Parametric optimization of the stability and weight of a minimal surface shell taking into account geometric nonlinearity under thermomechanical loading
DOI:
https://doi.org/10.32347/2410-2547.2025.115.231-243Keywords:
optimization, parametric optimization, multicriteria optimization, objective function optimization, design variables, constraints, minimum surface envelopes, geometric nonlinearity, finite element methodAbstract
Optimal design plays an important role in the approach to and formation of building structures. This stage of structural calculation has been little studied and is virtually unused by practicing engineers in the field of mechanical resistance and stability.
The active development of optimal design began in the mid-20th century with the development of computers. The first works were performed on proprietary software in the Fortran language. Over more than half a century, computers have been modernized into PCs, and software complexes such as Femap and Ansys have been created, which include sections on optimal design. For the optimal design of fairly unique structures, it is not enough to have a basic functional set in these calculation complexes, so for interesting target functions such as stability and weight, it is necessary to add this part to the optimization functionality.
The object of study is thin-walled shells of minimal surfaces. The essence of these spatial structures lies in the uniqueness of their surface, which has been optimized using the parameter continuation method based on the defined contour and height of the future shell of the minimal surface. After integration, the optimal shape for the future structure is derived, which has a minimum area and minimum internal forces, which are compensated by the geometric shape of the thin-walled shell of the minimal surface.
Optimal design in construction and applied mechanics is divided into four types. The first type is shape optimization. The second type is parametric optimization. The third type is topological optimization. The fourth type is optimization of physical and mechanical characteristics.
To study multi-criteria parametric optimization of a minimum surface shell, taking into account geometric nonlinearity, a special additional optimizer module created by the authors is used, which is linked to the Femap with Nastran calculation complex [12].
This scientific article reveals the essence of four types of optimal design and an approach to the optimal design scheme. A numerical study of multi-criteria parametric optimization of the stability and weight of a minimal surface shell with a square plan consisting of two straight lines and two semicircles was performed. The thickness of the shell after optimization calculation ranges from 40 to 1 mm under thermo-mechanical loading. A graph of the target functions of weight and stability loss coefficient λ has been constructed. The weight on the target function graph decreased from 31 tons to 25.5 tons, which is 17.75% in percentage terms, while the stability loss coefficient decreased from 2.12 to 1.08, which means the maximum use of structural material in this optimization calculation.
References
Ivanchenko H.M., Koshevyi O.O., Koshevyi O.P. Chyselna realizatsiia bahatokryterialnoi parametrychnoi optymizatsii obolonky minimalnoi poverkhni na kvadratnomu konturi pry termosylovomu navantazhenni (Numerical implementation of multicriteria parametric optimization of minimum surface shellon a square contour under thermforce loading) // Strength of Materials and Theory of Structures: Scientific-and-technicalcollectedarticles – Kyiv: KNUBA, 2022. – Issue 109. – P. 50-65.
Ivanchenko H.M., Koshevyi O.O., Koshevyi O.P., Grigoryеva L.O. Chyselne doslidzhennia parametrychnoi optymizatsii vymushenykh chastot kolyvannia obolonky minimalnoi poverkhni na trapetsevydnomu konturi pry termosylovomu navantazhenni (Numerical study of the parametric optimization of the force doscillation frequencies of theshell of a minimal surfaceon a trapezoidal contour under thermal and power loading) // Strength of Materials and Theory of Structures: Scientific-and-technicalcollectedarticles – Kyiv: KNUBA, 2023. – Issue 110. – P. 430-446.
Perelmuter A.V., Perelmuter M.A. Enerhetychna otsinka hranychnoho stanu fizychno neliniinoi konstruktsii (Energy-Based Assessment of the Ultimate Limit State of a Physically Nonlinear Structure) // Strength of Materials and Theory of Structures: Scientific-and-technical collected articles. – K.: KNUCA, 2024. – Issue 113. – P. 56- 62.
Ivanchenko H.M., Koshevyi O.O., Zatyliuk Gh.A Bahatokryterialna parametrychna optymizatsiia peremishchennia i vahy obolonky minimalnoi poverkhni na kruhlomu konturi, shcho skladaietsia iz dvokh pokhylykh elipsiv pry termosylovomu navantazhenni z urakhuvanniam heometrychnoi neliniinosti (Multi-criteria parametric optimization of the displacement and weight of a shell of a minimum surface on a circular contour consisting of two inclined ellipses under thermal and power loading with consideration of geometric nonlinearity) // Strength of Materials and Theory of Structures: Scientific-and-technical collected articles – Kyiv: KNUBA, 2024. – Issue 112. – P. 209-221.
Koshevyi O.O. Optymalne proektuvannia tsylindrychnykh rezervuariv z zhorstkymy obolonkamy pokryttia. (Optimal design of cylindrical tanks with rigid coating shells) // Opirmaterialiv i teoriyasporud: nauk.-tekh. zbirnyk. – K.: KNUBA, 2019. – №. 103. – P. 253-265.
