TY - JOUR
T1 - QR-patterns
T2 - artefacts in multiresolution topology optimization
AU - Gupta, Deepak K.
AU - Langelaar, Matthijs
AU - van Keulen, Fred
PY - 2018
Y1 - 2018
N2 - 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.
AB - 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.
KW - Artefacts
KW - Artificial stiffness
KW - Multiresolution topology optimization
KW - p-refinement
KW - QR-patterns
UR - http://resolver.tudelft.nl/uuid:a36fed17-1aba-4c75-8f27-877de94ccad2
UR - http://www.scopus.com/inward/record.url?scp=85051708965&partnerID=8YFLogxK
U2 - 10.1007/s00158-018-2048-6
DO - 10.1007/s00158-018-2048-6
M3 - Article
SN - 1615-147X
VL - 58
SP - 1335
EP - 1350
JO - Structural and Multidisciplinary Optimization
JF - Structural and Multidisciplinary Optimization
IS - 4
ER -