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A new Meshless Local Petrov-Galerkin (MLPG) approach in computational mechanics
Computational Mechanics, 1998A local symmetric weak form (LSWF) for linear potential problems is developed, and a truly meshless method, based on the LSWF and the moving least squares approximation, is presented for solving potential problems with high accuracy. The essential boundary conditions in the present formulation are imposed by a penalty method.
Atluri, S. N., Zhu, T.
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Mixed meshless local Petrov–Galerkin collocation method for modeling of material discontinuity
Computational Mechanics, 2016A mixed Meshless Local Petrov-Galerkin (MLPG) collocation method is proposed for solving the two- dimensional boundary value problem of heterogeneous structures. The heterogeneous structures are defined by partitioning the total material domain into subdomains with different linear-elastic isotropic properties which define homogeneous materials.
Jarak, Tomislav +2 more
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Meshless Local Petrov-Galerkin Method for Nonlinear Heat Conduction Problems
Numerical Heat Transfer, Part B: Fundamentals, 2010The meshless local Petrov-Galerkin (MLPG) method is an effective meshless method to solve partial differential equations. In this article, the MLPG method is used to solve nonlinear steady and transient heat conduction problems. The essential boundary condition is enforced by the method of direct interpolation.
Harishchandra Thakur +2 more
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Meshless Local Petrov-Galerkin Method for Heat Transfer Analysis
Volume 8A: Heat Transfer and Thermal Engineering, 2013A meshless local Petrov-Galerkin (MLPG) method is proposed to obtain the numerical solution of nonlinear heat transfer problems. The moving least squares scheme is generalized, to construct the field variable and its derivative continuously over the entire domain. The essential boundary conditions are enforced by the direct scheme.
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Radial Basis Meshless Local Petrov-Galerkin Method for Thick Beams
45th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics & Materials Conference, 2004*† An MLPG method that uses radial basis functions (RBF) in the study of thick beams governed by the Timoshenko beam theory is presented. The weak form of the governing differential equations is derived such that the locking phenomenon observed in the finite element method is avoided.
I Raju, D Phillips
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Meshless Local Petrov-Galerkin Approach in Solving Microwave Guide Problems
IEEE Transactions on Magnetics, 2011This paper describes a meshless approach to obtain solutions for propagating microwave problems. The Meshless Local Petrov-Galerkin (MLPG) method is used, based on a local weak form tested with the Heaviside step function. The field is approximated by the Point Interpolation method using radial basis function with additional polynomial basis (RPIMp ...
Bruno C. Correa +4 more
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Meshless Local Petrov-Galerkin Formulation for Problems in Composite Micromechanics
AIAA Journal, 2007In this paper we present the meshless local Petrov-Galerkin formulation for the generalized plane strain problem with specific emphasis on micromechanics of composite materials containing material discontinuities. The problem requires the introduction of an extra discrete degree of freedom, the out-of-plane uniform normal strain.
Thi D. Dang, Bhavani V. Sankar
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Meshless Local Petrov-Galerkin Method for Solving Radiative Transfer Equation
Journal of Thermophysics and Heat Transfer, 2006Ā = matrix defined in Eq. (7) a = Coefficients for the moving least-squares (MLS) approximation in Eq. (4) a = vector of coefficient a B = matrix defined in Eq. (8) C j = expansion coefficient of scattering phase function f = coefficients in linear equations g = quartic spline function defined in Eq.
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Characterizing soil properties by the meshless local Petrov-Galerkin method
Geotechnical and Geological Engineering, 2007This study presents a preliminary development of a direct back analysis procedure by the meshless local Petrov-Galerkin (MLPG) method and its application to characterize soil properties using in-situ test results. As compared to a direct back analysis based on the finite element method (FEM), it is intended to show that doing a direct back analysis by ...
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Simulating Couette Flow Using the Meshless Local Petrov-Galerkin Method
Applied Mechanics and Materials, 2014The paper deals with use of the meshless method for incompressible fluid flow analysis. There are many formulations of the meshless methods. The article presents the Meshless Local Petrov-Galerkin method (MLPG) – local weak formulation of the Navier-Stokes equations. The shape function construction is the crucial part of the meshless numerical analysis
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