Anti-plane dynamic hole–crack interaction in a functionally graded piezoelectric media

Abstract

The anti-plane dynamic problem of a functionally graded piezoelectric plane containing a holecrack system is treated by a non-hypersingular traction-based boundary integral equation method. The material parameters vary exponentially in the same manner in an arbitrary direction. The system is loaded by an incident SH-type wave, and impermeable boundary conditions are assumed. Using a frequency-dependent fundamental solution of the wave equation, the boundary value problem is transformed into a system of integro-differential equations along the boundary of the hole and on the crack line. Its numerical solution yields the dynamic stress intensity factors and stress concentration factors. A parametric study reveals their dependence on the hole-crack scenario and its geometry, characteristics of the dynamic load and magnitude and direction of material inhomogeneity.

Dynamic performance for piezoelectric bi-materials with an interfacial crack near an eccentric elliptical hole under anti-plane shearing

“…Because of the time-harmonic behaviour of all field quantities, the common multiplier e Àivt is suppressed here and in the following [27]. The governing equations expressed by elastic displacement and electric potential, in the absence of body forces and free charges, can be written as…”

Dynamic intensity factors for multiple permeable cracks in piezoelectric materials

“…Singh et al [31] presented an extended isogeometric analysis to model the crack in FGPMs. The fracture problems of FGPMs have been reported by [32][33][34][35].…”

Stress field of a radially functionally graded panel with a circular elastic inclusion under static anti-plane shear loading

“…Using a Frobenius series solution, Mohammadi et al [9] considered the stress concentration factor around a circular hole in an infinite FGM plate subjected to uniform biaxial tension and pure shear. By a non-hyper singular traction-based boundary integral equation method, Müller et al [10] treated the anti-plane dynamic problem of an FGM piezoelectric plane containing a hole-crack system. Sburlati [11] proposed analytical solutions for thick-walled cylinders subjected to internal and external pressure in which the entire wall is made of FGM or of only a thin FGM coating present on the internal homogeneous wall.…”