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Modulation of heat flux and thermal stress at the double interface by nano-coating thickness

ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK 2024年第1期75卷 20-20页

作者： Huang, Haojie Song, Kun Univ Shanghai Sci & Technol Sch Energy & Power Engn Shanghai Peoples R China Nanjing Tech Univ Sch Mech & Power Engn 30 Puzhu South Rd Nanjing Jiangsu Peoples R China

Nano-coatings hold the key to unlocking the vital potential of three-phase nanocomposites by urgently addressing thermal stress concentration. Consequently, the characteristics of double-interfacial heat flux and thermal stress have garnered considerable attention. In this paper, we introduce a set of interfacial conditions aimed at modeling double-interfacial phonon scattering and double-interfacial elasticity in three-phase nanocomposites. We derive closed-form solutions for the thermo-elastic field surrounding a circular nano-inclusion containing the nano-coatings. Through control over the nano-coating thickness and their properties, including thermal conductivity and interfacial phonon scattering coefficient, we can achieve a "neutral inclusions and coatings" temperature field, promoting uniform heat transfer. However, it is important to note that this approach leads to a noticeable increase in thermal stresses at the interfaces and the emergence of stress discontinuities due to the double-interfacial phonon scattering effect. Furthermore, the impact of coating thickness, coating thermal conductivity, and coating thermal expansion coefficient on the maximum interfacial thermal stress exhibits significant variability. Crucially, our findings reveal that adjusting the coating parameters can result in a substantial reduction in the overall thermal stress field's maximum value. This discovery carries significant implications for the design of nanocomposites and holds great promise for various applications.

关键词： Thermal stress Nano-coating Double-interfacial phonon scattering Interfacial elasticity complex variable method

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Analysis of layered soil under general time-varying loadings by fractional-order viscoelastic model

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APPLIED MATHEMATICAL MODELLING 2024年 126卷 232-248页

作者： Sha, Xiangyu Lu, Aizhong Zhang, Ning North China Elect Power Univ Sch Water Resources & Hydropower Engn Beijing 102206 Peoples R China

Time-varying loading is a frequently encountered loading type in geotechnical engineering. As the deformation of viscoelastic soil is related to its loading history, studying the viscoelastic problems under time-varying loads has important practical engineering significance. In this paper, the stress and displacement of a layered soil with fractional-order viscoelastic model under time-varying loads were solved using the complex variable method and the corresponding principle. Under the assumption of quasi-static and linear elasticity, this paper derives the quasi-static elastic solutions of a layered soil under time-varying strip loads. By introducing the fractional order viscoelastic model and using the corresponding principle, the Laplace-domain analytical solutions are obtained. Finally, numerical methods are utilized to perform the Laplace inverse transform and obtain the solutions in the physical domain. The correctness of this paper is validated by comparing the numerical results with the ANSYS software, as well as by comparison with previous literature. Based on the experimental data, the material parameters of frozen soil at two temperatures are fitted. The settlement patterns of soil under two engineering loads were analyzed through case studies. By controlling variables, the influence of parameters of the fractional viscoelastic model on elastic aftereffect was investigated.

关键词： Fractional-order viscoelastic model Layered soil General time-varying loadings complex variable method Analytical solution

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A liquid inclusion having an n-fold axis of symmetry in an infinite isotropic elastic matrix

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CONTINUUM MECHANICS AND THERMODYNAMICS 2024年第1期36卷 229-239页

作者： Wang, Xu Schiavone, Peter East China Univ Sci & Technol Sch Mech & Power Engn 130 Meilong Rd Shanghai 200237 Peoples R China Univ Alberta Donadeo Innovat Ctr Engn 10 203 Dept Mech Engn Edmonton AB T6G 1H9 Canada

We first study the plane strain problem associated with an incompressible liquid inclusion having an n-fold axis of symmetry which is embedded in an infinite isotropic elastic matrix subjected to uniform remote hydrostatic stresses. A closed-form solution is derived using Muskhelishvili's complex variable formulation, a four-term conformal mapping function and the application of analytic continuation. The pair of analytic functions characterizing the elastic field in the matrix is completely determined in elementary closed-form. Explicit expressions are obtained and graphically illustrated for the internal uniform hydrostatic stresses within the liquid inclusion and the hoop stress along the liquid-solid interface on the matrix side. The closed-form solution for a linearly compressible liquid inclusion having an n-fold axis of symmetry is also obtained.

