Bounds for decoupled design and analysis discretizations in topology optimization. (7th February 2017)

• Record Type: Journal Article
• Authors: Gupta, D. K.; van der Veen, G. J.; Aragón, A. M.; Langelaar, M.; van Keulen, F.
• Is Part Of: International journal for numerical methods in engineering. Volume 111:Number 1(2017)
• Page Start: 88
• Page End: 100
• Publication Date: 2017-02-07
• Subjects: topology design -- finite element methods -- structures; Numerical analysis -- Periodicals; Engineering mathematics -- Periodicals; 620.001518
• DOI: 10.1002/nme.5455
• Languages: English
• ISSNs: 0029-5981

Abstract

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.