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Node‐by‐node meshless approach and its applications to structural analyses
Author(s) -
Nagashima Toshio
Publication year - 1999
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/(sici)1097-0207(19990930)46:3<341::aid-nme678>3.0.co;2-t
Subject(s) - regularized meshless method , discretization , meshfree methods , node (physics) , interpolation (computer graphics) , solver , galerkin method , mathematics , mathematical optimization , computer science , computation , eigenvalues and eigenvectors , moving least squares , singular boundary method , computational science , algorithm , finite element method , mathematical analysis , engineering , structural engineering , artificial intelligence , boundary element method , motion (physics) , physics , quantum mechanics
The meshless method is expected to become an effective procedure for realizing a CAD/CAE seamless system for analyses ranging from modelling to computation, because time‐consuming mesh generation processes are not required. In the present study, a new meshless approach, referred to as the Node‐By‐Node Meshless method is proposed, in which only nodal data is utilized to discretize the governing equations, which are derived using either the principle of virtual work or the Galerkin method. In this method, three key methodologies are utilized: (i) nodal integration using stabilization terms, (ii) interpolation by the Moving Least‐Squares Method, and (iii) a node‐by‐node iterative solver. This paper presents the formulation of the proposed method along with numerical results obtained for two‐dimensional elastostatic and eigenvalue problems. Copyright © 1999 John Wiley & Sons, Ltd.