关键词： Liquid inclusion n-fold axis of symmetry complex variable method Conformal mapping Analytic continuation Internal uniform hydrostatic tension Hoop stress

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Stress solution for an arbitrarily shaped tunnel with a neighboring circular cavity

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MATHEMATICS AND MECHANICS OF SOLIDS 2024年第1期29卷 83-98页

作者： Zeng, Xiang-Tai Wang, Shao-Jie Lv, Zhi-Tao Nanchang Univ Sch Infrastruct Engn Nanchang Peoples R China China Nucl Power Engn Co Ltd Beijing Peoples R China Nanchang Univ Sch Infrastruct Engn Nanchang 330031 Peoples R China

This paper gives an analytical stress solution for the plane strain problem that the deep rock mass contains an arbitrarily shaped tunnel and a circular cavity subjected to in situ stresses. Based on the discovery that the mapping function for an arbitrarily shaped hole can also manage a tunnel and a circular hole mapping into two circles, the plate bounded by the two holes is conformally mapped onto an annulus. The complex variable method is used to establish the stress boundary condition, and then the two analytical functions are solved by the power series method. Comparison with ANSYS solution is made to validate the correctness of deductions and solving process. To consider practical underground engineering, the cases of different lateral stresses, distances of the two holes, sizes, and positions of the cavity are discussed.

关键词： An arbitrarily shaped tunnel and a circular cavity stress solution complex variable method conformal mapping analytical function

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An analytical solution to account for the earthquake body force for twin circular tunnels in elastic media using complex variable approach

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ACTA GEOTECHNICA 2024年第12期19卷 8023-8049页

作者： Jain, Hemant Kumar, Jyant Indian Inst Sci Dept Civil Engn Bengaluru 560012 India

By using the complex variable approach, an analytical solution for non-uniformly deforming twin circular tunnels has been determined for a linear elastic weighty medium under the influence of earthquake pseudo-static inertial force. The non-uniform radial displacements along both the tunnels' peripheries have been imposed by using the Gaussian distribution function keeping the ground volume loss (GVL\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\it {\text{GVL}}$$\end{document}) as the basic input parameter. By using the Schwarz iterative technique, the effect of interference of the twin tunnels on stresses and displacements' patterns has been explored. The analytical solution satisfies (i) the prescribed non-uniform displacement boundary conditions along the tunnels' peripheries, (ii) the existence of buoyant and pseudo-static earthquake inertial forces due to the formation of tunnels, (iii) the geostatic stresses in the presence of horizontal earthquake (inertial) forces in a zone far away from the tunnels, and (iv) the stress-free ground surface. The ground displacements and stresses in the domain have been determined and presented in terms of a number of contour plots showing the effect of spacing, orientation and size of the tunnels for a given magnitude of pseudo-static earthquake acceleration. The results obtained from the analytical approach have been found to compare well with the solution separately determined on the basis of the finite element analysis.

关键词： Analytical solution complex variable method Earthquakes Finite element analysis Ground surface settlements Twin tunnels

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Fractional viscoelastic solution of stratum displacement of a shallow tunnel under the surface slope condition

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Underground Space 2023年第3期10卷 233-247页

作者： Fanchao Kong Dechun Lu Chao Ma Chenpeng Shen Xiaodong Yang Xiuli Du Institute of Geotechnical and Underground Engineering Beijing University of TechnologyBeijing 100124China School of Civil and Transportation Engineering Beijing University of Civil Engineering and ArchitectureBeijing 102626China Beijing Urban Construction Design&Development Group Co. LimitedThe Third Design Institute of Railway InstituteBeijing 100034China College of Mechanical Engineering Beijing University of TechnologyBeijing 100124China

The unified displacement function(UDF)is presented to describe the deformation behaviours of the tunnel profile along with time under the surface slope *** on the discrete Fourier method,the third-order UDF in the physical plane is expanded to the Laurent series in the complex variable *** complex variable method is employed to derive the elastic analytical solution of stra-tum displacement,when the third-order UDF is taken as the displacement boundary condition of tunnel cross-section(DBCTC).The proposed elastic solution agrees well with the results of the finite element method for the consistent model,which verifies the correctness of the proposed analytical *** the corresponding principle and fractional Generalized Kelvin viscoelastic constitutive model,the fractional viscoelastic solution under the surface slope condition is *** time effect of stratum displacement is presented in two aspects:time-dependent DBCTC and time-dependent material *** parameter analysis is performed to investigate influences of deformation modes of the third-order UDF,slope angle,tunnel radius and fractional order on the time effect of stratum vertical and horizontal displacement.

