boundary of the elastic body does not provide a coercivity of the problem. The inclusion is delaminated from the surrounding elastic material that implies a presence of the interfacial crack. Constraint boundary conditions at the crack faces describe a mutual nonpenetration and have an inequality type form. We prove a solution existence of the equilibrium problem, analyze a passage to the limit as the rigidity parameter of the inclusion tends to zero, and prove a solution existence of an inverse problem. The inverse problem assumes that along with the displacement field we have to find an elasticity coefficient for the inclusion provided that an additional information is given which can be found from a measurement. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
7. On Numerical Solving of Junction Problem for the Thin Rigid and Elastic Inclusions in Elastic Body.
- Author
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Popova, T. S.
- Abstract
We consider a multiphysics problem of equilibrium for a two-dimensional elastic body containing a thin rigid and thin elastic inclusions. The inclusions delaminate from the elastic matrix, forming a crack; therefore, the problem is posed in a nonsmooth domain with a cut. The mathematical model of the delaminated thin rigid inclusion was developed on the assumption that the function of rigid inclusion displacement has a prescribed structure. The elastic inclusion is modeled in the framework of theory of Timoshenko beam. The problem statement is presented both in a form of a variational inequality and in the form of a boundary value problem including the junction conditions in a common point of inclusions. The boundary condition on the crack faces has a form of inequality and as a result, the problem is non-linear. As a consequence, the construction of an algorithm for the numerical solution of the problem requires the use of additional analytical methods. The methods of domain decomposition, the method of Lagrange multipliers, and the finite element method are used. An algorithm for the numerical solution of the problem is constructed, and a computational example is provided. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
8. Variational Approach to Modeling of Curvilinear Thin Inclusions with Rough Boundaries in Elastic Bodies: Case of a Rod-Type Inclusion.
- Author
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Rudoy, Evgeny and Sazhenkov, Sergey
- Subjects
- *
ELASTICITY , *NUMERICAL calculations , *DIFFERENTIAL inclusions , *CELLULAR inclusions - Abstract
In the framework of 2D-elasticity, an equilibrium problem for an inhomogeneous body with a curvilinear inclusion located strictly inside the body is considered. The elastic properties of the inclusion are assumed to depend on a small positive parameter δ characterizing its width and are assumed to be proportional to δ − 1 . Moreover, it is supposed that the inclusion has a curvilinear rough boundary. Relying on the variational formulation of the equilibrium problem, we perform the asymptotic analysis, as δ tends to zero. As a result, a variational model of an elastic body containing a thin curvilinear rod is constructed. Numerical calculations give a relative error between the initial and limit problems depending on δ. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
9. Elastic Equilibrium of Anisotropic Bimaterial Bodies with Thin Elastic Anisotropic Inclusions Under Longitudinal Shear
- Author
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Vasil’ev, K. V. and Sulym, H. T.
- Published
- 2024
- Full Text
- View/download PDF
10. Method of Direct Cutting-Out in Modeling Orthotropic Solids with Thin Elastic Inclusions Under Longitudinal Shear.
- Author
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Vasil'ev, K. V. and Sulym, H. T.
- Subjects
- *
ELASTIC solids , *CELLULAR inclusions , *ELASTIC modulus , *STRESS intensity factors (Fracture mechanics) - Abstract
By the method of direct cutting-out, the problems of longitudinal shear of an orthotropic half space, a layer, and a wedge with thin elastic orthotropic inclusions are reduced to the basic problem of interaction of thin inhomogeneities in the orthotropic space. We establish the conditions of interaction of loaded elastic anisotropic inclusions with the matrix of the body. We study the influence of elastic moduli both of the inclusion and of the body, as well as of the geometric parameters of the problems on the generalized stress intensity factors. The level lines of stresses are plotted in the vicinity of the inclusion. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
11. Elasticity Tensor Identification in Elastic Body with Thin Inclusions: Non-coercive Case.
- Author
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Khludnev, Alexander and Rodionov, Alexander
- Subjects
- *
ELASTICITY , *TENSOR fields , *LAMINATED composite beams , *BOUNDARY value problems , *DIGITAL image correlation - Abstract
In the paper, we analyze problems of elasticity tensor identification for an elastic body with incorporated thin elastic and rigid inclusions in a non-coercive case. The inclusions are assumed to be delaminated from the surrounding elastic body, thus forming interfacial cracks. We consider inequality-type boundary conditions at the crack faces with unknown set of a contact to provide a mutual non-penetration between the crack faces. The considered problems are characterized by unknown displacement field and elasticity tensor. A formulation of identification problems includes an additional information, which can be found from a measurement. A solution existence of these problems is proved. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
12. Indentation of an Absolutely Rigid Thin Inclusion into One of the Crack Faces in an Elastic Plane Under Slippage at the Ends
- Author
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Hakobyan, Vahram N., Amirjanyan, Harutyun A., Dashtoyan, Lilit L., Sahakyan, Avetik V., Öchsner, Andreas, Series Editor, da Silva, Lucas F. M., Series Editor, Altenbach, Holm, Series Editor, Bauer, Svetlana M., editor, Belyaev, Alexander K., editor, Indeitsev, Dmitri A., editor, Matveenko, Valery P., editor, and Petrov, Yuri V., editor
- Published
- 2022
- Full Text
- View/download PDF
13. Stress State of a Compound Plane with Interface Absolutely Rigid Inclusion and Crack Having Common Tip
- Author
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Hakobyan, Vahram, Sahakyan, Avetik, Amirjanyan, Harutyun, Öchsner, Andreas, Series Editor, da Silva, Lucas F. M., Series Editor, Altenbach, Holm, Series Editor, Eremeyev, Victor A., editor, Galybin, Alexander, editor, and Vasiliev, Andrey, editor
- Published
- 2022
- Full Text
- View/download PDF
14. Elasticity Problem with a Cusp between Thin Inclusion and Boundary
- Author
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Alexander Khludnev
- Subjects
elastic body ,thin inclusion ,cusp ,non-penetration boundary condition ,damage parameter ,optimal control ,Mathematics ,QA1-939 - Abstract
This paper concerns an equilibrium problem for an an elastic body with a thin rigid inclusion crossing an external boundary of the body at zero angle. The inclusion is assumed to be exfoliated from the surrounding elastic material that provides an interfacial crack. To avoid nonphysical interpenetration of the opposite crack faces, we impose inequality type constraints. Moreover, boundary conditions at the crack faces depend on a positive parameter describing a cohesion. A solution existence of the problem with different conditions on the external boundary is proved. Passages to the limit are analyzed as the damage parameter tends to infinity and to zero. Finally, an optimal control problem with a suitable cost functional is investigated. In this case, a part of the rigid inclusion is located outside of the elastic body, and a control function is a shape of the inclusion.
