Singularity aware de-homogenization for high-resolution topology optimized structures
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Singularity aware de-homogenization for high-resolution topology optimized structures F. C. Stutz1
· J. P. Groen2 · O. Sigmund2 · J. A. Bærentzen1
Received: 10 April 2020 / Revised: 2 July 2020 / Accepted: 6 July 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract Homogenization-based topology optimization has been shown to be effective but does not directly create mechanical structures. Instead, the method gives a multi-scale description of the optimized design, e.g., lamination thicknesses and directions. To obtain a realizable single-scale design, one can perform a subsequent de-homogenization step. This is done by converting the lamination directions to integrable vector fields from which it is possible to compute a parameterization of the domain. Unfortunately, however, singularities often make it impossible to find integrable vector fields that align with lamination directions. We present a short introduction to homogenization-based topology optimization followed by an overview of different types of singularities and how they impinge on the problem. Based on this, we propose a singularity aware de-homogenization pipeline, where we use a method for vector field combing which produces consistent labeling of the lamination directions but also introduces necessary seams in the domain. We demonstrate how methods from computer graphics can subsequently be used to compute the final parameterization from which the mechanical structure can easily be extracted. We demonstrate the method on several test cases. Keywords De-homogenization · Singularities · Topology optimization · High-resolution structures
1 Introduction Topology optimization, a numerical tool for determining optimal mechanical layouts, has a broad spectrum of possible industrial applications. Over the last decades, the development and accessibility of computational power have made it an interesting design tool for the industry. However, further developments are still needed before large-scale, real-time topology optimization is possible on desktop computers. Homogenization-based topology optimization, as proposed by Bendsøe and Kikuchi (1988), allows for composite material properties, which contain much more information
Responsible Editor: Hyunsun Alicia Kim F. C. Stutz
[email protected] 1
Department of Applied Mathematics and Computer Science, Technical University of Denmark, 2800 Kgs. Lyngby, Denmark
2
Department of Mechanical Engineering, Technical University of Denmark, 2800 Kgs. Lyngby, Denmark
compared to the isotropic material used in the SIMP (Solid Isotropic Material with Penalisation) approach (Bendsøe 1989). Hence, performing homogenization-based topology optimization allows us to solve the problem on a coarse grid while still enabling near-optimal, high-resolution results as shown in Groen and Sigmund (2018). In homogenizationbased topology optimization, we can describe the composite material as infinitesimally small periodic unit cells on a microscopic level. On a macroscopic level, we can assume
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