Plane strain problems in piezoelectricity
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.
scientific article; zbMATH DE number 4053123