Natural element method: Difference between revisions

Revision as of 01:55, 13 April 2020

Revision as of 19:35, 28 August 2020

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[[Image:Euclidean Voronoi diagram.svg|thumb|20 points and their Voronoi cells]]

The '''natural element method (NEM)'''<ref>{{cite journal|url=|title=The natural element method in solid mechanics|first1=N.|last1=Sukumar|first2=B.|last2=Moran|first3=T.|last3=Belytschko|date=21 June 1998|journal=International Journal for Numerical Methods in Engineering|volume=43|issue=5|pages=839–887|doi=10.1002/(SICI)1097-0207(19981115)43:5<839::AID-NME423>3.0.CO;2-R|bibcode=1998IJNME..43..839S}}</ref><ref>{{cite journal| title=A new extension of the natural element method for non‐convex and discontinuous problems: the constrained natural element method (C‐NEM)| author1=J. Yvonnet| author2=D. Ryckelynck| author3=P. Lorong| author4=F. Chinesta| publisher=International Journal for Numerical Methods in Engineering| pages=1451–1474}}</ref><ref>{{cite journal|url=https://www.researchgate.net/publication/332678382|title=Large deformation analysis of elastic bodies by nonlinear Petrov–Galerkin natural element method | journal=Advances in Mechanical Engineering | date=April 2019}}</ref> is a [[meshless method]] to solve [[partial differential equation]], where the ''elements'' do not have a predefined shape as in the [[finite element method]], but depend on the geometry.<ref>{{Cite journal |title=Research on Natural Element Method and the application to simulate metal forming processes |lastlast1=Lu |firstfirst1=Ping |last2=Shu |first2=Yang |date=2017-01-01 |journal=Procedia Engineering |volume=207 |series=International Conference on the Technology of Plasticity, ICTP 2017, 17-22 September 2017, Cambridge, United Kingdom |publisher=[[ScienceDirect]] |pages=1087–1092 |doi=10.1016/j.proeng.2017.10.1135 |last3=Lu |first3=Dahai |last4=Jiang |first4=Kaiyong |last5=Liu |first5=Bin |last6=Huang |first6=Changbiao|doi-access=free }}</ref><ref>{{Cite web |url=https://www.researchgate.net/post/What_is_the_difference_between_nem_natural_element_method_and_cnem_constrained_natural_element_method |title=What is the difference between nem (natural element method) and cnem (constrained natural element method)? |website=ResearchGate |publisher=[[ResearchGate]] |language=en |access-date=2019-07-15}}</ref><ref>{{Cite book |chapter=Vector interpolation on natural element method: Mesh sensitivity analysis |lastlast1=Botelho |firstfirst1=D. P. |last2=Marechal |first2=Y. |date=November 2016 |publisher=[[Institute of Electrical and Electronics Engineers]] |page=1 |doi=10.1109/CEFC.2016.7816353 |last3=Ramdane |first3=B.|title=2016 IEEE Conference on Electromagnetic Field Computation (CEFC) |isbn=978-1-5090-1032-5 |s2cid=27851390 }}</ref>

A [[Voronoi diagram]] partitioning the space is used to create each of these elements.