关键词： Third-order unified displacement function Surface slope condition Fractional viscoelastic solution complex variable method Discrete Fourier method

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Interfacial thermal stresses of segmented thermoelectric generators

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JOURNAL OF THERMAL STRESSES 2023年第7期46卷 574-587页

作者： Yan, Zipeng Yi, Longbing Xu, Haowei Huang, Shaolin Song, Kun Pan, Chunrong Jiang, Jun Jiangxi Univ Sci & Technol Sch Mech & Elect Engn Ganzhou Peoples R China Chinese Acad Sci Ningbo Inst Mat Technol & Engn Ningbo Peoples R China Nanjing Tech Univ Sch Mech & Power Engn Nanjing Peoples R China Nanjing Tech Univ Sch Mech & Power Engn 30 Puzhu South Rd Nanjing 211816 Peoples R China Jiangxi Univ Sci & Technol Sch Mech & Elect Engn Ganzhou 341000 Peoples R China Chinese Acad Sci Ningbo Inst Mat Technol & Engn Ningbo 315201 Peoples R China

The segmented structure can effectively improve the performance of a thermoelectric generator (TEG), but the interfacial thermal stress between adjacent segments seriously threatens the reliability of segmented TEGs. Noticing this, we investigate the mechanical performance of a segmented TEG via theoretical and numerical methods. Results show that the structural stress depends on the ratio of cross-sectional areas between p- and n-type TE legs rather than the absolute cross-sectional areas, while the height ratio of different segments has a significant influence on structural stress. Different from structural stress, the thermal stress induced by unmatched thermal expansion between different segments increases rapidly with the increase of cross-sectional area, and can easily exceed 20% of the total interfacial stress. Besides, both the conversion efficiency and interfacial stress can be optimized by adjusting the ratio of cross-sectional areas. Our results provide the theoretical basis and guidance in the design of segmented TEGs.

关键词： complex variable method interfacial stress segmented structure structural force thermoelectric generator

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An Eshelby inclusion of arbitrary shape in a nonlinearly coupled thermoelectric material

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ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK 2023年第2期74卷 1-10页

In this paper, we present a general method, based on the techniques of analytic continuation and conformal mapping, for the analytic solution of Eshelby's problem concerned with a two-dimensional inclusion of arbitrary shape in an infinite homogeneous and isotropic nonlinearly coupled thermoelectric plane. The inclusion is subjected to a prescribed uniform electric current-free thermoelectric potential gradient and a uniform energy flux-free temperature gradient. The corresponding boundary value problem is studied in both the physical and image planes. The closed-form general solution is found to be exact provided that the associated mapping function contains only a finite number of terms. Elementary expressions for the internal electric current density and energy flux in the physical plane are obtained. Examples of elliptical, hypotrochoidal and rectangular inclusions are presented to demonstrate the solution method. Interestingly, in this case Eshelby's uniformity property is found invalid for an elliptical inclusion.

关键词： Nonlinear thermoelectricity Eshelby's problem complex variable method Conformal mapping Analytic continuation

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A nonlinearly coupled thermoelectric material with a parabolic inhomogeneity

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JOURNAL OF THERMAL STRESSES 2023年第5期46卷 399-414页

作者： Wang, Xu Schiavone, Peter East China Univ Sci & Technol Sch Mech & Power Engn Shanghai Peoples R China Univ Alberta Dept Mech Engn Edmonton AB Canada East China Univ Sci & Technol Sch Mech & Power Engn 130 Meilong Rd Shanghai 200237 Peoples R China Univ Alberta Dept Mech Engn 10 203 Donadeo Innovat Ctr Engn Edmonton AB T6G 1H9 Canada

We use complex variable methods to study the two-dimensional thermoelectric and thermoelastic problems associated with a nonlinearly coupled thermoelectric parabolic inhomogeneity embedded in an infinite nonlinearly coupled thermoelectric matrix subjected to uniform remote electric current density and uniform remote energy flux. Exact closed-form solutions to the problems are derived primarily with the aid of an identity established on the parabolic interface. Our analysis indicates that the electrically and thermally induced stresses exhibit quadratic distributions inside the parabolic inhomogeneity.

关键词： Closed-form solution complex variable method nonlinear thermoelectricity parabolic inhomogeneity thermoelastic field thermoelectric field

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An elliptical inhomogeneity under nonuniform heat flux

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MATHEMATICS AND MECHANICS OF SOLIDS 2023年第8期28卷 1790-1797页

作者： Wang, Xu Schiavone, Peter East China Univ Sci & Technol Sch Mech & Power Engn 130 Meilong Rd Shanghaxi 200237 Peoples R China Univ Alberta Dept Mech Engn 10-203 Donadeo Innovat Ctr Engn Edmonton AB T6G 1H9 Canada

We use complex variable techniques to study the decoupled two-dimensional steady-state heat conduction and thermoelastic problems associated with an elliptical elastic inhomogeneity perfectly bonded to an infinite matrix subjected to a nonuniform heat flux at infinity. Specifically, the nonuniform remote heat flux takes the form of a linear distribution. It is found that the internal temperature and thermal stresses inside the elliptical inhomogeneity are quadratic functions of the two in-plane coordinates. Explicit closed-form expressions of the analytic functions characterizing the temperature and thermoelastic field in the matrix are derived.

关键词： Elliptical inhomogeneity nonuniform heat flux complex variable method

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