Bounds for decoupled design and analysis discretizations in topology optimization

Summary Topology optimization formulations using multiple design variables per finite element have been proposed to improve the design resolution. This paper discusses the relation between the number of design variables per element and the order of the elements used for analysis. We derive that beyo...

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Bibliographic Details
Published in:International journal for numerical methods in engineering 2017-07, Vol.111 (1), p.88-100
Main Authors: Gupta, D. K., van der Veen, G. J., Aragón, A. M., Langelaar, M., van Keulen, F.
Format: Article
Language:English
Subjects:
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Design analysis
Design engineering
Design improvements
Design optimization
Discretization
Finite element method
finite element methods
Formulations
Numerical methods
structures
topology design
Topology optimization
Uniqueness
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Summary:Summary Topology optimization formulations using multiple design variables per finite element have been proposed to improve the design resolution. This paper discusses the relation between the number of design variables per element and the order of the elements used for analysis. We derive that beyond a maximum number of design variables, certain sets of material distributions cannot be discriminated based on the corresponding analysis results. This makes the design description inefficient and the solution of the optimization problem non‐unique. To prevent this, we establish bounds for the maximum number of design variables that can be used to describe the material distribution for any given finite element scheme without introducing non‐uniqueness. Copyright © 2016 The Authors. International Journal for Numerical Methods in Engineering Published by John Wiley & Sons Ltd.
ISSN:0029-5981
1097-0207
DOI:10.1002/nme.5455