Meshless Local Petrov-Galerkin (MLPG) Mixed Collocation Method For Elasticity Problems

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The MLPG Mixed Collocation Method for Material Orientation and Topology Optimization of Anisotropic Solids and Structures (2008, methodology): “In this paper, the equilibrium equations of the topology optimization problem are solved by a Meshless Local Petrov-Galerkin (MLPG) “mixed collocation” method which was presented by Atluri, Liu, and Han (2006).”
Infinite domain potential problems by a new formulation of singular boundary method (2013, background): “In order to alleviate some of these difficulties, recent decades have witnessed a fast development of meshless/meshfree numerical techniques [10–13].”
Thermal Analysis of Reissner-Mindlin Shallow Shells with FGM Properties by the MLPG (2008, methodology): “…and rotations [Han et al (2006)]; in the development of the mixed scheme to interpolate the elastic displacements and stresses independently [Atluri et al (2006a), (2006b)]; in proposal of a direct solution method for the quasi-unsymmetric sparse matrix arising in the MLPG [Yuan et al…”
Examination and Analysis of Implementation Choices within the Material Point Method (MPM) (2008, methodology): “…the Meshless Local Petrov-Galerkin Method (MLPG) [Atluri and Zhu (1998); Han, Rajendran, and Atluri (2005); Han, Liu, Rajendran, and Atluri (2006); Atluri (2006); Atluri, Liu, and Han (2006)], MPM utilizes a background mesh to perform differentiation, integration, and solve the equations of motion.”