Investigation of notch effect in the optimum weight design of steel truss towers via Particle Swarm Optimization and Firefly Algorithm

Abstract

In this study, the optimal weight designs of steel truss towers are determined, considering the notch effect. Thus, the impact of discontinuities in the cross-sections of steel elements on the total weight of the structure is revealed. For this purpose, the optimal weight designs of different truss towers analyzed by other researchers in previous years are reexamined using Particle Swarm Optimization and Firefly Algorithm. The main program where finite element analyses and optimization algorithms are encoded has been developed in MATLAB. Displacement, stress, geometric, and section height constraints are used in optimization methods. The effectiveness of these methods has been demonstrated by comparing both the results in the literature and with each other under un-notched conditions. Subsequently, considering the notch effect on the tension bar with the highest stress capacity in each structure, the impact of stress concentration on the minimum weight sizing of the structure is investigated using these proven methods. When the analysis results of both cases are examined, it is observed that the optimum weights of all structures under the notch effect have slightly increased. The stress concentration around the notch severely raises the nominal stress in the cross-section. In this case, the cross-section becomes insufficient due to the overcapacity, requiring larger profiles. The structure’s weight shows an increasing trend depending on the number of notched elements and the severity of stress concentration. Additionally, SAP2000 software is utilized for numerical simulations of the structures under identical conditions, enhancing the research content and providing further support for the comprehensive design optimization analyses. Consequently, minimizing the adverse effects of notches through careful material selection, proper manufacturing and assembly techniques, and regular maintenance is essential. The effects of notches should be considered in structural analysis and design, with measures taken to mitigate these effects when necessary.

Graphical abstract

Keywords

steel truss towers / optimum weight design / notch effect / particle swarm optimization / firefly algorithm

References

[1] Wang L, Xi R, Guo X, Ma Y. The structural design and optimization of top-stiffened double-layer steel truss bridges based on the response surface method and particle swarm optimization. Applied Sciences, 2023, 13(19): 11033

[2] Aydogdu I, Ormecioglu T O, Tunca O, Carbas S. Design of large-scale real-size steel structures using various modified grasshopper optimization algorithms. Neural Computing & Applications, 2022, 34(16): 13825–13848

[3] Kaveh A, Amirsoleimani P, Dadras Eslamlou A, Rahmani P. Frequency-constrained optimization of large-scale dome-shaped trusses using chaotic water strider algorithm. Structures, 2021, 32: 1604–1618

[4] Carvalho J P G, Carvalho É C R, Vargas D E C, Hallak P H, Lima B S L P, Lemonge A C C. Multi-objective optimum design of truss structures using differential evolution algorithms. Computers & Structures, 2021, 252: 106544

[5] Awad R. Sizing optimization of truss structures using the political optimizer (PO) algorithm. Structures, 2021, 33: 4871–4894

[6] Kaveh A, Biabani Hamedani K, Milad Hosseini S, Bakhshpoori T. Optimal design of planar steel frame structures utilizing meta-heuristic optimization algorithms. Structures, 2020, 25(3): 335–346

[7] Carvalho J P G, Lemonge A C C, Hallak P H, Vargas D E C. Simultaneous sizing, shape, and layout optimization and automatic member grouping of dome structures. Structures, 2020, 28: 2188–2202

[8] Kaveh A, Seddighian M R. Simultaneously multi-material layout, and connectivity optimization of truss structures via an enriched firefly algorithm. Structures, 2020, 27: 2217–2231

[9] Kaveh A, Mahjoubi S. Optimum design of double-layer barrel vaults by lion pride optimization algorithm and a comparative study. Structures, 2018, 13: 213–229

[10] Kaveh A, Moradveisi M. Optimal design of double-layer barrel vaults using CBO and ECBO algorithms. Civil Engineering, 2016, 40(3): 167–178

[11] Tejani G G, Savsani V J, Patel V K. Adaptive symbiotic organisms search (SOS) algorithm for structural design optimization. Journal of Computational Design and Engineering, 2016, 3(3): 226–249

[12] Gonçalves M S, Lopez R H, Miguel L F F. Search group algorithm: A new metaheuristic method for the optimization of truss structures. Computers & Structures, 2015, 153: 165–184

[13] Dede T, Atmaca B, Grzywinski M, Venkata Rao R. Optimal design of dome structures with recently developed algorithm: Rao series. Structures, 2022, 42: 65–79

