A two-stage approach to the optimization design of multi-cell square tubal structures
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A two-stage approach to the optimization design of multi-cell square tubal structures Hamza Sulayman Abdullahi1,2
· Shuming Gao1
Received: 1 April 2020 / Revised: 28 August 2020 / Accepted: 3 September 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract Multi-cell tubal structures have widely been used in the automobile industry due to proven superior crashworthiness performance than single-cell and foam-filled tubes. This superior performance is attributed to the number of corners within the cross-sectional profile of the tube. In this paper, a two-stage optimization design of a multi-cell tubal structure is presented to address an important design problem by combining a discrete and continuous optimization process into a sequential optimization that generates an overall optimum. The first stage entails a configurational optimization which is realized by formulating a discrete topological optimization problem where the webs within the tube configuration are taken as the topological design variables. Each topological configuration is represented using a binary scheme that shows the presence or not of an edge to create different combinations of the corners. The constraints in the first stage are connectivity, mass ratio, and peak crushing force (PCF). The binary genetic algorithm (BGA) is utilized in searching for the optimal configuration in the first stage. The second stage entails parameter optimization where the cell sizes are the design variables. The objective functions in the second stage are defined using meta-models. Multi-objective particle swarm optimization (MOPSO) is employed for Pareto searching and Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) is used to find the optimal point for each of the mass ratios considered. Compared with the baseline configuration, the optimized tubal structures demonstrated superior crashworthiness performance. The two-stage discrete and continuous optimization approach has demonstrated that it not only provides a systematic approach to searching optimal structure but also creates a series of novel multi-cell topological configurations with enhanced crashworthiness. Keywords Two-stage optimization · Multi-cell tube · Multi-corner tube · Energy absorption · Topology optimization · Crash analysis
1 Introduction Thin-walled tubal structures, when used as crash energy absorbers in automobiles, improve passenger safety. During a frontal impact, front rails and crash boxes absorb Responsible Editor: Erdem Acar Electronic supplementary material The online version of this article (https://doi.org/10.1007/s00158-020-02735-9) contains supplementary material, which is available to authorized users. Shuming Gao
[email protected] 1
State Key Lab of CAD & CG, Zhejiang University, Hangzhou, 310058, Zhejiang, People’s Republic of China
2
Department of Mechanical Engineering, Bayero University, Kano, 700241, Nigeria
the kinetic energy and dissipate it in the form of plastic deformation. The energy ab
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