Structure of Optimal Control in Optimal Shaping of the Steel Arch

• Autorzy: Mikulski Leszek , Jasińska Dorota , Dąbrowska Olga

Identyfikatory

DOI

10.2478/ceer-2022-0033

• Języki publikacji: EN

Abstrakty

EN

The paper presents the problem of optimal shaping of the H-bar cross-section of a steel arch that ensures minimal mass. Nineteen combinations of nine basic load states are considered simultaneously in the problem formulation. The optimal shaping task is formulated as a control theory problem within the formal structure of the maximum Pontriagin’s principle. Since the ranges of constraint activity defining the control structure are a priori unknown and must be determined numerically, assuming the proper control structure plays a key role in the task solution. The main achievement of the present work is the determination of a solution of the multi-decision and multi-constraint optimization problem of the arch constituting a primary structural system of the existing building assuring the reduction of the structure mass up to 42%. In addition, the impact of the assumed state constraint value on the solution structure is examined.

Słowa kluczowe

EN

shape optimization; optimal control; steel arch; shaping the cross-section

PL

optymalizacja kształtu; optymalna kontrola; łuk stalowy; kształtowanie przekroju

• Wydawca: Oficyna Wydawnicza Uniwersytetu Zielonogórskiego
• Czasopismo: Civil and Environmental Engineering Reports
• Rocznik: 2022
• Tom: Vol. 32, no. 3
• Strony: 143--165
• Opis fizyczny: Bibliogr. 31 poz., rys., tab., wykr.

Twórcy

autor

Mikulski Leszek

• Faculty of Civil Engineering, Cracow University of Technology

autor

Jasińska Dorota

• Faculty of Civil Engineering, Cracow University of Technology

autor

Dąbrowska Olga

• Faculty of Civil Engineering, Cracow University of Technology

Bibliografia

• 1. Allen, E and Zalewski, W 2009. Form and Forces: Designing Efficient, Expressive Structures. Hoboken:John Wiley \& Sons, Incorporated.
• 2. Bessini, J, Shepherd, P, Monleón, S and Lázaro, C 2020. Design of bending-active tied arches by using a multi-objective optimization method. Structures. 27. 2319-2328.
• 3. EN 1991-1-1: Eurocode 1: Actions on structures - Part 1-1: General actions - Densities, self-weight, imposed loads for buildings [Authority: The European Union Per Regulation 305/2011, Directive 98/34/EC, Directive 2004/18/EC].
• 4. Fiore, A, Marano, GC, Greco, R and Mastromarino, E 2016. Structural optimization of hollow-section steel trusses by differential evolution algorithm. Int. J. Steel Struct 16(2). 411–423.
• 5. Hartl, RF, Sethi, SP and Vickson, RG 1995. A Survey of the Maximum Principles for Optimal Control Problems with State Constraints. SIAM Rev. 37 (2). 181–218.
• 6. Jasińska, D and Kropiowska, D 2018. The Optimal Design of an Arch Girder of Variable Curvature and Stiffness by Means of Control Theory. Math. Probl. Eng. 2018 p. 8239464.
• 7. Karamzin, D and Pereira, FL 2019. On a Few Questions Regarding the Study of State-Constrained Problems in Optimal Control. J. Optim. Theory Appl. 180 (1). 235-255.
• 8. Kimura, T, Ohsaki, M.; Fujita, S, Michiels, T and Adriaenssens, S 2020. Shape optimization of no-tension arches subjected to in-plane loading. Structures. 28. 158–169.
• 9. Korytowski, A and Szymkat, M 2021. Necessary Optimality Conditions for a Class of Control Problems with State Constraint. Games. 12(9), doi:10.3390/g12010009.
• 10. Kropiowska, D and Mikulski, L 2009.Optimal design of two-hinged arches of the rational centre line. Pomiary Autom. Kontrola. 55(6). 338–341.
• 11. Kropiowska, D, Mikulski, L and Styrna, M 2012. Optimal shaping of elastic arches in terms of stability. Pomiary Autom. Kontrola . 58(10). 896–900.
• 12. Laskowski,H, Mikulski,L and Ostaficzuk, J 2007. Theoretical solutions and their practical applications in structure optimization. Pomiary Autom. Kontrola. 53(8). 38–43.
• 13. Lewis, WJ 2016. Mathematical model of a moment-less arch. Proceedings. Math. Phys. Eng. Sci. 472(2190). 20160019.
• 14. Mao, Y, Dueri, D, Szmuk, M and Açıkmeşe, B 2017. Successive Convexification of Non-Convex Optimal Control Problems with State Constraints. IFAC-PapersOnLine. 50(1). 4063–4069.
• 15. Marano, G.C, Trentadue, F and Petrone, F 2014. Optimal arch shape solution under static vertical loads. Acta Mech. 225(3). 679–686.
• 16. Marano, G.C, Trentadue, F, Greco, R, Vanzi, I and Briseghella, B 2018. Volume/thrust optimal shape criteria for arches under static vertical loads. J. Traffic Transp. Eng. 5(6). 503–509.
• 17. Mikulski, L 2004. Control Structure in Optimization Problems of Bar Systems. Int. J. Appl. Math. Comput. Sci. 14(4). 515–529.
• 18. Mikulski, L 2007. Theory of Control in Optimization of Structures and Systems (Teoria sterowania w problemach optymalizacji konstrukcji i systemów). Cracow. Cracow University of Technology Press.
• 19. Mikulski, L 2019. The Structure of the Optimal Control in the Problems of Strength Optimization of Steel Girders. Arch. Civ. Eng. 65(4). 277–293.
• 20. Nodargi, NA and Bisegna, P 2020. Thrust line analysis revisited and applied to optimization of masonry arches. Int. J. Mech. Sci.179(2).105690.
• 21. Pesch, HJ 1996. A practical guide to the solution of real-life optimal control problems, Control Cybern. 23(1).7–60.
• 22. Pesch, HJ and Plail, M 2009. The Maximum Principle of optimal control : A history of ingenious ideas and missed opportunities. Control Cybern. 38(4). 973-995.
• 23. Pipinato, A 2018. Structural Optimization of Network Arch Bridges with Hollow Tubular Arches and Chords. Mod. Appl. Sci. 12(2). 36-53.
• 24. Trentadue, F, Marano, G.C.; Vanzi, I and Briseghella, B 2018. Optimal arches shape for single-point-supported deck bridges. Acta Mech. 229(5). 2291–2297.
• 25. Trentadue, F, Fiore, A, Greco, R, Marano, GC and Lagaros, ND 2020. Structural optimization of elastic circular arches and design criteria. Procedia Manuf. 44. 425–432.
• 26. Trentadue, F et al. 2020. Volume optimization of end-clamped arches. Hormigon y Acero. 71. 71–76.
• 27. Trentadue, F, Fiore, A, Greco, R, Marano, GC and Lagaros, ND 2020. Optimal Design of Elastic Circular Plane Arches. Front. Built Environ. 6. art.74.
• 28. Vanderplaats, GN and Han, SH 1990. Arch shape optimization using force approximation methods. Struct. Optim. 2(4). 193–201.
• 29. von Stryk, O 2002. Users Guide. A Direct Collocation Method for the Numerical Solution of Optimal Control Problems. Darmstadt. TU Darmstadt press.
• 30. Wang, CY and Wang, CM 2015. Closed-form solutions for funicular cables and arches. Acta Mech. 226(5). 1641–1645.
• 31. Wilson, A 2005. Practical Design of Concrete Shells. Italy(TX). Monolithic Dome Institute.

Uwagi

Opracowanie rekordu ze środków MEiN, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2022-2023)