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Mathematics Without Boundaries pp 217–262Cite as

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

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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.

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Author information

Authors and Affiliations

  1. Dept. Applied Mathematics, Sumy State University, 2 Rimskogo-Korsakova St., 40007, Sumy, Ukraine

    Leonid Filshtinsky

  2. Dept. Computer Sciences and Computer Methods, Pedagogical University, ul. Podchorazych 2, Krakow, 30-084, Poland

    Vladimir Mityushev

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  1. Leonid Filshtinsky
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  2. Vladimir Mityushev
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Correspondence to Vladimir Mityushev .

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Editors and Affiliations

  1. Dept. Industrial & Systems Engineering, University of Florida, Gainesville, Florida, USA

    Panos M. Pardalos

  2. Department of Mathematics, National Technical University of Athens, Athens, Greece

    Themistocles M. Rassias

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Filshtinsky, L., Mityushev, V. (2014). Mathematical Models of Elastic and Piezoelectric Fields in Two-Dimensional Composites. In: Pardalos, P., Rassias, T. (eds) Mathematics Without Boundaries. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-1124-0_8

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