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Construction of Design Guidelines for Optimal Automotive Frame Shape Based on Statistical Approach and Mechanical Analysis

Masanori Honda1,3, Chikara Kawamura1,3, Isamu Kizaki1, Yoichi Miyajima1, Akihiro Takezawa2,*, Mitsuru Kitamura3

1 Mazda Motor Corporation, 3-1 Shinchi, Fuchu-cho, Aki-gun, Hiroshima, 730-8670, Japan
2 Department of Applied Mechanics and Aerospace Engineering, School of Fundamental Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjuku-ku, Tokyo, 169-8555, Japan
3 Division of Advanced Science and Engineering, Graduate School of Advanced Science and Engineering, Hiroshima University, 1-4-1 Kagamiyama, Higashihiroshima, Hiroshima, 739-8527, Japan

* Corresponding Author: Akihiro Takezawa. Email:

(This article belongs to this Special Issue: New Trends in Structural Optimization)

Computer Modeling in Engineering & Sciences 2021, 128(2), 731-742.


A body frame composed of thin sheet metal is a crucial structure that determines the safety performance of a vehicle. Designing a correct weight and high-performance automotive body is an emerging engineering problem. To improve the performance of the automotive frame, we attempt to reconstruct its design criteria based on statistical and mechanical approaches. At first, a fundamental study on the frame strength is conducted and a cross-sectional shape optimization problem is developed for designing the cross-sectional shape of an automobile frame having a very high mass efficiency for strength. Shape optimization is carried out using the nonlinear finite element method and a meta-modeling-based genetic algorithm. Data analysis of the obtained set of optimal results is performed to identify the dominant design variables by employing the smoothing spline analysis of variance, the principal component analysis, and the self-organizing map technique. The relationship between the cross-sectional shape and the objective function is also analyzed by hierarchical clustering. A design guideline is obtained from these statistical approach results. A comparison between the statistically obtained design guideline and the conventional one based on the designers’ experience is performed based on mechanical interpretation of the optimal cross-sectional frame. Finally, a mechanically reasonable new general-purpose design guideline is proposed for the cross-sectional shape of the automotive frame.


Cite This Article

Honda, M., Kawamura, C., Kizaki, I., Miyajima, Y., Takezawa, A. et al. (2021). Construction of Design Guidelines for Optimal Automotive Frame Shape Based on Statistical Approach and Mechanical Analysis. CMES-Computer Modeling in Engineering & Sciences, 128(2), 731–742.


This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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