[14] Kaveh A, Khayatazad M. Ray optimization for size and shape optimization of truss structures. Computers & Structures, 2013, 117: 82–94

[15] DegertekinS O. Improved harmony search algorithms for sizing optimization of truss structures. Computers & Structures, 2012, 92–93: 229–241

[16] Kaveh A, Zolghadr A. Democratic PSO for truss layout and size optimization with frequency constraints. Computers & Structures, 2014, 130: 10–21

[17] Gomes H M. Truss optimization with dynamic constraints using a particle swarm algorithm. Expert Systems with Applications, 2011, 38(1): 957–968

[18] ZhuJ JZhaoG BSunY M. Optimization of steel lattice trusses considering members stability. Applied Mechanics and Materials, 2014, 578–579: 97–105

[19] KavehAMirzaeiBJafarvandA. Shape-size optimization of single-layer barrel vaults using improved magnetic charged system search. International Journal of Civil Engineering, 2014, 12(4)

[20] Keleş M, Artar M, Ergün M. Investigation of temperature effect on the optimal weight design of steel truss bridges using Cuckoo Search Algorithm. Structures, 2023, 2024: 59

[21] Es-Haghi M S, Shishegaran A, Rabczuk T. Evaluation of a novel Asymmetric Genetic Algorithm to optimize the structural design of 3D regular and irregular steel frames. Frontiers of Structural and Civil Engineering, 2020, 14(5): 1110–1130

[22] Bekdaş G, Yücel M, Nigdeli S M. Estimation of optimum design of structural systems via machine learning. Frontiers of Structural and Civil Engineering, 2021, 15(6): 1441–1452

[23] Degertekin S O, Tutar H, Lamberti L. School-based optimization for performance-based optimum seismic design of steel frames. Engineering with Computers, 2021, 37(4): 3283–3297

[24] Kumar S, Tejani G G, Pholdee N, Bureerat S. Performance enhancement of meta-heuristics through random mutation and simulated annealing-based selection for concurrent topology and sizing optimization of truss structures. Soft Computing, 2022, 26(12): 5661–5683

[25] Carbas S, Tunca O. Numerical design optimization of real size complex steel space frame structures using a novel adaptive cuckoo search method. International Journal for Numerical Methods in Engineering, 2024, 125(4): e7386

[26] Tayfur B, Yilmaz H, Daloğlu A T. Hybrid tabu search algorithm for weight optimization of planar steel frames. Engineering Optimization, 2021, 53(8): 1369–1383

[27] Cao T S, Nguyen T T T, Nguyen V S, Truong V H, Nguyen H H. Performance of six metaheuristic algorithms for multi-objective optimization of nonlinear inelastic steel trusses. Buildings, 2023, 13(4): 868

[28] Li P, Zhao X, Ding D, Li X, Zhao Y, Ke L, Zhan X, Jian B. Optimization design for steel trusses based on a Genetic Algorithm. Buildings, 2023, 13(6): 1496

[29] Zakian P. Meta-heuristic design optimization of steel moment resisting frames subjected to natural frequency constraints. Advances in Engineering Software, 2019, 135(4): 102686

[30] Abbasi M, Zakian P. Optimal design of truss domes with frequency constraints using seven metaheuristic algorithms incorporating a comprehensive statistical assessment. Mechanics of Advanced Materials and Structures, 2024, 31(30): 12533–12559

[31] Zakian P, Kaveh A. Multi-objective seismic design optimization of structures: A Review. Archives of Computational Methods in Engineering, 2024, 31(2): 579–594

[32] Yaren Aydoğdu A, Artar M, Ergün M. Optimum weight design of steel truss roof systems considering corrosion effect. Structures, 2023, 49(January): 88–105

[33] Pham H A, Tran T D. Optimal truss sizing by modified rao algorithm combined with feasible boundary search method. Expert Systems with Applications, 2022, 191: 116337

[34] Carbas S, Artar M. Optimum design of cold-formed steel frames via five novel nature-inspired metaheuristic algorithms under consideration of seismic loading. Structures, 2021, 33(7): 4011–4030

[35] Lemonge A C C, Carvalho J P G, Hallak P H, Vargas D E C. Multi-objective truss structural optimization considering natural frequencies of vibration and global stability. Expert Systems with Applications, 2021, 165: 113777

