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A three‐dimensional computational procedure for reproducing meshless methods and the finite element method
Author(s) -
Schembri Philip,
Crane David L.,
Reddy J. N.
Publication year - 2004
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1095
Subject(s) - meshfree methods , finite element method , moving least squares , regularized meshless method , mathematics , mathematical optimization , computational mechanics , function (biology) , polynomial , computer science , algorithm , mathematical analysis , singular boundary method , structural engineering , boundary element method , evolutionary biology , engineering , biology
A flexible computational procedure for solving 3D linear elastic structural mechanics problems is presented that currently uses three forms of approximation function (natural neighbour, moving least squares—using a new nearest neighbour weight function—and Lagrange polynomial) and three types of integration grids to reproduce the natural element method and the finite element method. The addition of more approximation functions, which is not difficult given the structure of the code, will allow reproduction of other popular meshless methods. Results are presented that demonstrate the ability of the first‐order meshless approximations to capture solutions more accurately than first‐order finite elements. Also, the quality of integration for the three types of integration grids is compared. The concept of a region is introduced, which allows the splitting of a domain into different sections, each with its own type of approximation function and spatial integration scheme. Copyright © 2004 John Wiley & Sons, Ltd.