Structure of Optimal Control in Optimal Shaping of the Steel Arch
More details
Hide details
Cracow University of Technology
Online publication date: 2022-10-13
Publication date: 2022-09-01
Civil and Environmental Engineering Reports 2022;32(3):143-165
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.
Allen, E and Zalewski, W 2009. Form and Forces: Designing Efficient, Expressive Structures. Hoboken:John Wiley \& Sons, Incorporated.
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.
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].
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.
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.
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.
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.
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.
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.
Kropiowska, D and Mikulski, L 2009.Optimal design of two-hinged arches of the rational centre line. Pomiary Autom. Kontrola. 55(6). 338–341.
Kropiowska, D, Mikulski, L and Styrna, M 2012. Optimal shaping of elastic arches in terms of stability. Pomiary Autom. Kontrola. 58(10). 896–900.
Laskowski,H, Mikulski,L and Ostaficzuk, J 2007. Theoretical solutions and their practical applications in structure optimization. Pomiary Autom. Kontrola. 53(8). 38–43.
Lewis, WJ 2016. Mathematical model of a moment-less arch. Proceedings. Math. Phys. Eng. Sci. 472(2190). 20160019.
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.
Marano, G.C, Trentadue, F and Petrone, F 2014. Optimal arch shape solution under static vertical loads. Acta Mech. 225(3). 679–686.
Marano, GC, 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.
Mikulski, L 2004. Control Structure in Optimization Problems of Bar Systems. I nt.J.Appl.Math.Comput.Sci. 14(4). 515–529.
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.
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.
Nodargi, NA and Bisegna, P 2020. Thrust line analysis revisited and applied to optimization of masonry arches. Int. J. Mech. Sci. 179(2).105690.
Pesch, HJ 1996. A practical guide to the solution of real-life optimal control problems, Control Cybern. 23(1).7–60.
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.
Pipinato, A 2018. Structural Optimization of Network Arch Bridges with Hollow Tubular Arches and Chords. Mod. Appl. Sci. 12(2). 36–53.
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.
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.
Trentadue, F et al. 2020. Volume optimization of end-clamped arches. Hormigon y Acero. 71. 71–76.
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.
Vanderplaats, GN and Han, SH 1990. Arch shape optimization using force approximation methods. Struct. Optim. 2(4). 193–201.
von Stryk, O 2002. Users Guide. A Direct Collocation Method for the Numerical Solution of Optimal Control Problems. Darmstadt. TU Darmstadt press.
Wang, CY and Wang, CM 2015. Closed-form solutions for funicular cables and arches. Acta Mech. 226(5). 1641–1645.
Wilson, A 2005. Practical Design of Concrete Shells. Italy(TX). Monolithic Dome Institute.
Journals System - logo
Scroll to top