Numerical implementation of multicriteria parametric optimization of minimum surface shell on a rectangular contour under the rmalloading

Authors

DOI:

https://doi.org/10.32347/2410-2547.2022.108.309-324

Keywords:

optimization, parametric optimization, multicriteria parametric optimization, shape optimization, topological optimization, minimum surface shell, objective function, pair of objective functions, design variables, constraints, limit, Mises stress

Abstract

The article considers the numerical study of multicriteria optimization of the minimum surface shell of a rectangular contour taking into account the thermal load. The authors cover the theoretical formulation of multicriteria parametric optimization. A method of constructing this minimal surface on a rectangular contour is described. The specifics of the issuance of thermal power load in the optimization calculation, which is in all initial indicators and coefficients. The types of work of target functions are shown, namely: under what conditions they conflict, under what conditions they consolidate, under what conditions they are independent of each other. The numerical study uses the author's software, which allows in automatic mode a multicriteria optimization calculation with target functions - weight and Mises stress, design variables - thickness from 1 to 200 mm, presented as a Mises voltage of 240 MPa. The result showed that the target functions of the conflict change, but the weight decreases by 20%, and the Mises voltage decreases by 37% of the elements. From the graph of the change of objective functions according to the optimal height, what is the point for the objective functions - weight and stress according to Mises is absence. The overall purpose of the study shows the possibility of using authoring software to use two types of optimization: optimization of shapes in the form of these minimum surface parameters on rectangular and multicriteria optimization together on the object under study, which is interesting and applied research in structural mechanics.

Author Biographies

Oleksandr Koshevyi, Kyiv National University of Construction and Architecture

Doctor of Philosophy, Associate Professor of the Department of Theoretical Mechanics

Oleksandr Koshevyi, Kyiv National University of Construction and Architecture

Candidate of Technical Science, Associate Professor, Head of the Department of Strength of Materials

Liudmyla Grigoryеva, Kyiv National University of Construction and Architecture

Candidate of Physical and Mathematical Science, Associate Professor of the Department Strength of Materials

References

Herasymov, E.N., Pochtman YU.M., Skalozub V.V. Mnohokryteryalʹnaya optymyzatsyya konstruktsyy (Multicriteria optimization of structures). – Donetsk: Vyshchashk. HlavnoeYzd-vo – Kyev – 1985 – 134 s.

Hyll F., Myurrey U., Rayt M. Praktycheskaya optymyzatsyya (Practical optimization). – M.: Myr, 1985. – 509 s.

Ihnatyshyn M.I. Mekhaniko-matematychne modelyuvannya elementiv mostovykh konstruktsiy (opora, balka, plyta) (Mechanical and mathematical modeling of elements of bridge structures (support, beam, slab)): monohrafiya. – Mukachevo: RVV MDU, 2017. – 172 s.

Koshevyy O.O. Optymalʹne 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. – Vyp. 103. – S. 253-265.

Koshevyy O.O. Optymizatsiya stalʹnoho zvarenoho rezervuaru pry obmezhenni: napruzhenʹ, peremishchenʹ, vlasnykh chastot kolyvannya (Optimization of steel welded tank with limitation: stresses, displacements, natural frequencies of oscillations) // Budivelʹni konstruktsiyi. Teoriya i praktyka: nauk.-tekhn. zbirnyk. K.: KNUBA. 2018. Vyp.3.– S.34 – 50.

Hotsulyak Ye.O., Koshevyy O.P., Morskov Yu.A. Chyselʹne modelyuvannya obolonok, utvorenykh minimalʹnymy poverkhnyamy (Numerical modeling of shells formed by minimal surfaces) // Prykladna heometriya ta inzhenerna hrafika: nauk.-tekhn. zbirnyk. K.: KNUBA. 2001. Vyp. 69.- S.47-51.

Koshevyy O.P. Koshevyy O.O. Chyselʹne doslidzhennya vlasnykh kolyvanʹ roztyahnutykh obolonok utvorenykh minimalʹnymy poverkhnyamy (Numerical study of natural oscillations of stretched shells formed by minimal surfaces) // Mistobuduvannya ta terytorialʹne planuvannya, Vyp. 55. – Kyyiv, KNUBA, 2015. – s. 215-227.

Koshevyy O.P. Koshevyy O.O. Vlasni kolyvannya obolonok minimalʹnykh poverkhonʹ na kruhlomu ta kvadratnomu konturi (Own oscillations of shells of minimal surfaces on a round and square contour) // Mistobuduvannya ta terytorialʹneplanuvannya, Vyp. 59. – Kyyiv, KNUBA, 2016. – s. 234-244

Kryvoshapko S.V., Yvanov V.N., Khalaby S.M. Analytycheskye poverkhnosty: materyaly po heometryy 500 poverkhnostey y ynformatsyya k raschetu na prochnostʹ tonkykh obolochek (Analytical surfaces: materials on the geometry of 500 surfaces and information for the calculation of the strength of thin shells). – M.: Nauka, 2006. – 544 s.

Manyta, L.A. Uslovyya optymyzatsyy v konechnomernykh nelyneynykh zadachakh optymyzatsyy (Optimization conditions in finite-dimensional nonlinear optimization problems). – M.: Moskovskyy hosudarstvennyy ynstytut élektronyky y matematyky, 2010. – 81 s.

Melʹkumova E.M. O nekotorykh podkhodakh k reshenyyu mnohokryteryalʹnykh zadach (About some approaches to solving multicriteria problems) // Vestnyk VHU. Seryya Systemnyy analyz y ynformatsyonnye tekhnolohyy. – V.: VHU– №2– 2010– 3 s.

Peleshko I.D., Yurchenko V.V. Optymalʹne proektuvannya metalevykh konstruktsiy na suchasnomu etapi (ohlyad pratsʹ) (Optimal design of metal structures at the present stage (review of works)) // Metalevi konstruktsiyi: zbirnyk naukovykh pratsʹ. – 2009. – №15 – S. 13–21.

Peleshko I.D., Baluk I.M. Optymizatsiya poperechnykh pereriziv stryzhniv stalevykh konstruktsiy (Optimization of cross sections of rods of steel structures). // Zbirnyk naukovykh pratsʹ UkrNDIPSKim. V. M. Shymanovsʹkoho. – K.: Stalʹ, Vyp. 4. – 2009. – S. 142–151.

Peleshko I.D., Lisotsʹkyy R.V., Baluk I.M. Optymalʹne proektuvannya stalevoyi stryzhnevoyi konstruktsiyi pokryttya torhovo-rozvazhalʹnoho kompleksu (Optimal design of a steel rod cover structure of a shopping and entertainment complex) // Zbirnyk naukovykh pratsʹ UkrNDIPSKim. V. M. Shymanovsʹkoho. – K.: Stalʹ, Vyp. 5. – 2010. – S. 181–191.

Sakharov A.S., Kyslookyy V.N., Kyrychevskyy V.V., Alʹtenbakh Y., Habbert U., Dankert YU., Keppler KH., Kochyk Z. Metod konechnykh élementov v mekhanyke tverdykh tel (Finite element method in solid mechanics) // Vydavnytstvo Vyshcha shkola. Holovnoe yzdatelʹstvo – Kyev, 1982. – 480 s.

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 Monte Carlo 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 analysis 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 of structures. // Appl. Mech. Rew. – 1963. Vol. 16 no. 5. – P. 341-35.

Published

2022-05-30

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