Plane strain problems in piezoelectricity
type: Item
instance of: scholarly article
title: Plane strain problems in piezoelectricity
zbMATH Open document ID: 0645.73017
DOI: 10.1016/0020-7225(87)90029-2
published in: International Journal of Engineering Science
publication date: 1987-01-01T00:00:00Z
review text: This paper is addressed to certain boundary-value problems in the static linear theory of a homogeneous and anisotropic piezoelectric material. In the first part of the paper, the fundamental solutions are derived for the generalized plain strain problems of linear piezoelectricity. In addition, the relations of Somigliana type are established. In the second part of the paper, by means of the method of potentials, the boundary- value problems of generalized plain strain are reduced to the singular integral equations for which Fredholm's basic theorems are valid. In the third part of the paper, the existence theorems are derived for interior and exterior problems. The paper is especially in need of further elaboration in order to examine the uniqueness in solutions of the linear boundary-value problems and to incorporate the dynamic effect that is of special importance in piezoelectricity. With its purely mathematical nature, the paper is of particular value to researchers interested in static solutions of piezoelectricity.
Mathematics Subject Classification ID: 74B99
Mathematics Subject Classification ID: 74F15
Mathematics Subject Classification ID: 45E05
zbMATH DE Number: 4053123
zbMATH Keywords: boundary-value problems
zbMATH Keywords: static linear theory
zbMATH Keywords: homogeneous
zbMATH Keywords: anisotropic piezoelectric material
zbMATH Keywords: fundamental solutions
zbMATH Keywords: generalized plain strain problems
zbMATH Keywords: relations of Somigliana type
zbMATH Keywords: method of potentials
zbMATH Keywords: existence theorems
author: D. Ieşan
reviewed by: M. Cengiz Dökmeci
MaRDI profile type: Publication
full work available at URL: 0020-7225(87)90029-2
OpenAlex ID: W2104953810
cites work: Q5730679
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description: scientific article; zbMATH DE number 4053123