The Crack Tip Fields for Anti-Plane Crack in FGPM of <i>x</i> Linear Function

Abstract

The higher order crack tip fields for an anti-plane crack in functionally graded piezoelectric materials (FGPMs) under mechanical and electrical loadings are studied. Different from previous analyses, all material properties of FGPMs are assumed to be linear functions of x parallel to the crack. The boundary conditions on crack surfaces are assumed to be the stress free and electrically impermeable. By using the eigen-expansion method, the problem is reduced to solving the system of ordinary differential equations. The higher order stress and electric displacement crack tip fields for FGPMs are obtained by solving the ordinary differential equations.