Structural and Multidisciplinary Optimization

, Volume 60, Issue 6, pp 2531–2558 | Cite as

3D multi-material and multi-joint topology optimization with tooling accessibility constraints

  • Vlad Florea
  • Manish Pamwar
  • Balbir Sangha
  • Il Yong KimEmail author
Research Paper


This paper proposes a method for performing both multi-material topology optimization and multi-joint topology optimization. The algorithm can determine the optimum placement and selection of material while also optimizing the choice and placement of joint material between components. This method can simultaneously minimize the compliance of the structure as well as the total joint cost while subjected to a mass fraction constraint. A decomposition approach is used to break up the coupling between optimum structural design and optimum joint design. Multi-material and multi-joint topology optimization are then solved sequentially, controlled by an outer loop. By decomposing the problem, gradient-based optimization algorithms can be utilized, enabling the algorithm to solve large computational models efficiently. The proposed process is applied to three 3D standard TO problems. Through these example problems, the need for an iterative process is demonstrated. Improvements to joint manufacturability using the tooling and stress constraints are discussed. Finally, a review of computational cost is performed.


Structural optimization Multi-material topology optimization Multi-joint topology optimization Manufacturability in topology optimization Joint design Tooling constraints 



This research was funded by the Natural Sciences and Engineering Research Council of Canada (NSERC) and General Motors of Canada. Technical advice and direction were gratefully received from Derrick Chow, and Chandan Mozumder, at General Motors.

Compliance with ethical standards

Conflict of interests

The authors declare that they have 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
  2. 2.General Motors of Canada Company Canadian Technical CentreOshawaCanada

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