Mathematical Models of Elastic and Piezoelectric Fields in Two-Dimensional Composites

Leonid Filshtinsky () and Vladimir Mityushev ()
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Leonid Filshtinsky: Sumy State University, Dept. Applied Mathematics
Vladimir Mityushev: Pedagogical University, Dept. Computer Sciences and Computer Methods

A chapter in Mathematics Without Boundaries, 2014, pp 217-262 from Springer

Abstract: Abstract This paper is devoted to boundary value problems for harmonic and biharmonic equations which arise in modeling of elastic and piezoelectric fields in two-dimensional composites. All the problems are investigated by the method of complex potentials. The considered boundary value problems for analytic functions are reduced to integral equations. We discuss methods based on the integral equations for multiply connected domains and in the double periodic statement. Relations to the alternating scheme of Schwarz and to the method of perturbations are considered. Applications to calculation of the effective properties tensor are discussed. This paper also contains results published from 1964 in Russian and not known in English literature.

Keywords: Harmonic and biharmonic equations; Elastic and piezoelectric fields; Effective properties of composites; Complex potential; Multiply connected domain; Schwarz alternating method; Integral equations (search for similar items in EconPapers)
Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4939-1124-0_8

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DOI: 10.1007/978-1-4939-1124-0_8

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