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On an implicit particle method for simulation of forming processes
Author(s) -
Schilling O.,
Reese S.
Publication year - 2005
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200510199
Subject(s) - finite element method , galerkin method , boundary (topology) , moving least squares , penalty method , computer science , particle (ecology) , basis function , basis (linear algebra) , mathematics , mathematical analysis , mathematical optimization , geometry , structural engineering , engineering , geology , oceanography
Task is the simulation of forming processes using particle methods. We implemented some mesh‐free methods (the element free Galerkin method [1] and others) and the finite element method in one programme system which permits a direct comparison. For the mesh‐free methods a moving least squares approximation is applied. The shape functions are not zero or one at the nodes, thus essential boundary conditions cannot be imposed directly [2]. We use a penalty method to enforce essential boundary conditions and contact conditions. The contact algorithm (normal contact of nodes to C 1 ‐continuous surfaces) is checked by means of the element free Galerkin method and the FEM on the basis of numerical examples which deal with forming processes. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)