Dynamic Anti-plane Crack Analysis in Functional Graded Piezoelectric Semiconductor Crystals

Abstract: This paper presents a dynamic analysis of an anti-plane crack in func-tionally graded piezoelectric semiconductors. General boundary conditions and sample geometry are allowed in the proposed formulation. The coupled governing partial differential equations (PDEs) for shear stresses, electric displacement field and current are satisfied in a local weak-form on small fictitious subdomains. The derived local integral equations involve one order lower derivatives than the origi-nal PDEs. All field quantities are approximated by the moving least-squares (MLS) scheme. After performing spatial integrations, we obtain a system of ordinary d-ifferential equations for the involved nodal unknowns. It is noted that the stresses and electric displacement field in functionally graded piezoelectric semiconductors exhibit the same singularities at crack tips as in a homogeneous piezoelectric sol-id. The influence of the initial electron density on the intensity factors and energy release rate is also investigated