Analysis of 3D solids using the natural neighbour radial point interpolation method

被引：139
作者：
Dinis, L. M. J. S.
Jorge, R. M. Natal
Belinha, J.
机构：
[1] Univ Porto, Fac Engn, FEUP, P-4200465 Oporto, Portugal
[2] Inst Engn Mech, IDMEC, P-4200465 Oporto, Portugal
来源：
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING | 2007年 / 196卷 / 13-16期
关键词：
radial point interpolation method (RPIM); radial basis function (RBF); natural neighbours; meshfree method;
D O I：
10.1016/j.cma.2006.11.002
中图分类号：
T [工业技术];
学科分类号：
08 ;
摘要：
In this work an improved meshless method is proposed, based on the combination of the natural neighbour finite element method with the radial point interpolation method, the natural neighbour radial point interpolation method - NNRPIM. The nodal connectivity and the node dependent integration background mesh are constructed resorting to the Voronoi tessellation and to the Delaunay triangulation. Within NNRPIM the obtained shape functions pass through all nodes inside the influence-cell providing shape functions with the delta Kronecker property. Optimization tests and examples of well-known, 2D and 3D problems are solved in order to prove the high accuracy and convergence rate of the proposed method. (c) 2006 Elsevier B.V. All rights reserved.
引用
收藏
页码：2009 / 2028
页数：20
相关论文
共 56 条
[1]   A new meshless local Petrov-Galerkin (MLPG) approach in computational mechanics [J].
Atluri, SN ;
Zhu, T .
COMPUTATIONAL MECHANICS, 1998, 22 (02) :117-127
[2]  
Bathe K, 2007, Finite element procedures
[3]   ELEMENT-FREE GALERKIN METHODS [J].
BELYTSCHKO, T ;
LU, YY ;
GU, L .
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, 1994, 37 (02) :229-256
[4]   Meshless methods: An overview and recent developments [J].
Belytschko, T ;
Krongauz, Y ;
Organ, D ;
Fleming, M ;
Krysl, P .
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 1996, 139 (1-4) :3-47
[5]   A NUMERICAL-METHOD FOR SOLVING PARTIAL-DIFFERENTIAL EQUATIONS ON HIGHLY IRREGULAR EVOLVING GRIDS [J].
BRAUN, J ;
SAMBRIDGE, M .
NATURE, 1995, 376 (6542) :655-660
[6]   Buckling of rectangular functionally graded material plates subjected to nonlinearly distributed in-plane edge loads [J].
Chen, XL ;
Liew, KM .
SMART MATERIALS AND STRUCTURES, 2004, 13 (06) :1430-1437
[7]  
Cueto E, 2000, INT J NUMER METH ENG, V49, P519, DOI 10.1002/1097-0207(20001010)49:4<519::AID-NME958>3.0.CO
[8]  
2-0
[9]   Overview and recent advances in natural neighbour Galerkin methods [J].
Cueto, E ;
Sukumar, N ;
Calvo, B ;
Martínez, MA ;
Cegoñino, J ;
Doblaré, M .
ARCHIVES OF COMPUTATIONAL METHODS IN ENGINEERING, 2003, 10 (04) :307-384
[10]   Inelastic analysis of 2D solids using a weak-form RPIM based on deformation theory [J].
Dai, K. Y. ;
Liu, G. R. ;
Han, X. ;
Li, Y. .
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 2006, 195 (33-36) :4179-4193
123456