- Published
- 2023
- Full Text
- View/download PDF
15. Effect of the Transverse Functional Gradient of the Thin Interfacial Inclusion Material on the Stress Distribution of the Bimaterial under Longitudinal Shear.
- Author
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Piskozub, Yosyf, Piskozub, Liubov, and Sulym, Heorhiy
- Subjects
- *
MECHANICAL behavior of materials , *STRAINS & stresses (Mechanics) , *THERMOELASTICITY , *STRESS concentration , *THERMAL conductivity - Abstract
The effect of a functional gradient in the cross-section material (FGM) of a thin ribbon-like interfacial deformable inclusion on the stress–strain state of a piecewise homogeneous linear–elastic matrix under longitudinal shear conditions is considered. Based on the equations of elasticity theory, a mathematical model of such an FGM inclusion is constructed. An analytic–numerical analysis of the stress fields for some typical cases of the continuous functional gradient dependence of the mechanical properties of the inclusion material is performed. It is proposed to apply the constructed solutions to select the functional gradient properties of the inclusion material to optimize the stress–strain state in its vicinity under the given stresses. The derived equations are suitable with minor modifications for the description of micro-, meso- and nanoscale inclusions. Moreover, the conclusions and calculation results are easily transferable to similar problems of thermal conductivity and thermoelasticity with possible frictional heat dissipation. [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
- View/download PDF
16. Multiscale analysis of stationary thermoelastic vibrations of a composite material.
- Author
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Fankina, Irina V., Furtsev, Alexey I., Rudoy, Evgeny M., and Sazhenkov, Sergey A.
- Subjects
- *
ASYMPTOTIC expansions , *ASYMPTOTIC homogenization , *THERMOELASTICITY , *COMPOSITE materials - Abstract
The problem of description of stationary vibrations is studied for a planar thermoelastic body incorporating thin inclusions. This problem contains two small positive parameters δ and ε , which describe the thickness of an individual inclusion and the distance between two neighbouring inclusions, respectively. Relying on the variational formulation of the problem, by means of the modern methods of asymptotic analysis, we investigate the behaviour of solutions as δ and ε tend to zero. As the result, we construct two models corresponding to the limit cases. At first, as δ→0 , by the version of the method of formal asymptotic expansions we derive a limit model in which inclusions are thin (of zero width). Then, from this limit model, as ε→0 , we derive a homogenized model, which describes effective behaviour on the macroscopic scale, i.e. on the scale where there is no need to take into account each individual inclusion. The limiting passage as ε→0 is based on the use of the two-scale convergence theory. This article is part of the theme issue 'Non-smooth variational problems and applications'. [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
- View/download PDF
17. Variational Approach to Modeling of Curvilinear Thin Inclusions with Rough Boundaries in Elastic Bodies: Case of a Rod-Type Inclusion
- Author
-
Evgeny Rudoy and Sergey Sazhenkov
- Subjects
asymptotic analysis ,inhomogeneous elastic body ,thin inclusion ,rough boundary ,interface condition ,Mathematics ,QA1-939 - Abstract
In the framework of 2D-elasticity, an equilibrium problem for an inhomogeneous body with a curvilinear inclusion located strictly inside the body is considered. The elastic properties of the inclusion are assumed to depend on a small positive parameter δ characterizing its width and are assumed to be proportional to δ−1. Moreover, it is supposed that the inclusion has a curvilinear rough boundary. Relying on the variational formulation of the equilibrium problem, we perform the asymptotic analysis, as δ tends to zero. As a result, a variational model of an elastic body containing a thin curvilinear rod is constructed. Numerical calculations give a relative error between the initial and limit problems depending on δ.
- Published
- 2023
- Full Text
- View/download PDF
18. Thermomagnetoelectroelasticity of Bimaterial Solids with High Temperature Conducting Interface and Thin Internal Inhomogeneities
- Author
-
Vasylyshyn, Andrii, Pasternak, Iaroslav, Sulym, Heorhiy, Correia, José A. F. O., Series Editor, De Jesus, Abílio M. P., Series Editor, Ayatollahi, Majid Reza, Advisory Editor, Berto, Filippo, Advisory Editor, Fernández-Canteli, Alfonso, Advisory Editor, Hebdon, Matthew, Advisory Editor, Kotousov, Andrei, Advisory Editor, Lesiuk, Grzegorz, Advisory Editor, Murakami, Yukitaka, Advisory Editor, Carvalho, Hermes, Advisory Editor, Zhu, Shun-Peng, Advisory Editor, Bordas, Stéphane, Advisory Editor, Fantuzzi, Nicholas, Advisory Editor, Gdoutos, Emmanuel, editor, and Konsta-Gdoutos, Maria, editor
- Published
- 2020
- Full Text
- View/download PDF
19. Method of Direct Cutting-Out in Modeling Orthotropic Solids with Thin Elastic Inclusions Under Longitudinal Shear
- Author
-
Vasil’ev, K. V. and Sulym, H. T.
