Method and algorithm for constructing a geometric shell of a multi-body assembly based on a mathematical model of elastic deformation

Аuthors

Zakharov A. A., Pankin A. A., Subbotina N. M., Fevralskikh A. V.^*

Group Head, TESIS LLC, Moscow, Russia

*e-mail: a.fevralskih@gmail.com

Abstract

This paper presents a method for constructing a triangulated shell of a CAD model composed of multiple bodies, developed on the basis of a mathematical model of elastic deformation. The mathematical model includes the computation of deformation and elasticity «forces» implemented within a computer simulation algorithm in a way that prevents triangle degeneration and self-intersections. The computation comprises: determining stretching/compression forces acting on edges and on triangle heights of the shell; determining shell bending forces; and determining the attraction force that pulls the shell toward the original geometry. To ensure numerical stability, the algorithm introduces a parameter used in the iterative integration step calculation that limits the maximum displacement of vertices per iteration (a CFL-type restriction in the sense of bounding per-iteration motion by a characteristic local length scale). The advantages of the developed method and algorithm are stated as robustness to small features and geometric defects, preservation of triangle connectivity, and achieving smoothness in accordance with prescribed geometric tolerances and the characteristics of the wrapped bodies. The algorithm is intended for use in CAD/CAE software families and can be applied to a wide range of computer modeling tasks. The method and algorithm are tested on an example related to setting up boundary conditions in a computational fluid dynamics (CFD) flow simulation based on the finite volume method, using a hexahedral mesh generator with hanging nodes. The method is validated on a defective multi-body assembly example, including a car geometry case. The results demonstrate that combining elastic constraints with attraction to the source geometry enables obtaining a closed shell and improves shape stability compared with a variant that relies on attraction only. The resulting triangulated shell is intended for practical application in geometry processing pipelines and preparation of computational models based on surface envelopes.

Keywords:

multibody assembly; shell generation; elastic deformation; CFD modeling

References

1. Nushtaev D.V., Volkov-Bogorodskii D.B., Ardatov K.V. K voprosu postroeniia upakovannoi konfiguratsii obolochki ballona sistemy dostavki koronarnykh stentov. Rossiiskii zhurnal biomekhaniki. 2020;(2). Available at: [https://cyberleninka.ru/article/n/k-voprosu-postroeniya-upakovannoy-konfiguratsii-obolochki-ballona-... (accessed 15.12.2025). (In Russ.). 
2. Tislenko I.V., Kuz'michev V.E. Teoreticheskii raschet plotnooblegaiushchikh obolochek iz tekstil'nykh materialov (Chast' 1). Shveinaia promyshlennost'. 2014;(5):28–31. EDN TIRFBJ. (In Russ.). 
3. Voloboi A.G., Ershov S.V., Valiev I.V. Optimizatsiia rascheta osveshcheniia inter'ernykh stsen dlia stokhasticheskoi trassirovki luchei. Programmnye produkty i sistemy. 2020;(4). Available at: [https://cyberleninka.ru/article/n/optimizatsiya-rascheta-osvescheniya-interiernyh-stsen-dlya-stohast... (accessed 15.12.2025). (In Russ.). 
4. Kholodilov A.A., Faleeva E.V., Kholodilova M.V. Analiz tekhnologii perevoda trekhmernoi modeli iz CAD-formata v upravliaiushchii kod pri 3D-pechati. Nauchno-tekhnicheskoe i ekonomicheskoe sotrudnichestvo stran ATR v XXI veke. 2020;2:296–301. EDN KLUEIV. (In Russ.). 
5. Gramuzov E.M., Liubimov V.I., Smirnov K.V., Sosnov A.V., Fevralskikh A.V. Avtomatizirovannaia optimizatsiia komponovki kryla i gorizontal'nogo opereniia ekranoplana po rezul'tatam chislennogo modelirovaniia aerodinamiki. Morskie intellektual'nye tekhnologii. 2019;1(43);3:38–47. (In Russ.). 
6. Vshivkov Iu.F., Galushko E.A., Krivel' S.M. Aerodinamicheskoe proektirovanie ekranoplana s vysokimi nesushchimi svoistvami na osnove chislennogo modelirovaniia s primeneniem ANSYS. In: Aviamashinostroenie i transport Sibiri. Proceedings of the IV All-Russian Scientific and Practical Conference. Irkutskii gosudarstvennyi tekhnicheskii universitet; 2014. p. 51–55. (In Russ.). 
7. Khasenova S.M., Akaev A.S., Martynenko E.A. Razrabotka optimizatsionnoi modeli v programme ANSYS FLUENT dlia teploobmennika natrievoi petli. Vestnik NIaTs RK. 2020;(4):88–91. (In Russ.). 
8. Nigmatzyanov A.R., Salin A.A. Chislennoe modelirovanie kozhukhotrubchatogo teploobmennika v programmnom komplekse ANSYS CFX. Vestnik Tekhnologicheskogo universiteta. 2024;27(3):96–100. (In Russ.). 
9. Ivanov N.V. Primenimost' programmnogo kompleksa ANSYS CFX dlia resheniia zadach aerodinamicheskoi ustoichivosti i stabilizatsii letatel'nykh apparatov. In: Molodezh'. Tekhnika. Kosmos: Proceedings of the X All-Russian Youth Scientific and Technical Conference, Saint Petersburg, 18–20 April 2018. Saint Petersburg: Baltiiskii gosudarstvennyi tekhnicheskii universitet “Voenmekh”; 2018. p. 86–91. (In Russ.). 
10. Turganbaeva A.B., Kurbanaliev A.Y. Raschet obtekaniia gory Sulaiman v pakete OpenFOAM. Vestnik Oshskogo gosudarstvennogo universiteta. Matematika. Fizika. Tekhnika. 2022;(1):92–101. (In Russ.). 
11. Khadse N.A., Zaweri S.R. Modal Analysis of Aircraft Wing using Ansys Workbench Software Package. International Journal of Engineering Research & Technology (IJERT). 2015;4(7):225–230. 
12. Makhnev M.S., Fevralskikh A.V. Verifikatsiia rezul'tatov opredeleniia vrashchatel'nykh proizvodnykh po krenu LA v shirokom diapazone uglov ataki. Trudy MAI. 2019;(109):23. (In Russ.). 
13. Ragulin I.A. Chislennoe modelirovanie obtekaniia model'nogo grebnogo vinta. Trudy MAI. 2025;(143). (In Russ.). 
14. Glazkov V.S., Ignatkin Iu.M. Verifikatsiia programmnogo paketa ANSYS Fluent pri issledovanii aerodinamicheskikh kharakteristik vetrokolesa Savoniusa. Trudy MAI. 2018;(100):11. (In Russ.). 
15. Pavlovic D., Todorovic M., Jovanovic M., Milosavljevic P. Comparison of Commercial CFD Software Packages. In: Proceedings of the 3rd International Conference on Application of Information and Communication Technology and Statistics in Economy and Education (ICAICTSEE–2013), Sofia, Bulgaria, December 6–7, 2013. Sofia: UNWE; 2013. p. 361–371. 
16. Yakunin V.I. Metodologicheskie voprosy geometricheskogo proektirovaniia i konstruirovaniia slozhnykh poverkhnostei. Uchebnoe posobie. MAI; 1990. (In Russ.).

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