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Modified element stacking method for multi-material topology optimization with anisotropic materials

  • Daozhong Li
  • Il Yong KimEmail author
Research Paper
  • 109 Downloads

Abstract

This article presents a modified element stacking method for anisotropic multi-material topology optimization. This method can transform standard multi-material topology optimization formulations into a series of equivalent single-material topology optimization ones to overcome the various limitations inherent to conventional techniques. First, typical multi-material topology optimization methods utilize material interpolation schemes that restrict the study to the isotropic domain with a constant Poisson’s ratio, limiting practical applications and solution accuracy. Additionally, in attempts to further extend these classical multi-material topology optimization methods to anisotropic materials, preparing the necessary element information matrices becomes increasingly laborious or even impossible for complex models, preventing the application of sensitivity analysis for robust gradient-based optimization methods. To directly address these limitations, the element interpolation method replaces material interpolation schemes with an element interpolation framework, where each design cell property is determined using a weighted sum of various coincident single-material elements. This paper provides a thorough description of element interpolation and presents several numerical examples demonstrating successful implementation.

Keywords

Topology optimization Multi-material Element interpolation Modified element stacking method SIMP SAMP 

Notes

Acknowledgements

Technical advice and direction were gratefully received from Balbir Sangha, Manish Pamwar, Derrick Chow, and Chandan Mozumder, at General Motors.

Funding information

This research was funded by the Natural Sciences and Engineering Research Council of Canada (NSERC) and General Motors of Canada.

Compliance with ethical Standards

Conflict of interest

On behalf of all authors, the corresponding author states that there is no conflict of interest.

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Mechanical and Materials EngineeringQueen’s UniversityKingstonCanada

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