- Published
- 2023
- Full Text
- View/download PDF
20. Effect of the Transverse Functional Gradient of the Thin Interfacial Inclusion Material on the Stress Distribution of the Bimaterial under Longitudinal Shear
- Author
-
Yosyf Piskozub, Liubov Piskozub, and Heorhiy Sulym
- Subjects
functionally graded material ,thin inclusion ,composites ,nonperfect contact ,frictional heating ,crack ,Technology ,Electrical engineering. Electronics. Nuclear engineering ,TK1-9971 ,Engineering (General). Civil engineering (General) ,TA1-2040 ,Microscopy ,QH201-278.5 ,Descriptive and experimental mechanics ,QC120-168.85 - Abstract
The effect of a functional gradient in the cross-section material (FGM) of a thin ribbon-like interfacial deformable inclusion on the stress–strain state of a piecewise homogeneous linear–elastic matrix under longitudinal shear conditions is considered. Based on the equations of elasticity theory, a mathematical model of such an FGM inclusion is constructed. An analytic–numerical analysis of the stress fields for some typical cases of the continuous functional gradient dependence of the mechanical properties of the inclusion material is performed. It is proposed to apply the constructed solutions to select the functional gradient properties of the inclusion material to optimize the stress–strain state in its vicinity under the given stresses. The derived equations are suitable with minor modifications for the description of micro-, meso- and nanoscale inclusions. Moreover, the conclusions and calculation results are easily transferable to similar problems of thermal conductivity and thermoelasticity with possible frictional heat dissipation.
- Published
- 2022
- Full Text
- View/download PDF
21. Скінченноелементне дослідження пружної фільтрації в ґрунтах із тонкими включеннями.
- Author
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Мічута, О. Р., Іванчук, Н. В., Мартинюк, П. М., and Остапчук, О. П.
- Subjects
FINITE element method ,COMPUTER simulation ,HEAD injuries ,NONLINEAR equations ,ENVIRONMENTAL soil science ,DIFFERENTIAL inclusions - Abstract
Copyright of Eastern-European Journal of Enterprise Technologies is the property of PC TECHNOLOGY CENTER and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
- Published
- 2020
- Full Text
- View/download PDF
22. On junction problem with damage parameter for Timoshenko and rigid inclusions inside elastic body.
- Author
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Khludnev, A.M. and Popova, T.S.
- Subjects
INFINITY (Mathematics) ,MATHEMATICAL equivalence - Abstract
The paper is concerned with an equilibrium problem for 2D elastic body with a thin elastic Timoshenko inclusion and a thin rigid inclusion. The elastic inclusion is assumed to be delaminated from the elastic body thus forming an interfacial crack with the matrix. Inequality type boundary conditions are imposed at the crack faces to prevent a mutual penetration. A connection between two inclusions at a given point is characterized by a positive damage parameter. Existence of solutions of the problem considered is proved, and different equivalent formulations of the problem are analyzed; junction conditions at the connection point are found. A convergence of solutions as the damage parameter tends to zero and to infinity as well as the rigidity parameter of the elastic inclusion tends to infinity is analyzed. An analysis of the limit models is performed. A solution existence of an inverse problem for finding the damage and rigidity parameters is proved provided that an additional information concerning the derivative of the energy functional with respect to the delamination length is given. [ABSTRACT FROM AUTHOR]
- Published
- 2020
- Full Text
- View/download PDF
23. Inverse problem for elastic body with thin elastic inclusion.
- Author
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Khludnev, Alexander M.
- Subjects
- *
INVERSE problems , *CELLULAR inclusions , *INFINITY (Mathematics) - Abstract
An inverse problem for an elastic body with a thin elastic inclusion is investigated. It is assumed that the inclusion crosses the external boundary of the elastic body. A connection between the inclusion and the elastic body is characterized by the damage parameter. We study a dependence of the solutions on the damage parameter. In particular, passages to infinity and to zero of the damage parameter are investigated. Limit models are analyzed. Assuming that the damage and rigidity parameters of the model are unknown, inverse problems are formulated. Sufficient conditions for the inverse problems to have solutions are found. Estimates concerning solutions of the inverse problem are established. [ABSTRACT FROM AUTHOR]
- Published
- 2020
- Full Text
- View/download PDF
24. Optimal Control of Parameters for Elastic Body with Thin Inclusions.
- Author
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Khludnev, Alexander, Esposito, Antonio Corbo, and Faella, Luisa
- Subjects
- *
INVERSE problems , *INFINITY (Mathematics) - Abstract
In this paper, an equilibrium problem for 2D non-homogeneous anisotropic elastic body is considered. It is assumed that the body has a thin elastic inclusion and a thin rigid inclusion. A connection between the inclusions at a given point is characterized by a junction stiffness parameter. The elastic inclusion is delaminated, thus forming an interfacial crack with the matrix. Inequality-type boundary conditions are imposed at the crack faces to prevent interpenetration. Existence of solutions is proved; different equivalent formulations of the problem are discussed; junction conditions at the connection point are found. A convergence of solutions as the junction stiffness parameter tends to zero and to infinity as well as the rigidity parameter of the elastic inclusion tends to infinity is investigated. An analysis of limit models is provided. An optimal control problem is analyzed with the cost functional equal to the derivative of the energy functional with respect to the crack length. A solution existence of an inverse problem for finding the junction stiffness and rigidity parameters is proved. [ABSTRACT FROM AUTHOR]
- Published
- 2020
- Full Text
- View/download PDF
25. The homogenized quasi-static model of a thermoelastic composite stitched with reinforcing threads.
- Author
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Fankina, Irina V., Furtsev, Alexey I., Rudoy, Evgeny M., and Sazhenkov, Sergey A.
