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Fundamental solution for a penny-shaped crack in a piezoelectric medium. (English) Zbl 0959.74019
Summary: We present a general three-dimensional analysis of a penny-shaped crack subjected to normal mechanical loads and to free surface electric charges symmetrically applied on its upper and lower surfaces. To this end, we use the methods of potential theory and introduce a potential of simple layer, corresponding to the electric effect. As a typical example, we obtain a closed-form solution for a penny-shaped crack subjected to a pair of concentrated forces acting in opposite directions and to a pair of point charges on crack surfaces. We also derive exact expressions for stress and electric displacement intensity factors.

MSC:
74F15 Electromagnetic effects in solid mechanics
74G70 Stress concentrations, singularities in solid mechanics
74G05 Explicit solutions of equilibrium problems in solid mechanics
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