QR-patterns

QR-patterns: artefacts in multiresolution topology optimization

Gupta, D.K. (TU Delft Computational Design and Mechanics)
Langelaar, Matthijs (TU Delft Computational Design and Mechanics)
van Keulen, A. (TU Delft Computational Design and Mechanics)

2018

Recent multiresolution topology optimization (MTO) approaches involve dividing finite elements into several density cells (voxels), thereby allowing a finer design description compared to a traditional FE-mesh-based design field. However, such formulations can generate discontinuous intra-element material distributions resembling QR-patterns. The stiffness of these disconnected features is highly overestimated, depending on the polynomial order of the employed FE shape functions. Although this phenomenon has been observed before, to be able to use MTO at its full potential, it is important that the occurrence of QR-patterns is understood. This paper investigates the formation and properties of these QR-patterns, and provides the groundwork for the definition of effective countermeasures. We study in detail the fact that the continuous shape functions used in MTO are incapable of modeling the discontinuous displacement fields needed to describe the separation of disconnected material patches within elements. Stiffness overestimation reduces with p-refinement, but this also increases the computational cost. We also study the influence of filtering on the formation of QR-patterns and present a low-cost method to determine a minimum filter radius to avoid these artefacts.

Artefacts
Artificial stiffness
Multiresolution topology optimization
p-refinement
QR-patterns

http://resolver.tudelft.nl/uuid:a36fed17-1aba-4c75-8f27-877de94ccad2

https://doi.org/10.1007/s00158-018-2048-6

1615-147X

Structural and Multidisciplinary Optimization, 58 (4), 1335-1350

Institutional Repository

journal article

© 2018 D.K. Gupta, Matthijs Langelaar, A. van Keulen