- Subjects
- *
ASYMPTOTIC homogenization - Abstract
The problem of description of quasi-static behavior is studied for a planar thermoelastic body incorporating many thin inclusions, each of which geometrically is a straight line segment with the endpoints on the body edge. The inclusions (i.e. threads, filaments) are parallel to each other and the problem contains a small positive parameter ϵ , which describes the distance between two neighboring inclusions. Relying on the variational formulation of the problem, we investigate the behavior of solutions as ϵ tends to zero. As the result, we derive a well-posed homogenized model, which describes effective behavior on the macroscopic scale, i.e., on the scale where there is no need to take into account each individual inclusion. The limiting passage as ϵ → 0 is based on the use of the two-scale convergence theory. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
26. Effect of Frictional Slipping on the Strength of Ribbon-Reinforced Composite
- Author
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Yosyf Piskozub and Heorhiy Sulym
- Subjects
ribbon-like reinforcement ,composite ,thin inclusion ,bimaterial ,nonperfect contact ,friction ,Technology ,Electrical engineering. Electronics. Nuclear engineering ,TK1-9971 ,Engineering (General). Civil engineering (General) ,TA1-2040 ,Microscopy ,QH201-278.5 ,Descriptive and experimental mechanics ,QC120-168.85 - Abstract
A numerical–analytical approach to the problem of determining the stress–strain state of bimaterial structures with interphase ribbon-like deformable inhomogeneities under combined force and dislocation loading has been proposed. The possibility of delamination along a part of the interface between the inclusion and the matrix, where sliding with dry friction occurs, is envisaged. A structurally modular method of jump functions is constructed to solve the problems arising when nonlinear geometrical or physical properties of a thin inclusion are taken into account. A complete system of equations is constructed to determine the unknowns of the problem. The condition for the appearance of slip zones at the inclusion–matrix interface is formulated. A convergent iterative algorithm for analytical and numerical determination of the friction-slip zones is developed. The influence of loading parameters and the friction coefficient on the development of these zones is investigated.
- Published
- 2021
- Full Text
- View/download PDF
27. On modeling thin inclusions in elastic bodies with a damage parameter.
- Author
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Khludnev, A. M.
- Subjects
- *
CELLULAR inclusions - Abstract
In this paper, we analyze equilibrium problems for 2D elastic bodies with two thin inclusions in the presence of damage. A delamination of the inclusions from the matrix is assumed, thus forming a crack between the elastic body and the inclusions. Nonlinear boundary conditions at the crack faces are considered to prevent a mutual penetration between the faces. Weak and strong formulations of the problems are discussed. The paper provides an asymptotic analysis with respect to the damage parameter. An optimal control problem is analyzed with a cost functional to be equal to the derivative of the energy functional with respect to the crack length, and the damage parameter being a control function. [ABSTRACT FROM AUTHOR]
- Published
- 2019
- Full Text
- View/download PDF
28. On thin Timoshenko inclusions in elastic bodies with defects.
- Author
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Khludnev, Alexander
- Subjects
- *
CELLULAR inclusions - Abstract
The paper concerns an analysis of equilibrium problems for elastic bodies with elastic Timoshenko inclusion in the presence of defects. Defects are characterized by a positive damage parameter. This parameter is responsible for a connection between defect faces. Asymptotic properties of solutions are investigated with respect to the damage parameters as well as with respect to a rigidity parameter of the inclusions. Limit models are investigated; in particular, different equivalent problem formulations are proposed. [ABSTRACT FROM AUTHOR]
- Published
- 2019
- Full Text
- View/download PDF
29. Thin inclusion in elastic body: identification of damage parameter.
- Author
-
Khludnev, Alexander
- Subjects
ELASTICITY ,OPTIMAL control theory ,WAGE differentials ,EQUILIBRIUM ,DEFECTION - Abstract
In the paper, we consider an equilibrium problem for a 2D elastic body with a thin elastic inclusion crossing an external boundary. The elastic body has a defect which is characterized by a positive damage parameter. The presence of a defect means that the problem is formulated in a non-smooth domain. Non-linear boundary conditions at the defect faces are imposed to prevent the mutual penetration between the faces. Both variational and differential problem formulations are proposed, and existence of solutions is established. We study an asymptotics of solutions with respect to the damage parameter as well as with respect to a rigidity parameter of the inclusion. Identification problems for finding the damage parameter are investigated. To this end, existence of solutions of optimal control problems is proven. [ABSTRACT FROM AUTHOR]
- Published
- 2019
30. Equilibrium of an Elastic Body with Closely Spaced Thin Inclusions.
- Author
-
Khludnev, A. M.
- Subjects
- *
ELASTICITY , *EQUILIBRIUM , *SURFACE cracks , *FRACTURE mechanics , *BOUNDARY value problems - Abstract
Abstract: Problems with unknown boundaries describing an equilibrium of two-dimensional elastic bodies with two thin closely spaced inclusions are considered. The inclusions are in contact with each other, which means that there is a crack between them. On the crack faces, nonlinear boundary conditions of the inequality type that prevent the interpenetration of the faces are set. The unique solvability of the problems is proved. The passages to the limit as the stiffness parameter of thin inclusions tends to infinity are studied, and limiting models are analyzed. [ABSTRACT FROM AUTHOR]
- Published
- 2018
- Full Text
- View/download PDF
31. Asymptotic Justification of Models of Plates Containing Inside Hard Thin Inclusions
- Author
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Evgeny Rudoy
- Subjects
Kirchhoff-Love plate ,composite material ,thin inclusion ,asymptotic analysis ,Technology - Abstract
An equilibrium problem of the Kirchhoff–Love plate containing a nonhomogeneous inclusion is considered. It is assumed that elastic properties of the inclusion depend on a small parameter characterizing the width of the inclusion ε as εN with N<1. The passage to the limit as the parameter ε tends to zero is justified, and an asymptotic model of a plate containing a thin inhomogeneous hard inclusion is constructed. It is shown that there exists two types of thin inclusions: rigid inclusion (N<−1) and elastic inclusion (N=−1). The inhomogeneity disappears in the case of N∈(−1,1).
- Published
- 2020
- Full Text
- View/download PDF
32. Problems of Thin Inclusions in a Two-Dimensional Viscoelastic Body.
- Author
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Popova, T. S.
- Abstract
Under study are the equilibrium problems for a two-dimensional viscoelastic body with delaminated thin inclusions in the cases of elastic and rigid inclusions. Both variational and differential formulations of the problems with nonlinear boundary conditions are presented; their unique solvability is substantiated. For the case of a thin elastic inclusion modelled as a Bernoulli-Euler beam, we consider the passage to the limit as the rigidity parameter of the inclusion tends to infinity. In the limit it is the problem about a thin rigid inclusion. Relationship is established between the problems about thin rigid inclusions and the previously considered problems about volume rigid inclusions. The corresponding passage to the limit is justified in the case of inclusions without delamination. [ABSTRACT FROM AUTHOR]
- Published
- 2018
- Full Text
- View/download PDF
33. Nonlinear Deformation of a Thin Interface Inclusion.
- Author
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Sulym, H. T. and Piskozub, I. Z.
