Meshless Local Petrov-Galerkin Method for Solving Contact, Impact and Penetration Problems

Atluri, Satya N.

doi:10.21236/ada515552

Cited by 3 publications

(3 citation statements)

References 97 publications

(157 reference statements)

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“…MLPG discretization. Following MLPG1 discretization [2] with LSWF formulation, the governing equations for elasto-dynamic problems can be obtained…”

Section: Basic Formulationmentioning

confidence: 99%

Numerical Simulation for Dynamic Crack Propagation by MLPG

Liu

Gao

2006

KEM

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In this paper, a new algorithm based on Meshless Local Petrov-Galerking (MLPG) method is presented for analyzing the crack dynamic propagation. A new modified Moving Least Squares approximation is proposed to simplify the treatment of essential boundary conditions. Explicit central difference with lumped mass matrix is adopted for the time integral. Visibility criterion with crack edge node adding technique and the maximum hoop stress criterion are used to describe the crack propagation and forecast the crack propagation direction. Based on this algorithm, three-point bend specimen for impact fracture test is investigated. Comparing the results with those obtained by the laser caustic method and high-speed photographs, the accuracy of the present algorithm is proved.

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“…MLPG discretization. Following MLPG1 discretization [2] with LSWF formulation, the governing equations for elasto-dynamic problems can be obtained…”

Section: Basic Formulationmentioning

confidence: 99%

Numerical Simulation for Dynamic Crack Propagation by MLPG

Liu

Gao

2006

KEM

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“…Lagrange multipliers were used to apply the essential boundary conditions. The MLPG method was used in Reference [10] for solving the problem of a thin plate in bending with the penalty formulation being used to apply the essential boundary conditions. In Reference [11], the element free Galerkin (EFG) method was used to solve Kirchhoff plate problems.…”

Section: Introductionmentioning

confidence: 99%

Development of a genetic algorithm-based lookup table approach for efficient numerical integration in the method of finite spheres with application to the solution of thin beam and plate problems

BaniHani

2006

Int. J. Numer. Meth. Engng

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SUMMARYIt is observed that for the solution of thin beam and plate problems using the meshfree method of finite spheres, Gaussian and adaptive quadrature schemes are computationally inefficient. In this paper, we develop a novel technique in which the integration points and weights are generated using genetic algorithms and stored in a lookup table using normalized coordinates as part of an offline computational step. During online computations, this lookup table is used much like a table of Gaussian integration points and weights in the finite element computations. This technique offers significant reduction of computational time without sacrificing accuracy. Example problems are solved which demonstrate the effectiveness of the procedure.

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“…In recent years, a new class of methods has been developed which do not require polygonisation, but use a set of nodes to approximate the solution. The rapid development of this type of methods and their classification is elaborated in the very recent monographs [1,2]. A broad class of mesh-free methods that are in development today [3,4] are based on Radial Basis Functions (RBFs) [5].…”

Section: Introductionmentioning

confidence: 99%

Mesh-Free Simulation of Transport Phenomena in Continuous Castings of Aluminium Alloys

Šarler

Vertnik

2006

MSF

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This paper introduces a general numerical scheme for solving convective-diffusive problems that appear in the solution of microscopic and macroscopic transport phenomena in continuous castings and the heat treatment of aluminium alloys. The numerical scheme is based on spatial discretisation that involves pointisation only. The solution is based on diffuse collocation with multi-quadric radial basis functions. The application of the method is demonstrated in a simplified model of a billet DC casting and verified by a comparison with the classical finite volume method.

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Meshless Local Petrov-Galerkin Method for Solving Contact, Impact and Penetration Problems

Cited by 3 publications

References 97 publications

Numerical Simulation for Dynamic Crack Propagation by MLPG

Numerical Simulation for Dynamic Crack Propagation by MLPG

Development of a genetic algorithm-based lookup table approach for efficient numerical integration in the method of finite spheres with application to the solution of thin beam and plate problems

Mesh-Free Simulation of Transport Phenomena in Continuous Castings of Aluminium Alloys

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