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A solution for antiplane‐strain local problems using elliptic integrals of Cauchy type
Author(s) -
FelipeSosa Raul,
Otero J. A.,
Solis Francisco J.
Publication year - 2017
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.4379
Subject(s) - mathematics , piecewise , cauchy distribution , mathematical analysis , homogenization (climate) , type (biology) , asymptotic homogenization , singularity , composite number , ecology , biology , biodiversity , algorithm
Quasi‐periodic piecewise analytic solutions, without poles, are found for the local antiplane‐strain problems. Such problems arise from applying the asymptotic homogenization method to an elastic problem in a parallel fiber‐reinforced periodic composite that presents an imperfect contact of spring type between the fiber and the matrix. Our methodology consists of rewriting the contact conditions in a complex appropriate form that allow us to use the elliptic integrals of Cauchy type. Several general conditions are assumed including that the fibers are disposed of arbitrary manner in the unit cell, that all fibers present imperfect contact with different constants of imperfection, and that their cross section is smooth closed arbitrary curves. Finally, we obtain a family of piecewise analytic solutions for the local antiplane‐strain problems that depend of a real parameter. When we vary this parameter, it is possible to improve classic bounds for the effective coefficients. Copyright © 2017 John Wiley & Sons, Ltd.