Rozhok L.S., Onishchenko А.M., Kruk L.A., Naidonova Z.М. Chyselnyi analiz napruzhenoho stanu netonkykh hofrovanykh tsylindrychnykh obolonok z neperervno-neodnoridnykh materialiv (Numerical analysis of the stress state of non-thin corrugated cylindrical shells made of continuous-inhomogeneous materials) // Strength of Materials and Theory of Structures: Scientificand-technical collected articles – Kyiv: KNUBA, 2024. – Issue 113. – P. 108-115.
HotsulyakYe.O., Koshevyi O.P., MorskovYu.A. Chyselne modeliuvannia obolonok, utvorenykh minimalnymy poverkhniamy.. (Numerical modeling of shells formed byminimal surfaces). // Prykladna heometriya ta inzhenerna hrafika: nauk.-tekhn. zbirnyk. K.: KNUBA. 2001. №. 69.- P.47-51.
Lizunov P.P., Pogorelova O.S., Postnikova T.G. Optymizatsiia konstruktsii vibroudarnoho dempfera za dopomohoiu instrumentariiu MATLAB (Optimization of a vibro-impact damper design using MATLAB tools) //Strength of Materials and Theory of Structures: Scientific-and-technical collected articles. – K.: KNUBA. 2024. – Issue 112. – P. 3-18.
Lizunov P.P., Lukianchenko O.O., Paliy O.M, Kostina O.V. Vlasni chastoty i formy parametrychnykh kolyvan obolonky rezervuaru z nedoskonalostiamy formy (Natural frequencies and modes of parametric vibrations of reservoir shell with shape imperfections) // Strength of Materials and Theory of Structures. – 2024. – Issue. 112. – Р. 58-66.
Dzyuba A.P., Safronova I.A., Levitina L.D. Chyslove ta eksperymentalne modeliuvannia povedinky hnuchkykh obolonkovykh elementiv konstruktsii (Numerical and experimental modeling of the behavior of flexible shell elements of structures) // Strength of Materials and Theory of Structures: Scientific-and-technical collected articles. – K.: KNUCA, 2023. – Issue 110. – P. 3-20.
Koshevoy A.P. Ustoychivost plastin i obolochekslozhnoyformi (Stability of plates and shells of complexshape) // Soprotivleniyematerialov i teoriyasooruzheniy: nauch.-tekhsbornik. – K.: KISI, 1991. – Vip. 59. – P. 65–71.
Manyta L.A. Uslovyia optymyzatsyy v konechnomernыkh nelyneinыkh zadachakh optymyzatsyy (Optimization condition sinfinite-dimensional nonlinear optimization problems). – M.: Moskovskiy hosudarstvenniy instytuté lektronyky y matematiki, 2010. – 81 p.
Melkumova E.M. O nekotorykh podkhodakh k reshenyiu mnohokryteryalnыkh zadach. (About some approa chestosolving multicriteria problems). // Vestnyk VHU. Seryya Systemnyy analyz y ynformatsyonnye tekhnolohyy. – V.: VHU– №2– 2010– 3 p.
Peleshko I.D., Yurchenko V.V. Optymalne proektuvannia metalevykh konstruktsii na suchasnomu etapi (ohliad prats). (Optimaldesign of metalstructuresatthepresentstage (review of works)). // Metalevi konstruktsiyi: zbirnyk naukovy khprats. – 2009. – №15 – P. 13–21.
Peleshko I.D., Baluk I.M. Optymizatsiia poperechnykh pereriziv stryzhniv stalevykh konstruktsii (Optimization of crosssections of rods of steelstructures) // Zbirnyk naukovy khprats UkrNDIPSKim. V. M. Shymanovskoho. – K.: Stal, №. 4. – 2009. – P. 142–151.
Peleshko I.D., Lisotskyy R.V., Baluk I.M. Optymalne proektuvannia stalevoi stryzhnevoi konstruktsii pokryttia torhovo-rozvazhalnoho kompleksu. (Optimal design of a steel rod coverstructure of a shopping and entertainment complex). // Zbirnyknaukovykhprats UkrNDIPSKim. V. M. Shymanovskoho. – K.: Stal, №. 5. – 2010. – P. 181–191.
Sakharov A.S., Kyslookyy V.N., Kyrychevskyy V.V., Altenbakh Y., Habbert U., Dankert YU., Keppler KH., Kochyk Z. Metod konechnыkh эlementov v mekhanyke tverdыkh tel (Finite element methodin solidmechanics). // VydavnytstvoVyshchashkola. Holovnoeyzdatelstvo – Kyev – 1982. – 480 p.
18.Bazenov V.A., Gaidaichuk V.V., Koshevoy A.P. Stability of multiplyconnectedribbedshells and platesin a magneticfield. // Journal of SovietMathematics 66(6). –1993. – С. 2631–2636.
Cheung Y. K. TheFiniteStripMethod. Them. – BocaRaton. : CRC Press, 1997. – 416 p.
Guest J.K., Prievost J., Belytschko T. Achieving minimum length scale in topology optimization using nodal design variables and projectionfunctions. // International Journal for Numerical Methods in Engineering, 2004. –61(2) – P.238–254.
Kroese D.P., Taimre T., Botev Z.I. Hand book of Monte Carlo Methods. — NewYork: JohnWiley and Sons, 2011. — 772 p.
Downloads
Published
Issue
Section
License
This work is licensed under a Creative Commons Attribution 4.0 International License.
Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
