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Checkerboard‐free topology optimization using non‐conforming finite elements
Author(s) -
Jang GangWon,
Jeong Je Hyun,
Kim Yoon Young,
Sheen Dongwoo,
Park Chunjae,
Kim MyoungNyoun
Publication year - 2003
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.738
Subject(s) - checkerboard , homogenization (climate) , topology optimization , finite element method , topology (electrical circuits) , instability , convergence (economics) , shape optimization , limiting , mathematics , mathematical optimization , extended finite element method , stiffness matrix , computer science , structural engineering , geometry , engineering , mechanical engineering , mechanics , physics , combinatorics , biodiversity , ecology , economics , biology , economic growth
The objective of the present study is to show that the numerical instability characterized by checkerboard patterns can be completely controlled when non‐conforming four‐node finite elements are employed. Since the convergence of the non‐conforming finite element is independent of the Lamé parameters, the stiffness of the non‐conforming element exhibits correct limiting behaviour, which is desirable in prohibiting the unwanted formation of checkerboards in topology optimization. We employ the homogenization method to show the checkerboard‐free property of the non‐conforming element in topology optimization problems and verify it with three typical optimization examples. Copyright © 2003 John Wiley & Sons, Ltd.