Efficient boundary element analysis of cracks in 2D piezoelectric structures

A boundary integral approach for plane analysis of electrically semi-permeable planar cracks in a piezoelectric solid

“…Analytical closed form Green's functions which can be used to derive boundary element solutions for a single stress free planar crack which is either impermeable or conducting (permeable) are given in Rajapakse and Xu [17]. Garcia-Sanchez et al [12] and Groh and Kuna [13] presented numerical procedures based on boundary integral equations derived by using fundamental solution which does not satisfy the boundary conditions on the crack faces. In [13], opposite crack faces were modeled by using the socalled subdomain technique and quarter-point elements were employed to deal with the singular behaviors of the stress and electric displacement at the crack tips, while a dual (mixed) boundary integral formulation was used in [12] with the conditions on the cracks treated by a differentiated form of the usual boundary integral equations.…”

“…Garcia-Sanchez et al [12] and Groh and Kuna [13] presented numerical procedures based on boundary integral equations derived by using fundamental solution which does not satisfy the boundary conditions on the crack faces. In [13], opposite crack faces were modeled by using the socalled subdomain technique and quarter-point elements were employed to deal with the singular behaviors of the stress and electric displacement at the crack tips, while a dual (mixed) boundary integral formulation was used in [12] with the conditions on the cracks treated by a differentiated form of the usual boundary integral equations. Some earlier works on boundary element methods for electroelastic crack problems include Ding et al [10], Gao and Fan [11], Pan [16] and Xu and Rajapakse [19].…”

A non-conventional approach for crack problems in piezoelectric media under electromechanical loading

“…Theoretical investigation concerned with the problem of finding the electro-elastic field around a crack in piezoelectric material can be found in Parton (1976), Pak (1990Pak ( , 1992, Sih and Zuo (2000), Zuo and Sih (2000), Sih (2002), Landis (2004), Groh and Kuna (2005), Viola et al (2007) and others, and there have been many important achievements in this field over three decades. In the above studies several mathematic techniques have been used, such as the eigenfunction analysis, the integral transforms, the asymptotic tip analysis, the complex variable method.…”

BEM calculation of strain energy density and relative strain energy in QWR nanostructures

“…The bimaterial Green's functions in transversely isotropic piezoelectric solids [8], anisotropic elastic [9] and piezoelectric bodies [10][11][12], and in magnetoelectroelastic solids [13] were studied and applied to different mechanical and piezoelectric problems. We remark that these Green's functions were presented in the Lekhnitskii formalism (e.g., [9]).…”