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On the numerical stability and mass-lumping schemes for explicit enriched meshfree methods

  • Meshfree methods (MMs) such as the element free Galerkin (EFG)method have gained popularity because of some advantages over other numerical methods such as the finite element method (FEM). A group of problems that have attracted a great deal of attention from the EFG method community includes the treatment of large deformations and dealing with strong discontinuities such as cracks. One efficientMeshfree methods (MMs) such as the element free Galerkin (EFG)method have gained popularity because of some advantages over other numerical methods such as the finite element method (FEM). A group of problems that have attracted a great deal of attention from the EFG method community includes the treatment of large deformations and dealing with strong discontinuities such as cracks. One efficient solution to model cracks is adding special enrichment functions to the standard shape functions such as extended FEM, within the FEM context, and the cracking particles method, based on EFG method. It is well known that explicit time integration in dynamic applications is conditionally stable. Furthermore, in enriched methods, the critical time step may tend to very small values leading to computationally expensive simulations. In this work, we study the stability of enriched MMs and propose two mass-lumping strategies. Then we show that the critical time step for enriched MMs based on lumped mass matrices is of the same order as the critical time step of MMs without enrichment. Moreover, we show that, in contrast to extended FEM, even with a consistent mass matrix, the critical time step does not vanish even when the crack directly crosses a node.show moreshow less

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Metadaten
Document Type:Article
Author: Hossein Talebi, C. Samaniego, Esteban Samaniego, Timon RabczukORCiDGND
DOI (Cite-Link):https://doi.org/10.1002/nme.3275Cite-Link
Parent Title (English):International Journal for Numerical Methods in Engineering
Language:English
Date of Publication (online):2017/08/26
Year of first Publication:2012
Release Date:2017/08/26
Publishing Institution:Bauhaus-Universität Weimar
Institutes:Fakultät Bauingenieurwesen / Institut für Strukturmechanik
First Page:1009
Last Page:1027
GND Keyword:Angewandte Mathematik; Strukturmechanik
Dewey Decimal Classification:600 Technik, Medizin, angewandte Wissenschaften / 620 Ingenieurwissenschaften
500 Naturwissenschaften und Mathematik / 510 Mathematik / 519 Wahrscheinlichkeiten, angewandte Mathematik
BKL-Classification:31 Mathematik / 31.80 Angewandte Mathematik
50 Technik allgemein / 50.31 Technische Mechanik
Licence (German):License Logo Copyright All Rights Reserved - only metadata