Fundamental solution for a penny-shaped crack penny-shaped crack in a piezoelectric medium

摘要

This paper intends to present a general three-dimensional analysis of a penny-shaped crack subjected to normal mechanical loads and free surface electric charges symmetrically applied on its upper and lower surfaces. To this end, the potential theory method is employed and generalized to analyze the piezoelectric crack problem under consideration. In particular, another potential of a simple layer, corresponding to the electric effect, is introduced. As a typical example, a closed-form solution is first obtained for a penny-shaped crack subjected to a pair of concentrated forces acting in opposite directions and a pair of point charges on crack surfaces. Exact expressions for stress and electric displacement intensity factors are also presented.