Structural Design Optimization of Steel Beams and Frames with Web-Tapered Members Using the PSO-FEM Algorithm
This paper presents an algorithm for structural design optimization of steel beams and frames with web-tapered members using the particle swarm optimization (PSO) algorithm and the finite element method (FEM). The design optimization is done in accordance with Eurocode 3 (EC 3) for the minimum mass. The proposed algorithm is more flexible and efficient than traditional design methods based on a trial and error approach. The effectiveness of the presented PSO-FEM algorithm is evaluated on examples of the size optimization of web-tapered members cross-section. The results show that the PSO-FEM algorithm is feasible and effective for finding useful designs.
Keywordsstructural design optimization, particle swarm optimization, finite element method, FEM, web-tapered members,
References1. H. Aucamp, The optimisation of web-tapered portal frame buildings, Master’s thesis, Stellenbosch University, Republic of South Africa, 2017, https://scholar.sun.ac.za/bitstream/handle/10019.1/101099/aucamp_optmisation_2017.pdf?sequence=1.
2. P. Hradil, M. Mielonen, L. Fülöp, Optimization tools for steel portal frames-effective modelling of lateral supports, Research report VTT-R-00567-11, VTT Technical Research Centre of Finland, Espoo, 2011.
3. R.C. Kaehler, D.W. White, Y.D. Kim, Frame design using web-tapered members, American Institute of Steel Construction, 2011.
4. L. Marques, L.S. da Silva, C. Rebelo, A. Santiago, Extension of EC3-1-1 interaction formulae for the stability verification of tapered beam-columns, Journal of Constructional Steel Research, 100: 122–135, 2014.
5. W.Y. Jeong, Structural analysis and optimized design of general nonprismatic I-section members, Ph.D. thesis, Georgia Institute of Technology, USA, 2014.
6. A. Kaveh, M.H. Ghafari, Geometry and sizing optimization of steel pitched roof frames with tapered members using nine metaheuristics, Iranian Journal of Science and Technology, Transactions of Civil Engineering, 43(1): 1–8, 2019.
7. O. Hasançebi, S. Çarbas, E. Dogan, F. Erdal, M.P. Saka, Comparison of non-deterministic search techniques in the optimum design of real size steel frames, Computers & Structures, 88(17–18): 1033–1048, 2010.
8. R.E. Perez, K. Behdinan, Particle swarm approach for structural design optimization, Computers & Structures, 85(19–20): 1579–1588, 2007, https://www.sciencedirect.com/science/article/abs/pii/S0045794907000399.
9. M.G. Sahab, V.V. Toropov, A.H. Gandomi, A review on traditional and modern structural optimization: problems and techniques, [in:] A.H. Gandomi, X.-S. Yang, S. Talatahari, A.H. Alavi [Eds], Metaheuristic Applications in Structures and Infrastructures, pp. 25–47, Elsevier, 2013, https://www.sciencedirect.com/science/article/pii/
10. P. Christensen, A. Klarbring, An introduction to structural optimization, Springer Science & Business Media, 2009, https://link.springer.com/book/10.1007/978-1-4020-8666-3.
11. M. Kleiber (ed.), Handbook of computational solid mechanics: survey and comparison of contemporary methods, Springer, Berlin, Heidelberg, 1998, https://books.google.pl/books?id=YVvJMAEACAAJ.
12. J. Kennedy, R. Eberhart, Particle swarm optimization, [in:] Proceedings of ICNN’95 – International Conference on Neural Networks, Perth, Australia, Vol. 4, pp. 1942–1948, IEEE, 1995, https://ieeexplore.ieee.org/document/488968.
13. D. Wang, D. Tan, L. Liu, Particle swarm optimization algorithm: an overview, Soft Computing, 22(2): 387–408, 2018, https://link.springer.com/article/10.1007%2Fs00500-016-2474-6.
14. A.H. Gandomi, X.-S. Yang, S. Talatahari, A.H. Alavi, Metaheuristic algorithms in modeling and optimization, [in:] Metaheuristic Applications in Structures and Infrastructures, pp. 1–24, Elsevier, 2013, https://www.sciencedirect.com/science/article/pii/B9780123983640000012.
15. EN 1993, Eurocode 3: Design of steel structures, CEN, 2004.
16. M.P. Saka, Optimum design of steel frames with tapered members, Computers & Structures, 63(4): 797–811, 1997.
17. P. Hradil, M. Mielonen, L. Fülöp, Advanced design and optimization of steel portal frames, Journal of Structural Mechanics, 43(1): 44–60, 2010.
18. M.J. Turner, R.W. Clough, H.C. Martin, L.J. Topp, Stiffness and deflection analysis of complex structures, Journal of the Aeronautical Sciences, 23(9): 805–823, 1956.
19. O. Zienkiewicz, The finite element method, 3rd ed., McGraw-Hill, New York, 1977.
20. F. Sahin, A. Devasia, Distributed particle swarm optimization for structural Bayesian network learning, [in:] F. Chan, M.K. Tiwari [Eds], Swarm Intelligence, Focus on Ant and Particle Swarm Optimization, pp. 532 IntechOpen, Vienna, Austria, 2007, https://www.intechopen.com/books/swarm_intelligence_focus_on_ant_and_particle_swarm_optimization/distributed_particle_swarm_optimization_for_structural_bayesian_network_learning.