- Subjects
- *
DEFORMATIONS (Mechanics) , *NONLINEAR analysis , *INTERFACES (Physical sciences) , *ANISOTROPY , *INTEGRAL equations - Abstract
We develop a model of thin inclusion with nonlinear anisotropic mechanical properties of the general form. By using this model and the methods of the problem of conjugation of the limit values of analytic and jump functions, we construct a system of singular integral equations with variable coefficients (functions). The solution of the system enables us to describe any changes (monotonic or nonmonotonic) in the quasistatic load and its influence on the stress-strain state of the body with inhomogeneity on the basis of the incremental approach. For the numerical solution of the system, we propose an iterative numerical-analytic method. [ABSTRACT FROM AUTHOR]
- Published
- 2018
- Full Text
- View/download PDF
34. Thermo- and electroconductive properties of composites
- Author
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Gladwell, G. M. L., editor, Kanaun, S. K., and Levin, V. M.
- Published
- 2008
- Full Text
- View/download PDF
35. A finite-element study of elastic filtration in soils with thin inclusions
- Author
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Olga Michuta, Petro Martyniuk, Natalia Ivanchuk, and Oksana Ostapchuk
- Subjects
Work (thermodynamics) ,Materials science ,020209 energy ,0211 other engineering and technologies ,Energy Engineering and Power Technology ,elastic filtration ,02 engineering and technology ,Industrial and Manufacturing Engineering ,law.invention ,law ,Management of Technology and Innovation ,021105 building & construction ,lcsh:Technology (General) ,0202 electrical engineering, electronic engineering, information engineering ,lcsh:Industry ,Electrical and Electronic Engineering ,Filtration ,Series (mathematics) ,Applied Mathematics ,Mechanical Engineering ,conjugation conditions ,Mechanics ,Finite element method ,Computer Science Applications ,Discontinuity (linguistics) ,Nonlinear system ,Control and Systems Engineering ,finite-element method ,thin inclusion ,Head (vessel) ,lcsh:T1-995 ,lcsh:HD2321-4730.9 ,Inclusion (mineral) - Abstract
Soil environments are heterogeneous in their nature. This heterogeneity creates significant difficulties both in terms of construction practice and in terms of the mathematical modeling and computer simulation of the physical-chemical processes in these heterogeneous soil arrays. From the standpoint of mathematical modeling, the issue is the discontinuity of functions, which characterize the examined processes, on such inclusions. Moreover, the characteristics of such inclusions may depend on the defining functions of the processes studied (head, temperature, humidity, the concentration of chemicals, and their gradients). And this requires the modification of conjugation conditions and leads to the nonlinear boundary-value problems in heterogeneous areas. That is why this work has examined the impact of the existence of thin inclusions on the conjugation conditions for the defining functions of the filtration and geomigration processes on them. The conjugation condition for heads has also been modified while the mathematical model of an elastic filtration mode in a heterogeneous array of soil, which contains thin weakly permeable inclusions, has been improved. The improvement implies the modification of conjugation conditions for heads on thin inclusions when the filtering factor of the inclusion itself is nonlinearly dependent on the head gradient. The numerical solution to the corresponding nonlinear boundary-value problem has been found using a finite-element method. A series of numerical experiments were conducted and their analysis was carried out. The possibility of a significant impact on the head jump has been shown taking into consideration the dependence of filtration characteristics of an inclusion on head gradients. In particular, the relative difference of head jumps lies between 26% and 99% relative to the problem with a stable filtration factor for an inclusion. In other words, when conducting forecast calculations, the influence of such dependences cannot be neglected
- Published
- 2020
36. Thermoelasticity of Anisotropic Bimaterial Solids with Contact Thermal Resistance of the Interface Between Their Components and Thin Inclusions.
- Author
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Sulym, H., Томаshivs'kyi, М., and Pasternak, Ya.
- Subjects
- *
THERMOELASTICITY , *ANISOTROPIC crystals , *THERMAL resistance , *BOUNDARY element methods , *ANALYTIC functions - Abstract
We use the extended Stroh formalism and the theory of functions of complex variable to construct Somigliana-type integral relations and the corresponding equations for thermoelastic anisotropic bimaterial solids with imperfect thermal contact on the rectilinear interface between their components. Applying the mathematical model of thin deformable thermally insulated inclusion and the obtained integral relations, we solve the thermoelasticity problem for a finite anisotropic bimaterial solid containing a thin inhomogeneity with regard for the thermal resistance on the interface between the main components of the materials. [ABSTRACT FROM AUTHOR]
- Published
- 2017
- Full Text
- View/download PDF
37. Optimal control of rigidity parameters of thin inclusions in composite materials.
- Author
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Khludnev, A., Faella, L., and Perugia, C.
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- *
ENGINEERING design , *ENGINEERING , *COMPOSITE materials , *MICROMECHANICS , *GEOMETRIC rigidity - Abstract
In the paper, an equilibrium problem for an elastic body with a thin elastic and a volume rigid inclusion is analyzed. It is assumed that the thin inclusion conjugates with the rigid inclusion at a given point. Moreover, a delamination of the thin inclusion is assumed. Inequality type boundary conditions are considered at the crack faces to prevent a mutual penetration between the faces. A passage to the limit is justified as the rigidity parameter of the thin inclusion goes to infinity. The main goal of the paper is to analyze an optimal control problem with a cost functional characterizing a deviation of the displacement field from a given function. A rigidity parameter of the thin inclusion serves as a control function. An existence theorem to this problem is proved. [ABSTRACT FROM AUTHOR]
- Published
- 2017
- Full Text
- View/download PDF
38. Junction problem for rigid and Timoshenko elastic inclusions in elastic bodies.
- Author
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Khludnev, A. M., Faella, L., and Popova, T. S.