[36] Makiabadi M H, Maheri M R. An enhanced symbiotic organism search algorithm (ESOS) for the sizing design of pin connected structures. Civil Engineering, 2021, 45(3): 1371–1396

[37] Kaveh A, Biabani Hamedani K, Joudaki A, Kamalinejad M. Optimal analysis for optimal design of cyclic symmetric structures subject to frequency constraints. Structures, 2021, 33: 3122–3136

[38] Degertekin S O, Yalcin Bayar G, Lamberti L. Parameter free jaya algorithm for truss sizing-layout optimization under natural frequency constraints. Computers & Structures, 2021, 245: 106461

[39] EberhartRKennedyJ. A new optimizer using particle swarm theory. In: Proceedings of the Sixth International Symposium on Micro Machine and Human Science. Nagoya: IEEE, 1995, 39–43

[40] YangX S. Firefly algorithms for multimodal optimization. In: Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Berlin: Springer, 2009, 169–178

[41] Ming-Zhu D. An improved templeman’s algorithm for the optimum design of trusses with discrete member sizes. Engineering Optimization, 1986, 9(4): 303–312

[42] Rajeev S, Krishnamoorthy C S. Discrete optimization of structures using genetic algorithms. Journal of Structural Engineering, 1992, 118(5): 1233–1250

[43] Erbatur F, Hasançebi O, Tütüncü İ, Kılıç H. Optimal design of planar and space structures with genetic algorithms. Computers & Structures, 2000, 75(2): 209–224

[44] Zhang Y, Hou Y, Liu S. A new method of discrete optimization for cross-section selection of truss structures. Engineering Optimization, 2014, 46(8): 1052–1073

[45] Venkayya V B. Design of optimum structures. Computers & Structures, 1971, 1(1–2): 265–309

[46] Xicheng W, Guixu M. A parallel iterative algorithm for structural optimization. Computer Methods in Applied Mechanics and Engineering, 1992, 96(1): 25–32

[47] GellatlyRBerkeL. Optimal Structural Design. Technical Report AFFDL-TR-70-165. 1971

[48] Kaveh A, Gholipour Y, Rahami H. Optimal design of transmission towers using Genetic Algorithm and Neural Networks. International Journal of Space Structures, 2008, 23(1): 1–19

[49] ArtarMDalogluA T. Teaching learning based optimum design of transmission tower structures. In: Nature-Inspired Computing book series (STNIC). Singapore: Springer, 2021, 49–64.

[50] Wu S J, Chow P T. Steady-state genetic algorithms for discrete optimization of trusses. Computers & Structures, 1995, 56(6): 979–991

[51] Li Y, Lian S. Improved fruit fly optimization algorithm incorporating tabu search for optimizing the selection of elements in trusses. KSCE Journal of Civil Engineering, 2018, 22(12): 4940–4954

[52] Li Y, Wang S, Han M. Truss structure optimization based on improved chicken swarm optimization algorithm. Advances in Civil Engineering, 2019, 2019(1): 1–16

[53] Hasançebi O, Çarbaş S, Doǧan E, Erdal F, Saka M P. Performance evaluation of metaheuristic search techniques in the optimum design of real size pin jointed structures. Computers & Structures, 2009, 87(5–6): 284–302

[54] Artar M, Daloğlu A. Optimum design of steel space truss towers under seismic effect using jaya algorithm. Structural Engineering and Mechanics, 2019, 71(1): 1

[55] Artar M. A comparative study on optimum design of multi-element truss structures. Steel and Composite Structures, 2016, 22(3): 521–535

[56] SAP2000. Structural Analysis Program. California. Computers and Structures Inc. 2022

[57] MATLAB. The Language of Technical Computing. Natick, MA, The Mathworks. 2009

[58] AISC-ASD. Manual of Steel Construction: Allowable Stress Design. Chicago, IL: American Institute of Steel Construction, 1989

[59] Apostolopoulos T, Vlachos A. Application of the Firefly Algorithm for Solving the Economic Emissions Load Dispatch Problem. International Journal of Combinatorics, 2011, 2011: 1–23

[60] YaylaP. Cisimlerin Mukavemeti. Istanbul: Çağlayan Book & Publishing and Education, 2022

Competing interests

The authors declare that they have no competing interests.

RIGHTS & PERMISSIONS

2025 Higher Education Press