Two-stage optimal design of metro underframe structures : based on topology-size-shape co-optimization methodology

Du, Delei (author), Li, Yana (author), Song, Jian (author), He, Zhengping (author), Zhao, Shangchao (author), Xu, Jianxin (author)

The design of the metro body structure must balance both safety and cost indicators. The underframe is not only the main load-bearing component of the metro body but also accounts a significant portion of its overall mass. To reduce operational costs and enhance the safety performance of the metro body, this paper focuses on optimizing the design of the underframe. A two-stage optimization approach was proposed, addressing the limitation of existing methods and the challenges in balancing realistic operating conditions with manufacturability. First, manufacturing constraints were incorporated using the variable density method, and topology optimization of the underframe sub-model was carried out with the objective of minimizing flexibility-weighted strain energy. Next, the rough topology was refined through parametric optimization after determining the approximate shape of the cross section, resulting in a more precise model. The results show that the proposed optimization method reduces underframe mass by about 4.7 % while lowering the maximum deflection of the metro car body under the maximum vertical load case by 0.601 mm. This demonstrates that the proposed framework efficiently combines optimization capabilities with simplicity.

• Language: English
• Keywords: underframe, structural optimization, collaborative optimization, lightweighting
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: FS - Faculty of Mechanical Engineering
• Publication status: Published
• Publication version: Version of Record
• Year: 2025
• Number of pages: 8 str.
• Numbering: Vol. 71, no. 11/12
• PID: 20.500.12556/RUL-178153
• UDC: 629.4
• ISSN on article: 2536-3948
• DOI: 10.5545/sv-jme.2025.1308
• COBISS.SI-ID: 265344771
• Publication date in RUL: 20.01.2026

Record is a part of a journal

• Title: Strojniški vestnik
• Shortened title: Stroj. vestn.
• Publisher: Fakulteta za strojništvo
• ISSN: 2536-3948
• COBISS.SI-ID: 294943232

Secondary language

• Language: Slovenian

Abstract

Zasnova konstrukcije karoserije metroja mora zadoščati uravnoteženju varnostnih in stroškovnih kazalnikov. Spodnji okvir ni le glavni nosilni element karoserije metroja, temveč predstavlja tudi pomemben delež njene skupne mase. Ta članek se osredotoča na zmanjšanje obratovalnih stroškov in izboljšanje varnostne zmogljivosti karoserije metroja z optimizacijo zasnove spodnjega okvirja. Predlagan je bil dvostopenjski pristop k optimizaciji, ki nadgrajuje omejitve obstoječih metod in obravnava izzive pri uravnoteženju realnih obratovalnih pogojev s tehnologičnostjo. Najprej so bile v postopek vključene proizvodne omejitve z uporabo metode spremenljive gostote, pri čemer je bila izvedena topološka optimizacija delnega modela spodnjega okvirja z namenom minimizacije deformacijske energije, utežene glede na prožnost. Nato je bila groba topologija izboljšana s parametrično optimizacijo po določitvi približne oblike prereza, kar je privedlo do natančnejšega modela. Rezultati kažejo, da predlagana metoda optimizacije zmanjša maso spodnjega okvirja za približno 4,7 %, hkrati pa zmanjša največji upogibek karoserije metroja pri maksimalni navpični obremenitvi za 0,601 mm. To dokazuje, da predlagana metodologija učinkovito združuje optimizacijske zmogljivosti in preprostost.

• Keywords: spodnji okvir metroja, optimizacija strukture, kooperativna optimizacija, zmanjšanje mase