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On stability and reflection‐transmission analysis of the bipenalty method in contact‐impact problems: A one‐dimensional, homogeneous case study
Author(s) -
Kopačka Ján,
Tkachuk Anton,
Gabriel Dušan,
Kolman Radek,
Bischoff Manfred,
Plešek Jiří
Publication year - 2017
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.5712
Subject(s) - penalty method , stiffness , reflection (computer programming) , stability (learning theory) , finite element method , transmission (telecommunications) , boundary (topology) , contact analysis , boundary value problem , homogeneous , mathematical analysis , mathematics , mechanics , computer science , structural engineering , mathematical optimization , physics , engineering , telecommunications , combinatorics , machine learning , programming language
Summary The stability and reflection‐transmission properties of the bipenalty method are studied in application to explicit finite element analysis of one‐dimensional contact‐impact problems. It is known that the standard penalty method, where an additional stiffness term corresponding to contact boundary conditions is applied, attacks the stability limit of finite element model. Generally, the critical time step size rapidly decreases with increasing penalty stiffness. Recent comprehensive studies have shown that the so‐called bipenalty technique, using mass penalty together with standard stiffness penalty, preserves the critical time step size associated to contact‐free bodies. In this paper, the influence of the penalty ratio (ratio of stiffness and mass penalty parameters) on stability and reflection‐transmission properties in one‐dimensional contact‐impact problems using the same material and mesh size for both domains is studied. The paper closes with numerical examples, which demonstrate the stability and reflection‐transmission behavior of the bipenalty method in one‐dimensional contact‐impact and wave propagation problems of homogeneous materials.