An efficient 3D homogenization-based topology optimization methodology

Computational Mechanics (2021)Cite this article

Abstract

Homogenization theory forms the basis for solving the topology optimization problem (TOP) formulated for designing composite materials. Homogenization is proved to be an efficient approach to effectively determine the equivalent macroscopic properties of the composite material. It relies on the assumption that the composite material presents a periodic pattern on a microstructural level; the simplest repeating unit of the microstructure, that if isolated represents exactly the macroscopic behaviour of the material, is called the \(unit\ cell\). Scope of homogenization is to determine the macroscopic (or else effective) properties of the non-homogeneous unit cell, that is, determine the properties of the unit cell as if it was composed by homogeneous material. In this study, a simple methodology is proposed where homogenization is implemented on a 3D lattice unit cell, with its radius being considered as the alternating parameter for the homogenization procedure; different values of the radius result to different unit cell configurations and hence, to different equivalent properties. A fitting process takes place in order to appropriately model the variations of the obtained effective properties w.r.t the design parameter. The corresponding, homogenization-based TOP is formed and the accuracy of the proposed methodology is assessed on several case studies.

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Acknowledgements

This research has been co-financed by the European Union and Greek national funds through the Operational Program Competitiveness, Entrepreneurship and Innovation, under the call \({\textit{RESEARCH}}-{\textit{CREATE}}-{\textit{INNOVATE}}\) (project code: T1EDK-05603). Konstantinos Iason Ypsilantis acknowledges the support of the Research Foundation Flanders (FWO) under grant number 1SA8721N.

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Affiliations

  1. Reliable and Robust Design Lab, Department of Mechanical Engineering, KU Leuven, Katholieke Universiteit Leuven, 13, Oude Markt, 3000, Leuven, Belgium

    Konstantinos-Iason Ypsilantis

  2. Veltion Engineering and Applied Sciences Optimization Lab, Institute of Structural Analysis and Antiseismic Research, School of Civil Engineering, National Technical University of Athens, 15780, Athens, Greece

    George Kazakis & Nikos D. Lagaros

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  1. Konstantinos-Iason Ypsilantis
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  2. George Kazakis
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  3. Nikos D. Lagaros
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Correspondence to Nikos D. Lagaros.

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Ypsilantis, KI., Kazakis, G. & Lagaros, N.D. An efficient 3D homogenization-based topology optimization methodology. Comput Mech (2021). https://doi.org/10.1007/s00466-020-01943-w

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Keywords

  • Design of composite materials
  • Topology optimization
  • Homogenization approach
  • 3D lattice unit cell
  • Fitting process