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Optimum target stiffness allocation for design of a reinforcing member on an existing structure

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The reinforcing members are often added on an existing structure to improve stiffness of the structure up to required level. In general, the design targets for the reinforcing members need to be allocated for their designs. However, since the members are additively designed, it is difficult to predict behavior of the reinforcing members and their influence on the existing structure. Therefore, allocating the design targets is challenging task, and the targets based on engineering experience and intuition can lead to the repetitive design cycles. This paper proposes a method for determining target stiffness of a reinforcing member which makes an existing structure achieve the required performances. To utilize individual models of an existing structure and the reinforcing members in a design, the system of equations of the assembled structure is decomposed by using a substructuring technique. Additional boundary conditions are imposed on the interfaces between the structure and members to ensure consistency between models, and the target stiffness of the member is defined by using the boundary conditions. The optimal target stiffness and design of the members are determined through the use of a multidisciplinary design optimization technique, analytical target cascading. This method is applied to a simple portal frame and a body-in-white with reinforcing member of a vehicle manufactured by Hyundai Motor Company. By using the optimal target stiffness, reinforcing member of any shape can be designed independently and at little cost, without access of the existing structure model.

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Some contents of this research are part of the “Multidisciplinary design optimization of vehicle body reinforce members” funded by Hyundai Motor Company. The authors appreciate the partial financial support from Hyundai Motor Company.


This research is partially and financially supported by Hyundai Motor Company.

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Correspondence to Tae Hee Lee.

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Replication of results

For the purpose of replication of results, MATLAB codes of the portal frame example presented in Section 4.1 are provided as a supplementary material. Codes include static analysis of the portal frame, target stiffness allocation, re-design of the structure B with I-beam cross-section, and optimization using IDF method. MATLAB 2018b was used to generate the results. Codes and files related to vehicle BIW example presented in Section 4.2 cannot be provided for the purposes of confidentiality.

Responsible Editor: Jianbin Du

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Kim, S., Kim, S., Lee, T.H. et al. Optimum target stiffness allocation for design of a reinforcing member on an existing structure. Struct Multidisc Optim (2020).

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  • Target stiffness allocation
  • Reinforcing member
  • Structure reinforcement
  • Complex structure
  • Design optimization
  • Analytical target cascading