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A fast method for binary programming using first‐order derivatives, with application to topology optimization with buckling constraints
Author(s) -
Browne P. A.,
Budd C.,
Gould N. I. M.,
Kim H. A.,
Scott J. A.
Publication year - 2012
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.4367
Subject(s) - topology optimization , stiffness matrix , buckling , mathematical optimization , finite element method , minification , mathematics , binary number , stiffness , topology (electrical circuits) , computer science , structural engineering , engineering , combinatorics , arithmetic
SUMMARY We present a method for finding solutions of large‐scale binary programming problems where the calculation of derivatives is very expensive. We then apply this method to a topology optimization problem of weight minimization subject to compliance and buckling constraints. We derive an analytic expression for the derivative of the stress stiffness matrix with respect to the density of an element in the finite‐element setting. Results are presented for a number of two‐dimensional test problems.Copyright © 2012 John Wiley & Sons, Ltd.