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Topology design of structures using a dual algorithm and a constraint on the perimeter
Author(s) -
Jog C. S.
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.457
Subject(s) - perimeter , constraint (computer aided design) , upper and lower bounds , topology optimization , dual (grammatical number) , mathematics , topology (electrical circuits) , algorithm , network topology , mathematical optimization , computer science , combinatorics , engineering , finite element method , geometry , art , mathematical analysis , literature , structural engineering , operating system
Abstract Dual optimization algorithms are well suited for the topology design of continuum structures in discrete variables, since in these problems the number of constraints is small in comparison to the number of design variables. The ‘raw’ dual algorithm, which was originally proposed for the minimum compliance design problem, worked well when a perimeter constraint was added in addition to the volume constraint. However, if the perimeter constraint was gradually relaxed by increasing the upper bound on the allowable perimeter, the algorithm tended to behave erratically. Recently, a simple strategy has been suggested which modifies the raw dual algorithm to make it more robust in the absence of the perimeter constraint; in particular the problem of checkerboarding which is frequently observed with the use of lower‐order finite elements is eliminated. In this work, we show how the perimeter constraint can be incorporated in this improved algorithm, so that it not only provides a designer with a control over the topology, but also generates good topologies irrespective of the value of the upper bound on the perimeter. Copyright © 2002 John Wiley & Sons, Ltd.