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Topology optimization of periodic microstructures with a penalization of highly localized buckling modes
Author(s) -
Neves Miguel M.,
Sigmund Ole,
Bendsøe Martin P.
Publication year - 2002
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.449
Subject(s) - buckling , microscale chemistry , instability , microstructure , finite element method , stability (learning theory) , topology optimization , structural engineering , structural stability , mathematical analysis , mechanics , materials science , topology (electrical circuits) , mathematics , physics , computer science , engineering , composite material , mathematics education , combinatorics , machine learning
The problem of determining highly localized buckling modes in perfectly periodic cellular microstructures of infinite extent is addressed. A double scale asymptotic technique is applied to the linearized stability problem for a periodic structure built from linearly elastic microstructures. The obtained stability condition for the microscale level is then used to establish a comparative analysis between different material distributions in the base cell subjected to the same strain field at the macroscale level. The idea is illustrated by some two‐dimensional finite element examples and used to design materials with optimal elastic properties that are less prone to localized instability in the form of local buckling modes at the scale of the microstructure. Copyright © 2002 John Wiley & Sons, Ltd.