Local boundary integral equation (LBIE) method for solving problems of elasticity with nonhomogeneous material properties

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Meshless local Petrov-Galerkin method for continuously nonhomogeneous linear viscoelastic solids (2006, methodology): “The spatial variation of the field variable can be approximated either by standard domain-elements (Sladek et al. 2004c,e) or by meshless approximations such as the moving least-squares (MLS) scheme ( Sladek et al. 2000, 2003a, b, 2004a) or point interpolation methods (Sladek et al., 2004d,f).”
Enriched finite elements and level sets for damage tolerance assessment of complex structures (2006, methodology): “Numerical computation of fracture parameters Among the numerical methods for calculating fracture parameters, boundary integral methods [5,6] and the domain integral method [7–9] have proved adequate tools.”
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-”
Mesh-based numerical implementation of the localized boundary-domain integral-equation method to a variable-coefficient Neumann problem (2005, methodology): “Nakhova Another type of LBDIE for BVPs of elasticity with variable coefficients was described in [6], where the Green function for a corresponding homogeneous material on a sphere was employed as a parametrix.”