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Effective transport properties of composites with a doubly-periodic array of fiber pairs and with a triangular array of fibers
Yan P; Zhang ZA; Chen FL; Jiang CP(蒋持平); Wang XJ; Qiu ZP
Source PublicationZAMM-ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND MECHANIK
2018-02-01
Volume98Issue:2Pages:312-329
ISSN0044-2267
AbstractThis paper presents a complex variable solution for the effective transport properties of composites with a doubly-periodic array of fiber pairs. By using the centrosymmetry of the problem, the method of Rayleigh and Natanzon-Filshtinsky's approach can be simply extended to the problems with two fibers per unit cell. The infinite system constructed in this paper only slightly complicates Rayleigh's system for the problems with one fiber per unit cell. Approximate analytical formulae of the effective transport properties for different fiber-pair arrays are obtained. The influence of pairwise interaction in fiber pairs on the effective transport properties is discussed in the numerical examples. As a special case of a doubly-periodic array of fiber pairs, effective transport property of composites with a triangular array of fibers is obtained. The obtained approximate analytical formulae are written in a concise form with good accuracy, thus are convenient for engineering application in most cases, except for those approaching the limit case of percolation when the perfectly conducting fibers become touching. Besides the square array and hexagonal array, the triangular fiber array (similar to carbon atom arrangement in graphene) is another special symmetric fiber array which results into transversely isotropic effective property. Therefore, the present solution for the triangular array is an extension of those for the square array and hexagonal array. The comparison of the results for the three symmetric fiber arrays reveals that the triangular fiber array has the highest conductivity. In addition, accuracy of the present solution is analyzed in the numerical examples. (C) 2017 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
KeywordComposites fiber pairs triangular array effective transport properties complex variable method
DOI10.1002/zamm.201700063
URL查看原文
Indexed BySCI
Language英语
WOS IDWOS:000427146500009
WOS KeywordHIGHLY CONDUCTING CYLINDERS ; THERMAL-CONDUCTIVITY ; ELASTIC COMPOSITE ; IMPERFECT CONTACT ; REGULAR ARRAYS ; UNIT-CELL ; PERMEABILITY
WOS Research AreaMathematics, Applied ; Mechanics
WOS SubjectMathematics ; Mechanics
Funding OrganizationNational Natural Science Foundation of China [NNSFC 11302009] ; Aviation Science Foundation of China [2013ZBN3004] ; Fundamental Research Funds for the Central Universities ; Open Fund of LNM
Classification二类
Ranking4
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Document Type期刊论文
Identifierhttp://dspace.imech.ac.cn/handle/311007/77883
Collection非线性力学国家重点实验室
Affiliation1.[Yan, P.
2.Zhang, Z. A.
3.Jiang, C. P.
4.Wang, X. J.
5.Qiu, Z. P.] Beihang Univ BUAA, Sch Aeronaut Sci & Engn, Beijing 100191, Peoples R China
6.[Chen, F. L.] AVIC Acad Aeronaut Prop Technol, Beijing 101300, Peoples R China
7.[Jiang, C. P.] Chinese Acad Sci, Inst Mech, State Key Lab Nonlinear Mech LNM, Beijing 100190, Peoples R China
Recommended Citation
GB/T 7714
Yan P,Zhang ZA,Chen FL,et al. Effective transport properties of composites with a doubly-periodic array of fiber pairs and with a triangular array of fibers[J]. ZAMM-ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND MECHANIK,2018,98(2):312-329.
APA Yan P,Zhang ZA,Chen FL,蒋持平,Wang XJ,&Qiu ZP.(2018).Effective transport properties of composites with a doubly-periodic array of fiber pairs and with a triangular array of fibers.ZAMM-ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND MECHANIK,98(2),312-329.
MLA Yan P,et al."Effective transport properties of composites with a doubly-periodic array of fiber pairs and with a triangular array of fibers".ZAMM-ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND MECHANIK 98.2(2018):312-329.
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