Multi-criteria parametric optimization of the strength and weight of a shell of a minimum surface on a square contour under thermal and power loading, taking into account geometric nonlinearity
DOI:
https://doi.org/10.32347/2410-2547.2024.113.89-98Keywords:
optimization, parametric optimization, multicriteria optimization, objective function optimization, design variables, constraints, minimum surface envelopes, geometric nonlinearityAbstract
In applied and structural mechanics, many examples of optimal design with different objective functions are considered, but there is a need to take research in this area to a new level. The object under study with two or three simultaneous types of optimization is an actual applied problem in the field of construction and applied mechanics.
One of the main tasks of designing minimal surfaces is to find the optimal shell shapes for given overall dimensions and shape in plan, taking into account parametric optimization - it is necessary to implement a modern optimization algorithm in the calculation of this structure. Its solution should be brought to ready-made formulas, graphs, tables, calculation examples and practical.
The system of solving equations of the finite element method is formed using the Lagrange's variational principle, according to which the total potential energy P of a finite element model of a body is in a state of stability and equilibrium has a minimum value.
Within the framework of the study, a methodology for obtaining the ratio of the finite element method with regard to geometric nonlinearity is presented that does not depend on the shape and properties of the finite elements, so it can be implemented for a plate finite element of a shell of minimal surface.
To study the multicriteria parametric optimization of the minimum surface shell with regard to geometric nonlinearity, a special additional optimizer module created by the authors is used, which is linked to the Femap with Nastran calculation complex [12]. The computational model is built by the finite element method, which makes it possible to perform a qualitative study of optimization taking into account the objective functions: Mises stress and structural weight.
This methodology proves to be effective in the study of multi-criteria parametric optimization with consideration of geometric nonlinearity. Such an approach to the calculation of building structures makes it possible to use structural materials efficiently, and modern calculation complexes based on the finite element method (FEM) can be used in further development at the level of building codes of Ukraine.
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 shell on a square contour under therm force 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 trapetsiiepodibnomu konturi pry termosylovomu navantazhenni (Numerical study of the parametric optimization of the forced oscillation frequencies of the shell 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.
Ivanchenko H.M., Cheverda P.P., Kushnirenko M.H., Kozovenko A.M. Analiz reaktsiy v elementakh prostorovykh skhem pry riznykh sposobakh zyednannya (Analysis of reactions in elements of spatial schemes with different methods of connections) // Opirmaterialiv i teoriyasporud: nauk.-tekh. zbirnyk. – K.: KNUBA, 2012. – Vyp. 90. – P. 163-170.
Koshevyi O.O. Optymalne proektuvannya tsylindrychnykh rezervuariv z zhorstkymy obolonkamy pokryttya. (Optimal design of cylindrical tanks with rigid coating shells) // Opir materialiv i teoriya sporud: nauk.-tekh. zbirnyk. – K.: KNUBA, 2019. – №. 103. – P. 253-265.
Koshevyi O.O. Optymizatsiya stalnoho zvarenoho rezervuaru pry obmezhenni: napruzhen, peremishchen, vlasnykh chasto tkolyvannya. (Optimization of stee lwelded tank with limitations: stresses, displacements, natural frequencies of oscillations). // Budivelni konstruktsiyi. Teoriya i praktyka: nauk.-tekhn. zbirnyk. K.: KNUBA. 2018. №.3.– P.34 – 50.
Hotsulyak Ye.O., Koshevyi O.P., Morskov Yu.A. Chyselne modelyuvannya obolonok, utvorenykh minimalnymy poverkhnyamy. (Numerical modeling of shells formed by minimal surfaces) // Prykladna heometriya ta inzhenerna hrafika: nauk.-tekhn. zbirnyk. K.: KNUBA. 2001. №. 69.- P. 47-51.
Koshevyi O.P. Koshevyi O.O. Chyselne doslidzhennya vlasnykh kolyvan roztyahnutykh obolonok utvorenykh minimalnymy poverkhnyamy. (Numerical study of natural oscillations of stretched shells formed by minimal surfaces) // Mistobuduvannya ta terytorialne planuvannya, №. 55. – Kyiv, KNUBA, 2015. – P. 215-227.
Koshevyi O.P. Koshevyi O.O. Vlasni kolyvannya obolonok minimalnykh poverkhon na kruhlomu ta kvadratnomu konturi. (Own oscillations of shells of minimal surfaces on a round and square contour) // Mistobuduvannya ta terytorialne planuvannya, №. 59. – Kyiv, KNUBA, 2016. – P. 234-244.
Koshevyi O.O., Koshevyi O.P., Hryhoryeva L.O. Chyselna realizatsiya bahatokryterialnoyi parametrychnoyi optymizatsiyi obolonky minimalnoyi poverkhni na pryamokutnomu konturi pry termosylovomu navantazhenni (Numerical implementation of multi-criteria parametric optimization of minimum surface shellon a rectangular contour under therm forced loading) // Opir materialiv i teoriya sporud: nauk.-tekh.zbirnyk. – K.: KNUBA, 2021. – Vyp. 108. – S. 309–324.