- Subjects
- *
TIMOSHENKO beam theory , *RIGID bodies , *BOUNDARY value problems , *EXISTENCE theorems , *FRACTURE mechanics - Abstract
This paper concerns an equilibrium problem for a two-dimensional elastic body with a thin Timoshenko elastic inclusion and a thin rigid inclusion. It is assumed that the inclusions have a joint point and we analyze a junction problem for these inclusions. The existence of solutions is proved and the different equivalent formulations of the problem are discussed. In particular, the junction conditions at the joint point are found. A delamination of the elastic inclusion is also assumed. In this case, the inequality-type boundary conditions are imposed at the crack faces to prevent a mutual penetration between the crack faces. We investigate the convergence to infinity and zero of a rigidity parameter of the elastic inclusion. It is proved that in the limit, we obtain a rigid inclusion and a zero rigidity inclusion (a crack). [ABSTRACT FROM AUTHOR]
- Published
- 2017
- Full Text
- View/download PDF
39. Rigidity Parameter Identification for Thin Inclusions Located Inside Elastic Bodies.
- Author
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Khludnev, Alexander
- Subjects
- *
GEOMETRIC rigidity , *MATHEMATICAL inequalities , *BOUNDARY value problems , *MATHEMATICAL optimization , *MATHEMATICAL formulas - Abstract
The paper is concerned with an identification of a rigidity parameter for thin inclusions located inside elastic bodies. It is assumed that inclusions cross an external boundary of the elastic body. In addition to this, a delamination of the inclusions is assumed thus providing a crack between inclusions and the elastic body. To exclude a mutual penetration between crack faces, inequality-type boundary conditions are imposed. We consider elastic inclusions as well as rigid and rigid-elastic inclusions. To find a solution of the problem formulated, we solve an optimal control problem. A cost functional characterizes a displacement of the external part of the inclusion, and a rigidity parameter serves as a control function. We prove a solution existence of the problems formulated. [ABSTRACT FROM AUTHOR]
- Published
- 2017
- Full Text
- View/download PDF
40. Asymptotics of anisotropic weakly curved inclusions in an elastic body.
- Author
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Khludnev, A.
- Abstract
Under study are the boundary value problems describing the equilibrium of twodimensional elastic bodies with thin anisotropic weakly curved inclusions in presence of separations. The latter implies the existence of a crack between the inclusion and the matrix. Nonlinear boundary conditions in the form of inequalities are imposed on the crack faces that exclude mutual penetration of the crack faces. This leads to the formulation of the problems with unknown contact area. The passage to limits with respect to the rigidity parameters of the thin inclusions is inspected. In particular, we construct the models as the rigidity parameters go to infinity and analyze their properties. [ABSTRACT FROM AUTHOR]
- Published
- 2017
- Full Text
- View/download PDF
41. An Arbitrary Oriented Crack in the Box Shell
- Author
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Migdalski, V. I., Reut, V. V., Gohberg, I., editor, Adamyan, V. M., editor, Gorbachuk, M., editor, Gorbachuk, V., editor, Kaashoek, M. A., editor, Langer, H., editor, and Popov, G., editor
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- 2000
- Full Text
- View/download PDF
42. JUNCTION PROBLEM FOR EULER-BERNOULLI AND TIMOSHENKO ELASTIC INCLUSIONS IN ELASTIC BODIES.
- Author
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KHLUDNEV, A. M. and POPOVA, T. S.
- Subjects
EULER-Bernoulli beam theory ,TIMOSHENKO beam theory ,ELASTICITY ,BOUNDARY value problems ,STOCHASTIC convergence - Abstract
In the paper, we consider an equilibrium problem for a 2D elastic body with thin Euler-Bernoulli and Timoshenko elastic inclusions. It is assumed that inclusions have a joint point, and we analyze a junction problem for these inclusions. Existence of solutions is proved, and different equivalent formulations of the problem are discussed. In particular, junction conditions at the joint point are found. A delamination of the elastic inclusion is also assumed. In this case, inequality type boundary conditions are imposed at the crack faces to prevent a mutual penetration between crack faces. We investigate a convergence to infinity and to zero of a rigidity parameter of the elastic inclusions. Limit problems are analyzed. [ABSTRACT FROM AUTHOR]
- Published
- 2016
- Full Text
- View/download PDF
43. Mixed Boundary Value Problem for an Anisotropic Thermoelastic Half-Space Containing Thin Inhomogeneities
- Author
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Andrii Vasylyshyn, Iaroslav Pasternak, Mariia Smal, and Heorhiy Sulym
- Subjects
Physics ,Mechanical Engineering ,Mathematical analysis ,crack ,Mechanics of engineering. Applied mechanics ,History of engineering ,TA349-359 ,02 engineering and technology ,Half-space ,01 natural sciences ,boundary element method ,010101 applied mathematics ,thermoelasticity ,020303 mechanical engineering & transports ,Thermoelastic damping ,0203 mechanical engineering ,Control and Systems Engineering ,thin inclusion ,stroh formalism ,stress intensity factors ,Boundary value problem ,0101 mathematics ,anisotropic half-space ,Anisotropy ,Boundary element method - Abstract
The paper presents a rigorous and straightforward approach for obtaining the 2D boundary integral equations for a thermoelastic half-space containing holes, cracks and thin foreign inclusions. It starts from the Cauchy integral formula and the extended Stroh formalism which allows writing the general solution of thermoelastic problems in terms of certain analytic functions. In addition, with the help of it, it is possible to convert the volume integrals included in the equation into contour integrals, which, in turn, will allow the use of the method of boundary elements. For modelling of solids with thin inhomogeneities, a coupling principle for continua of different dimensions is used. Applying the theory of complex variable functions, in particular, Cauchy integral formula and Sokhotski–Plemelj formula, the Somigliana type boundary integral equations are constructed for thermoelastic anisotropic half-space. The obtained integral equations are introduced into the modified boundary element method. A numerical analysis of the influence of boundary conditions on the half-space boundary and relative rigidity of the thin inhomogeneity on the intensity of stresses at the inclusions is carried out.
