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A non‐reflecting layer method for non‐linear wave‐type equations on unbounded domains with applications to shape memory alloy rods
Author(s) -
Newman M.,
Safjan A.,
Popov P.,
Lagoudas D. C.
Publication year - 2005
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.1223
Subject(s) - shape memory alloy , rod , computation , type (biology) , layer (electronics) , domain (mathematical analysis) , mathematical analysis , wave equation , mathematics , stress (linguistics) , linear elasticity , geometry , materials science , algorithm , structural engineering , finite element method , composite material , engineering , geology , medicine , paleontology , linguistics , philosophy , alternative medicine , pathology
In this paper a new technique is introduced and applied in solving one‐dimensional linear and non‐linear wave‐type equations on an unbounded spatial domain. This new technique referred to as the non‐reflecting layer method (NRLM) extends the computational domain with an artificial layer on which a one‐way wave equation is solved. The method will be applied to compute stress waves in long rods consisting of NiTi shape memory alloy material subjected to impact loading and undergoing detwinning and pseudo‐elastic material responses. The NRLM has been tested on model problems and it has been found that the computed solutions agree well with the exact solutions, i.e. normalized error levels are in ranges acceptable for engineering computations. Copyright © 2005 John Wiley & Sons, Ltd.