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Robust Multi-material Topology Optimization for Lattice Structure Under Material Uncertainties

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Advances in Structural and Multidisciplinary Optimization (WCSMO 2017)

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Abstract

Recent advances in additive manufacturing have enabled the manufacture of hollow shapes with complex external geometry and multiple materials using networks of small periodic cells known as lattice structures. The porosity and high number of elements in these structures generate lightweight designs with improved performance and functionality. This paper proposes a design approach for lattice structures considering both multi-material design and uncertainty in material properties. A density-based multi-material topology optimization method is proposed to find the optimal geometry and material layout. In addition, a new interpolation scheme for using multiple and arbitrary materials is presented. For robustness of structural compliance against uncertainty in material properties, a weighted sum of the mean and standard deviation is chosen as an objective function. To estimate statistical moments by the material uncertainty, the univariate dimension-reduction (UDR) method combined with Gauss-type quadrature sampling is employed. Two numerical examples demonstrate the efficiency of the proposed approach and the effect of material uncertainty on the robust design results.

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Acknowledgements

This work was supported by the Walter P. Murphy Fellowship to Ms. Yu-Chin Chan at Northwestern University. The authors would also like to thank the Digital Manufacturing and Design Innovation Institute (DMDII) for their support through award number 15-07-07.

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Authors and Affiliations

  1. Department of Mechanical Engineering, Northwestern University, Evanston, IL, USA

    Kohei Shintani, Yu-Chin Chan & Wei Chen

Authors
  1. Kohei Shintani
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  2. Yu-Chin Chan
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  3. Wei Chen
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Corresponding author

Correspondence to Wei Chen .

Editor information

Editors and Affiliations

  1. Chair for Optimization of Mechanical Stuctures, Faculty for Mechanical Engineering and Safety Engineering, University of Wuppertal, Wuppertal, Germany

    Axel Schumacher

  2. Institute for Construction Enginnering, Technische Universität Braunschweig, Braunschweig, Germany

    Thomas Vietor

  3. Braunschweig, Germany

    Sierk Fiebig

  4. Chair of Structural Analysis, Technische University of Munich, Munich, Germany

    Kai-Uwe Bletzinger

  5. Engineering Center, ECAE 197, University of Colorado Boulder, Boulder, Colorado, USA

    Kurt Maute

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Shintani, K., Chan, YC., Chen, W. (2018). Robust Multi-material Topology Optimization for Lattice Structure Under Material Uncertainties. In: Schumacher, A., Vietor, T., Fiebig, S., Bletzinger, KU., Maute, K. (eds) Advances in Structural and Multidisciplinary Optimization. WCSMO 2017. Springer, Cham. https://doi.org/10.1007/978-3-319-67988-4_84

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  • DOI: https://doi.org/10.1007/978-3-319-67988-4_84

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-67987-7

  • Online ISBN: 978-3-319-67988-4

  • eBook Packages: EngineeringEngineering (R0)

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