- Published
- 2019
44. Effect of Frictional Slipping on the Strength of Ribbon-Reinforced Composite
- Author
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Heorhiy Sulym and Yosyf Piskozub
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Technology ,Materials science ,Iterative method ,45F15 ,74M15 ,friction ,Slip (materials science) ,bimaterial ,System of linear equations ,Article ,30E20 ,Matrix (mathematics) ,General Materials Science ,composite ,Slipping ,ribbon-like reinforcement ,Microscopy ,QC120-168.85 ,74M25 ,QH201-278.5 ,Delamination ,Mechanics ,Engineering (General). Civil engineering (General) ,TK1-9971 ,Nonlinear system ,Descriptive and experimental mechanics ,thin inclusion ,nonperfect contact ,00A06 ,Electrical engineering. Electronics. Nuclear engineering ,jump functions ,TA1-2040 ,Dislocation - Abstract
A numerical–analytical approach to the problem of determining the stress–strain state of bimaterial structures with interphase ribbon-like deformable inhomogeneities under combined force and dislocation loading has been proposed. The possibility of delamination along a part of the interface between the inclusion and the matrix, where sliding with dry friction occurs, is envisaged. A structurally modular method of jump functions is constructed to solve the problems arising when nonlinear geometrical or physical properties of a thin inclusion are taken into account. A complete system of equations is constructed to determine the unknowns of the problem. The condition for the appearance of slip zones at the inclusion–matrix interface is formulated. A convergent iterative algorithm for analytical and numerical determination of the friction-slip zones is developed. The influence of loading parameters and the friction coefficient on the development of these zones is investigated.
- Published
- 2021
45. Junction problem for rigid and semirigid inclusions in elastic bodies.
- Author
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Khludnev, Alexander and Popova, Tatiana
- Subjects
- *
ELASTICITY , *RIGID bodies , *BOUNDARY value problems , *FRACTURE mechanics , *VARIATIONAL inequalities (Mathematics) - Abstract
The paper is concerned with equilibrium problems for 2D elastic bodies having thin inclusions with different properties. In particular, rigid and semirigid inclusions are considered. It is assumed that inclusions have a joint point, and we analyze a junction problem for these inclusions. Existence of solutions is proved for each equilibrium problem, and different equivalent formulations of these problems are discussed. In particular, junction conditions at the joint point are found. A delamination of the inclusions is also assumed. This means that we have a crack, and inequality-type boundary conditions are imposed at the crack faces to prevent a mutual penetration between crack faces. We discuss a convergence to zero and infinity of a rigidity parameter of the semirigid inclusion and analyze limit problems. [ABSTRACT FROM AUTHOR]
- Published
- 2016
- Full Text
- View/download PDF
46. Junction problem for elastic and rigid inclusions in elastic bodies.
- Author
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Faella, Luisa and Khludnev, Alexander
- Subjects
- *
ELASTIC structures (Mechanics) , *DIFFERENTIAL inclusions , *GEOMETRIC rigidity , *ELASTIC analysis (Engineering) , *ELASTOMERIC fibers - Abstract
An equilibrium problem for an elastic body is considered. It is assumed that the body has a thin elastic inclusion and a thin rigid inclusion. We analyze a junction problem assuming that the inclusions have a joint point. Different equivalent problem formulations are discussed, and existence of solutions is proved. A set of junction conditions is found. We investigate a convergence to infinity and to zero of a rigidity parameter of the elastic inclusion. A delamination of the elastic inclusion is also investigated. In this case, inequality-type boundary conditions are imposed at the crack faces to prevent a mutual penetration between crack faces. Copyright © 2015 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]
- Published
- 2016
- Full Text
- View/download PDF
47. Numerical solution of the equilibrium problem for a two-dimensional elastic body with a thin semirigid inclusion
- Author
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Popova, T.S.
- Subjects
semirigid inclusion ,General Mathematics ,Mathematical analysis ,crack ,Problem statement ,non-penetration conditions ,Rigidity (psychology) ,Domain decomposition methods ,variational inequality ,Domain (mathematical analysis) ,Finite element method ,Uzawa algorithm ,domain decomposition ,symbols.namesake ,nonlinear boundary conditions ,Lagrange multiplier ,Variational inequality ,thin inclusion ,symbols ,Boundary value problem ,Mathematics - Abstract
The equilibrium problem for a two-dimensional elastic body containing a thin semirigid inclusion is considered. The inclusion delaminates from the elastic matrix, forming a crack; therefore, the problem is posed in a nonsmooth domain with a cut. The mathematical model of the delaminated thin semirigid inclusion was developed on the assumption that the rigidity of the material differs in different directions. The problem statement is presented both in the form of a variational inequality and in the form of a boundary value problem. The boundary condition on the crack faces has a form of inequality and, as a result, the problem is non-linear. Consequently, the construction of an algorithm for the numerical solution of the problem requires the use of additional analytical methods. The methods of domain decomposition, the method of Lagrange multipliers, and the finite element method are used. An algorithm for the numerical solution of the problem is constructed and a computational example is provided., Журнал «Математические заметки СВФУ», Выпуск 1 (109) 2021, Pages 51-66
- Published
- 2021
- Full Text
- View/download PDF
48. A weakly curved inclusion in an elastic body with separation.
- Author
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Khludnev, A.
- Abstract
A problem with unknown boundary, which describes the equilibrium of a two-dimensional elastic body with a thin weakly curved inclusion, is studied. The inclusion can separate, thus producing a crack. Nonlinear boundary conditions are posed as inequalities on the crack shores so as to ensure the mutual nonpenetration of the shores. The unique solvability of the problem is proved. The problems of passing to the limit with respect to the thin inclusion rigidity are considered. In particular, a model is constructed by letting the rigidity parameter tend to infinity, and its properties are investigated. On the other hand, it is shown that the zero rigidity parameter of the inclusion exactly corresponds to the problem of equilibrium of an elastic body with a crack satisfying the boundary conditions of mutual nonpenetration of its shores. [ABSTRACT FROM AUTHOR]
- Published
- 2015
- Full Text
- View/download PDF
49. SINGULAR INVARIANT INTEGRALS FOR ELASTIC BODY WITH DELAMINATED THIN ELASTIC INCLUSION.
- Author
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KHLUDNEV, A. M.
