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The ALE‐method with triangular elements: direct convection of integration point values
Author(s) -
van Haaren M. J.,
Stoker H. C.,
van den Boogaard A. H.,
Huétink J.
Publication year - 2000
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 - 10.1002/1097-0207(20001020)49:5<697::aid-nme976>3.0.co;2-u
Subject(s) - eulerian path , mathematics , finite element method , convection , point (geometry) , material point method , quadratic equation , block (permutation group theory) , convection–diffusion equation , scheme (mathematics) , lagrangian , mathematical analysis , mechanics , geometry , physics , engineering , structural engineering
Abstract The arbitrary Lagrangian–Eulerian (ALE) finite element method is applied to the simulation of forming processes where material is highly deformed. Here, the split formulation is used: a Lagrangian step is done with an implicit finite element formulation, followed by an explicit (purely convective) Eulerian step. The purpose of this study is to investigate the Eulerian step for quadratic triangular elements. To solve the convection equation for integration point values, a new method inspired by Van Leer is constructed. The new method is based on direct convection of integration point values without intervention of nodal point values. The Molenkamp test and a so‐called block test were executed to check the performance and stability of the convection scheme. From these tests it is concluded that the new convection scheme shows accurate results. The scheme is extended to an ALE‐algorithm. An extrusion process was simulated to test the applicability of the scheme to engineering problems. It is concluded that direct convection of integration point values with the presented algorithm leads to accurate results and that it can be applied to ALE‐simulations. Copyright © 2000 John Wiley & Sons, Ltd.