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Meshfree and finite element nodal integration methods
Author(s) -
Puso M. A.,
Chen J. S.,
Zywicz E.,
Elmer W.
Publication year - 2007
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.2181
Subject(s) - finite element method , meshfree methods , context (archaeology) , consistency (knowledge bases) , numerical integration , galerkin method , deformation (meteorology) , mathematics , computer science , mathematical optimization , mathematical analysis , geometry , structural engineering , engineering , physics , paleontology , meteorology , biology
Nodal integration can be applied to the Galerkin weak form to yield a particle‐type method where stress and material history are located exclusively at the nodes and can be employed when using meshless or finite element shape functions. This particle feature of nodal integration is desirable for large deformation settings because it avoids the remapping or advection of the state variables required in other methods. To a lesser degree, nodal integration can be desirable because it relies on fewer stress point evaluations than most other methods. In this work, aspects regarding stability, consistency, efficiency and explicit time integration are explored within the context of nodal integration. Both small and large deformation numerical examples are provided. Copyright © 2007 John Wiley & Sons, Ltd.