The local boundary integral equation (LBIE) and it's meshless implementation for linear elasticity

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Fracture Analyses in Continuously Nonhomogeneous Piezoelectric Solids by the MLPG (2007, background): “D problems in isotropic, homogeneous or continuously nonhomogeneous and linear elastic solids under static loading [Atluri et al. (2000); Sladek et al. (2000); Sellountos et al. (2005)] and for 3-”
Bending analyses of 1D orthorhombic quasicrystal plates (2013, result): “Previous results showed excellent convergence for linear problems (Krysl and Belytschko 1996; Liew et al., 2004; Atluri et al. 2000); however, up to now the formulation has not been applied to the deflection analysis of QC plates.”
Numerical integration of singularities in meshless implementation of local boundary integral equations (2000, methodology): “In order to get rid of the unknown tractions on the boundary oXs, Atluri et al. (1999) have considered the so-called ``companion solution'' ~uij associated with the fundamental solution u ij and the modi®ed test functions being given by ~u ij u ij ÿ ~uij and ~t ij t ij ÿ ~tij.”