- Subjects
INVARIANTS (Mathematics) ,BOUNDARY value problems ,ENERGY function ,DIFFERENTIAL equations ,COMPLEX variables - Abstract
We consider an equilibrium problem for a 2D elastic body with a thin elastic inclusion. It is assumed that the inclusion is partially delaminated, therefore providing the presence of a crack. Inequality type boundary conditions are imposed at the crack faces to prevent a mutual penetration of the faces. Differentiability properties of the energy functional with respect to the crack length are analyzed. We prove an existence of the derivative and find a formula for this derivative. It is shown that the formula for the derivative can be written in the form of a singular invariant integral. [ABSTRACT FROM AUTHOR]
- Published
- 2014
- Full Text
- View/download PDF
50. Скінченноелементне дослідження пружної фільтрації в ґрунтах із тонкими включеннями
- Author
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Michuta, Olga, Ivanchuk, Natalia, Martyniuk, Petro, and Ostapchuk, Oksana
- Subjects
UDC 519.61/.64:627.05 ,пружна фільтрація ,тонке включення ,умови спряження ,метод скінченних елементів ,elastic filtration ,thin inclusion ,conjugation conditions ,finite-element method ,упругая фильтрация ,тонкое включение ,условия сопряжения ,метод конечных элементов - Abstract
Soil environments are heterogeneous in their nature. This heterogeneity creates significant difficulties both in terms of construction practice and in terms of the mathematical modeling and computer simulation of the physical-chemical processes in these heterogeneous soil arrays. From the standpoint of mathematical modeling, the issue is the discontinuity of functions, which characterize the examined processes, on such inclusions. Moreover, the characteristics of such inclusions may depend on the defining functions of the processes studied (head, temperature, humidity, the concentration of chemicals, and their gradients). And this requires the modification of conjugation conditions and leads to the nonlinear boundary-value problems in heterogeneous areas. That is why this work has examined the impact of the existence of thin inclusions on the conjugation conditions for the defining functions of the filtration and geomigration processes on them. The conjugation condition for heads has also been modified while the mathematical model of an elastic filtration mode in a heterogeneous array of soil, which contains thin weakly permeable inclusions, has been improved. The improvement implies the modification of conjugation conditions for heads on thin inclusions when the filtering factor of the inclusion itself is nonlinearly dependent on the head gradient. The numerical solution to the corresponding nonlinear boundary-value problem has been found using a finite-element method. A series of numerical experiments were conducted and their analysis was carried out. The possibility of a significant impact on the head jump has been shown taking into consideration the dependence of filtration characteristics of an inclusion on head gradients. In particular, the relative difference of head jumps lies between 26 % and 99 % relative to the problem with a stable filtration factor for an inclusion. In other words, when conducting forecast calculations, the influence of such dependences cannot be neglected, Грунтовые среды по своей природе являются неоднородными. Эта неоднородность создает значительные трудности как с точки зрения практики строительства, так и с точки зрения математического и компьютерного моделирования физико-химических процессов в этих неоднородных грунтовых массивах. С точки зрения математического моделирования проблемой является разрывность функций, которыми характеризуются исследуемые процессы, на таких включениях. Более того, характеристики таких включений могут зависеть от определяющих функций исследуемых процессов (напор, температура, влажность, концентрация химических веществ и их градиенты). А это требует модификации условий сопряжения и приводит к нелинейным краевым задачам в неоднородных областях. Именно поэтому было исследовано влияние наличия тонких включений на условия сопряжения для определяющих функций фильтрационных и геомиграцийних процессов на них. Также модифицировано условие сопряжения для напоров и усовершенствована математическая модель упругого режима фильтрации в неоднородном массиве грунта, который содержит тонкие слабопроницаемые включения. Совершенствование заключается в модификации условий сопряжения для напоров на тонких включениях, когда коэффициент фильтрации самого включения нелинейно зависит от градиента напоров. Числовое решение соответствующей нелинейной краевой задачи найдено методом конечных элементов. Проведен ряд численных экспериментов и осуществлено их анализ. Показана возможность значительного влияния на скачок напоров учета зависимости фильтрационных характеристик включения от градиентов напоров. В частности, относительная разница прыжков напоров лежит в пределах от 26 % до 99 % относительно задачи с постоянным коэффициентом фильтрации для включения. То есть, при проведении прогнозных расчетов влиянием таких зависимостей пренебрегать нельзя, Ґрунтові середовища по своїй природі є неоднорідними. Ця неоднорідність створює значні труднощі як з точки зору практики будівництва, так і з точки зору математичного і комп’ютерного моделювання фізико-хімічних процесів в цих неоднорідних ґрунтових масивах. З точки зору математичного моделювання проблемою є розривність функцій, якими характеризуються досліджувані процеси, на таких включеннях. Більше того, характеристики таких включень можуть залежати від визначальних функцій досліджуваних процесів (напір, температура, вологість, концентрація хімічних речовин та їх градієнти). А це вимагає модифікації умов спряження та приводить до нелінійних крайових задач в неоднорідних областях. Саме тому в роботі було досліджено вплив наявності тонких включень на умови спряження для визначальних функцій фільтраційних та геоміграційних процесів на них. Також модифіковано умову спряження для напорів та вдосконалено математичну модель пружного режиму фільтрації в неоднорідному масиві ґрунту, який містить тонкі слабопроникні включення. Вдосконалення полягає у модифікації умов спряження для напорів на тонких включеннях, коли коефіцієнт фільтрації самого включення нелінійно залежить від градієнта напорів. Числовий розв’язок відповідної нелінійної крайової задачі знайдено методом скінченних елементів. Проведено ряд числових експериментів та здійснено їх аналіз. Показана можливість значного впливу на стрибок напорів урахування залежності фільтраційних характеристик включення від градієнтів напорів. Зокрема, відносна різниця стрибків напорів лежить в межах від 26 % до 99 % відносно задачі зі сталим коефіцієнтом фільтрації для включення. Тобто, при проведенні прогнозних розрахунків впливом таких залежностей нехтувати не можна
- Published
- 2020
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