The Development and Application of Meshless Method

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Meshless method or mesh free method has many advantages. So far, there are more than ten proposed meshless methods, each has their respective advantages and disadvantages. This paper will focus on the main several meshless methods, we will make a comparison and analysis of their respective adaptation range, at the same time, we will discuss the construction method of typical meshless approximation functions, and summarize the development of the meshless method, development trend and prospects.

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214-218

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October 2013

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© 2014 Trans Tech Publications Ltd. All Rights Reserved

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[1] Lucy L B. A numerical approach to the testing of the fission hypothesis[J]. The Astron J, 1977, 8( 12) , 1013-1024.

Google Scholar

[2] Lancaster P Salkauskas K. Surfaces generated by moving least sf uares methods [J]. Math Comput, 1981, 37( 155) : 141-158.

DOI: 10.1090/s0025-5718-1981-0616367-1

Google Scholar

[3] Nayroles B Touzot G Villon P. Generalizing the finite element method: diffuse approximation and diffuse elements [J]. Comput Mech 1992, 10: 307-318.

DOI: 10.1007/bf00364252

Google Scholar

[4] Belytschko T, Lu Y Y, Gu L. Element free Galerkin methods [ J ]. Int J Numer Methods Engrg 1994, 37: 229-256.

DOI: 10.1002/nme.1620370205

Google Scholar

[5] Liu W K, Chen Y, Jun S, et al. Overview and applications of the reproducing kernel particle methods[J]. Archives of Computational Methods in Engineering, State of the Art Review, 1996, 3(1) : 3-80.

Google Scholar

[6] Duarte C A, Oden J T. hp clouds: a h-p meshless method [ J ]. Numerical Methods for Partical Differential Equations, 1996, 12: 673-705.

DOI: 10.1002/(sici)1098-2426(199611)12:6<673::aid-num3>3.0.co;2-p

Google Scholar

[7] Melenk J M, Babuska I. The partition of unity finite element methods: Basic theory and application[J]. Comput Methods Appl Mech Engrg, 1996, 139: 263-288.

Google Scholar

[8] Atluri S N, Sladek J, et al. The loacl boundary integral equation ( LBIE ) and it's meshless implementation for linear elasticity [J ]. Comput Mech, 2000, 25: 180-198.

DOI: 10.1007/s004660050468

Google Scholar

[9] Atluri S N, Kim H G, et al. A critical assessment of the truly Meshless Local Petrov-Galerkin (MLPG) , and Local Boundary Integral Equation ( LBIE ) methods[J]. Comput Mech, 1999, 24: 348-372.

DOI: 10.1007/s004660050457

Google Scholar

[10] Zhang X, Liu X H, Song K Z, et al. Least-square collocation meshless method [J ]. Int J Numer Methods Engrg, 2001, 51( 9) : 1089-1100.

DOI: 10.1002/nme.200

Google Scholar