Exact solutions for the plane problem in piezoelectric materials with an elliptic hole or a crack
type: Item
instance of: scholarly article
title: Exact solutions for the plane problem in piezoelectric materials with an elliptic hole or a crack
zbMATH Open document ID: 0955.74024
DOI: 10.1016/S0020-7683(98)00120-6
author: Cunfa Gao
author: Wei-xun Fan
published in: International Journal of Solids and Structures
publication date: 2001-02-21T00:00:00Z
review text: The authors consider a plane problem for a transversely isotropic piezoelectric material. In this case the general solution to field equations can be expressed in terms of three analytical functions each of which depends solely on a single, though different, complex variable. Then the authors study the problem of elliptical hole in an infinite medium subjected to constant stresses and electric displacement vectors at infinity. The electric potential inside the hole is assumed to be a linear function of coordinates, and the standard conformal mapping technique is employed to fully determine complex potentials. The crack geometry is represented as a degenerate elliptic hole with vanishing minor axis, and the corresponding solution is obtained. Additionally, the authors evaluate intensity factors for the stress and electric displacement at crack tips.
Mathematics Subject Classification ID: 74F15
Mathematics Subject Classification ID: 74S30
Mathematics Subject Classification ID: 74G70
zbMATH DE Number: 1340962
zbMATH Keywords: plane problem
zbMATH Keywords: transversely isotropic piezoelectric material
zbMATH Keywords: analytical functions
zbMATH Keywords: elliptical hole
zbMATH Keywords: infinite medium
zbMATH Keywords: electric potential
zbMATH Keywords: conformal mapping technique
zbMATH Keywords: complex potentials
zbMATH Keywords: degenerate elliptic hole
zbMATH Keywords: intensity factors
zbMATH Keywords: crack tips
reviewed by: Erdoğan S. Şuhubi
MaRDI profile type: Publication
full work available at URL: s0020-7683(98)00120-6
OpenAlex ID: W2076112904
description: scientific article; zbMATH DE number 1340962