Bounds for decoupled design and analysis discretizations in topology optimization

Journal article (2017)

Authors

D.K. Gupta Computational Design and Mechanics - Mechanical, Maritime and Materials Engineering
G.J. van der Veen Computational Design and Mechanics - Mechanical, Maritime and Materials Engineering
A.M. Aragon Computational Design and Mechanics - Mechanical, Maritime and Materials Engineering
Matthijs Langelaar Computational Design and Mechanics - Mechanical, Maritime and Materials Engineering
A. van Keulen Computational Design and Mechanics - Mechanical, Maritime and Materials Engineering
Research Group
Computational Design and Mechanics (Mechanical, Maritime and Materials Engineering) (TU Delft)
Copyright: © 2017 D.K. Gupta, G.J. van der Veen, A.M. Aragon, Matthijs Langelaar, A. van Keulen
DOI: https://doi.org/10.1002/nme.5455
More Info
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Published Date

2017

Language

English

Faculty

Mechanical, Maritime and Materials Engineering

Department

Precision and Microsystems Engineering

Research Group

Computational Design and Mechanics

Abstract

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.