Structural and Multidisciplinary Optimization

, Volume 59, Issue 1, pp 291–310 | Cite as

An adaptive multi-step varying-domain topology optimization method for spot weld design of automotive structures

  • Shu Yang
  • Lei Yan
  • Chang QiEmail author
Industrial Application


Spot welds are widely used to join metal stamping parts in the automotive industry. The number and layout of spot welds have direct impacts on both the mechanical performances of the vehicle and the manufacturing cost. The traditional methods including the 0–1 programming method, the size optimization method, the direct optimization method, and the single-step topology optimization (SSTO) method all have major drawbacks and are not suitable or efficient for spot weld layout design of an automotive structure. In this work, we propose a new method called multi-step varying-domain topology optimization (MVTO) method for spot weld design of automotive structures to balance structural performance and manufacturing cost. Based on a multi-step topology optimization framework with adaptive and varying design domains, the MVTO method can find a better layout design of the spot welds in a more efficient way compared to the existing methods. Limited engineering experiences are required and adverse human factors are eliminated in the spot weld design process with MVTO. To assist the application of MVTO method and to realize design automation, a new modeling approach is also developed to connect the continuous connection elements (CCEs) of the spot welds to the shell elements of the welded structure. Two case studies involving a simple single-hat beam and an automotive B-pillar show that the proposed MVTO method is reliable and effective for spot weld design of automotive structures. It has also been demonstrated that the MVTO method is superior to the direct optimization method and the SSTO method in terms of spot weld number reduction and welded structure performances, thus has a great potential for spot weld design of complicated automotive structures.


Spot weld optimization Topology optimization SIMP Automotive structures 



We thank Prof. Zhen-Hua Lu of the State Key Laboratory of Automotive Safety and Energy, Tsinghua University, for his great assistance in conducting this research.

Funding information

This study received financial support from the State Key Laboratory of Automotive Safety and Energy (no. KF1809), the National Natural Science Foundation of China (no. 51475069, 51475070), and the Fundamental Research Funds for the Central Universities (no. DUT17GF212, DUT17LK42).


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.State Key Laboratory of Structural Analysis for Industrial Equipment, Faculty of Vehicle Engineering and Mechanics, School of Automotive EngineeringDalian University of TechnologyDalianChina
  2. 2.State Key Laboratory of Automotive Safety and EnergyTsinghua UniversityBeijingChina

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