Koshevoy A.P. Ustoychivost plastin i obolochek slozhnoy formi (Stability of plates and shells of complex shape) // Soprotivleniye materialov i teoriya sooruzheniy: nauch.-tekh. sbornik. – K.: KISI, 1991. – Vip. 59. – P. 65–71.
Ivanchenko, H., &Kosheviy, O. (2024). Chyselne doslidzhennia stiikosti obolonky minimalnoi poverkhni na kruhlomu plani z urakhuvanniam heometrychnoi neliniinosti pry termosylovomu navantazhenni (Numerical study of the stability of the shell of a minimal surface on a circular plane taking into account geometric nonlinearity under thermal force loading) // Shliakhy pidvyshchennia efektyvnosti budivnytstva v umovakh formuvannia rynkovykh vidnosyn. 2024. № 53. S. 39-48.
Kosheviy, O. (2023). Bahatokryterialna parametrychna optymizatsiia peremishchennia i vahy obolonky minimalnoi poverkhni z priamokutnym planom, yaka skladaietsia z dvokh priamykh linii i dvokh pivkil pry termosylovomu navantazhenni (Multi-criteria parametric optimization of the displacement and weight of a minimal surface shell with a rectangular plan consisting of two straight lines and two semicircles under thermal force loading) // Shliakhy pidvyshchennia efektyvnosti budivnytstva v umovakh formuvannia rynkovykh vidnosyn. 2023. № 52. S. 41-54.
Kosheviy, O. Bahatokryterialna parametrychna optymizatsiia peremishchennia i vahy obolonky minimalnoi poverkhni na trapetsepodibnomu konturi pry termosylovomu navantazhenni (Multi-criteria parametric optimization of the displacement and weight of the shell of a minimal surface on a trapezoidal contour under thermal force loading) // Mizhvidomchyi naukovo-tekhnichnyi zbirnyk: “Prykladna heometriia i inzhenerna hrafika”. 2023. №105. S. 134-150.
Kosheviy, O. Chyselne doslidzhennia stiikosti obolonky minimalnoi poverkhni na kvadratnomu konturi pry termosylovomu navantazhenni z urakhuvanniam heometrychnoi neliniinosti (Numerical study of the stability of the shell of a minimal surface on a square contour under thermal force loading taking into account geometric nonlinearity) // Mizhvidomchyi naukovo-tekhnichnyi zbirnyk: “Prykladna heometriia i inzhenerna hrafika”. 2024. №106. S. 133-147.
Kosheviy, O., Ivanchenko, H., Zatyliuk, G. 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 the shell of a minimal surface on a circular contour consisting of two inclined ellipses under thermal force loading taking into account geometric nonlinearity) // Opir materialiv i teoriia sporud: nauk.-tekh. zbirnyk. – K.: KNUBA, 2024. – Vyp. 112. – S. 209-221.
Sakharov A.S., Kyslookyy V.N., Kyrychevskyy V.V., Altenbakh Y., Habbert U., Dankert Yu., Keppler Kh., Kochyk Z. Metod konechnykh elementov v mekhanyke tverdykh tel (Finite element method in solid mechanics) // Vydavnytstvo Vyshcha shkola. Holovnoe yzdatelstvo – Kyev – 1982. – 480 p.
Bazenov V.A., Gaidaichuk V.V., Koshevoy A.P. Stability of multiply connected ribbed shells and plates in a magnetic field. // Journal of Soviet Mathematics 66(6). –1993. – С. 2631–2636.
Cheung Y. K. The Finite Strip Method. Them. – Boca Raton. : CRC Press, 1997. – 416 p.
Guest J.K., Prievost J., Belytschko T. Achieving minimum length scale in topology optimization using nodal design variables and projection functions // International Journal for Numerical Methods in Engineering, 2004. –61(2) – P.238–254.
Kroese D.P., Taimre T., Botev Z.I. Handbook of MonteCarlo Methods. — New York: John Wiley and Sons, 2011. — 772 p.
Lobo M.S., Vandenbeghe L., Boyd S. Applications of second-order cone programming // Linear Algebra and its Applications. – 1998. – Vol. 284, no. 1. – P. 193–228.
Yonekura K., Kanno Y. Second-order cone programming with warm start for elastoplastic analysi with von mises yield criterion. // Optimization and Engineering. – 2012. – Vol. 13, no. 2. – P. 181–218.
Wasiytynski Z., Brandt A. The present state of knowledge in the field of Optimum design o fstructures. // Appl. Mech. Rew. – 1963. Vol. 16 no. 5. – P. 341-35.
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