QR-patterns: artefacts in multiresolution topology optimization

Matthijs Langelaar,Fred van Keulen,Deepak K. Gupta

doi:10.1007/s00158-018-2048-6

Matthijs Langelaar, Fred van Keulen + Show 1 more

Open Access

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

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Abstract

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.

Highlights

In the traditional density-based topology optimization (TO) approaches, an element-wise constant density distribution is assumed
We explore whether there exist certain polynomial orders of the shape functions for which these QR-patterns can be eliminated at a reasonable computational cost
We have studied in detail the fact that the QR-patterns in multiresolution topology optimization (MTO) originate from the known incapability of the polynomial shape functions in modeling the displacement field that accompanies a discontinuous material distribution

Summary

Introduction

In the traditional density-based topology optimization (TO) approaches, an element-wise constant density distribution is assumed. A coarse analysis mesh is used and each finite element is divided into several density cells (voxels), which allows a finer density representation The MTO-based optimized designs are visually appealing, but it is important to determine whether the coarse analysis used in MTO approaches is capable of accurately modeling the high resolution material distributions. It is important to note that the use of large filter radii restricts the design field from expressing a high order material distribution. Fine structural features and crisp boundaries cannot appear in the solution Methods such as Heaviside projection (Guest et al 2004) can help to improve the crispness of the design (Groen et al 2017). The added computational cost associated with such schemes is not preferable for MTO, and it would be of great interest if smaller filter sizes can be used

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