APPLICATIONS OF MONTE CARLO SIMULATION TO STRUCTURAL ENGINEERING PROBLEMS
Keywords:
Structural Engineering, Optimization, Monté Carlo, Simulation, Metaheuristic
Abstract
This paper investigates the application of Monte Carlo simulations in structural engineering to address various design optimization and uncertainty analysis. These applications include its uses in solving optimization problems and conducting uncertainty analysis. Three design problems are presented which are the design of a pressure vessel, the design of a rectangular welded beam, and the design of a compression spring. The performance of the Monte Carlo simulation along with other metaheuristic algorithms is compared numerically in the example problems. The comparison shows that the Monte Carlo simulation is a valid technique for structural design problems. The study concludes that despite its limitations, the simplicity and ease of implementation render Monte Carlo simulations an attractive option for structural design optimization scenarios where computational complexity may pose challenges.
References
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2. B. K. Kannan and S. N. Kramer, An Augmented Lagrange Multiplier Based Method for Mixed Integer Discrete Continuous Optimization and Its Applications to Mechanical Design, Journal of Mechanical Design, vol. 116, no. 2, pp. 405–411, Jun. 1994, doi: https://www.doi.org/10.1115/1.2919393.
3. S. S. Rao, Engineering Optimization: Theory and Practice. Wiley, 2019.
4. M.-J. Kazemzadeh-Parsi, A modified firefly algorithm for engineering design optimization problems, Iranian Journal of Science and Technology - Transactions of Mechanical Engineering, vol. 38, pp. 403–421, Jan. 2014.
5. L. D. S. Coelho, Gaussian quantum-behaved particle swarm optimization approaches for constrained engineering design problems, Expert Systems with Applications, vol. 37, no. 2, pp. 1676–1683, Mar. 2010, doi: https://www.doi.org/10.1016/j.eswa.2009.06.044.
6. L. Cagnina, S. Esquivel, and C. Coello, Solving Engineering Optimization Problems with the Simple Constrained Particle Swarm Optimizer, Informatica (Slovenia), 2008.
7. E. Mezura-Montes, C. A. Coello Coello, J. Velázquez-Reyes, and L. Muñoz-Dávila, Multiple trial vectors in differential evolution for engineering design, Engineering Optimization, vol. 39, no. 5, pp. 567–589, Jul. 2007, doi: https://www.doi.org/10.1080/03052150701364022.
8. K. Deb, GeneAS: A Robust Optimal Design Technique for Mechanical Component Design, D. Dasgupta and Z. Michalewicz, Eds., Berlin, Heidelberg: Springer Berlin Heidelberg, 1997, pp. 497–514. doi: https://www.doi.org/10.1007/978-3-662-03423-1_27.
9. K. S. Lee and Z. W. Geem, A new meta-heuristic algorithm for continuous engineering optimization: harmony search theory and practice, Computer Methods in Applied Mechanics and Engineering, vol. 194, no. 36–38, pp. 3902–3933, Sep. 2005, doi: https://www.doi.org/10.1016/j.cma.2004.09.007.
10. S. He, E. Prempain, and Q. H. Wu, An improved particle swarm optimizer for mechanical design optimization problems, Engineering Optimization, vol. 36, no. 5, pp. 585–605, Oct. 2004, doi: https://www.doi.org/10.1080/03052150410001704854.
11. Xiaohui Hu, R. C. Eberhart, and Yuhui Shi, Engineering optimization with particle swarm, Proceedings of the 2003 IEEE Swarm Intelligence Symposium. SIS’03 (Cat. No.03EX706), pp. 53–57, 2003, doi: https://www.doi.org/10.1109/SIS.2003.1202247.
12. C. A. Coello Coello, Use of a self-adaptive penalty approach for engineering optimization problems, Computers in Industry, vol. 41, no. 2, pp. 113–127, Mar. 2000, doi: https://www.doi.org/10.1016/S0166-3615(99)00046-9.
13. A. Kaveh and S. Talatahari, Engineering Optimization With Hybrid Particle Swarm And Ant Colony Optimization, 2009.
14. T. Ray and P. Saini, Engineering Design Optimization Using A Swarm With An Intelligent Information Sharing Among Individuals, Engineering Optimization, vol. 33, no. 6, pp. 735–748, Aug. 2001, doi: https://www.doi.org/10.1080/03052150108940941.
15. C. A. Coello Coello and E. Mezura Montes, Constraint-handling in genetic algorithms through the use of dominance-based tournament selection, Advanced Engineering Informatics, vol. 16, no. 3, pp. 193–203, Jul. 2002, doi: https://www.doi.org/10.1016/S1474-0346(02)00011-3.
16. C. Zhang and H.-P. (Ben) Wang, Mixed-Discrete Nonlinear Optimization With Simulated Annealing, Engineering Optimization, vol. 21, no. 4, pp. 277–291, Sep. 1993, doi: https://www.doi.org/10.1080/03052159308940980.
17. A. H. Gandomi, X.-S. Yang, and A. H. Alavi, Cuckoo search algorithm: a metaheuristic approach to solve structural optimization problems, Engineering with Computers, vol. 29, no. 1, pp. 17–35, Jan. 2013, doi: https://www.doi.org/10.1007/s00366-011-0241-y.
18. E. Mezura-Montes and C. A. C. Coello, An empirical study about the usefulness of evolution strategies to solve constrained optimization problems, International Journal of General Systems, vol. 37, no. 4, pp. 443–473, Aug. 2008, doi: https://www.doi.org/10.1080/03081070701303470.
19. A. Kaveh and S. Talatahari, An improved ant colony optimization for constrained engineering design problems, Engineering Computations, vol. 27, no. 1, pp. 155–182, Jan. 2010, doi: https://www.doi.org/10.1108/02644401011008577.
20. B. Akay and D. Karaboga, Artificial bee colony algorithm for large-scale problems and engineering design optimization, J Intell Manuf, vol. 23, no. 4, pp. 1001–1014, Aug. 2012, doi: https://www.doi.org/10.1007/s10845-010-0393-4.
21. Q. He and L. Wang, An effective co-evolutionary particle swarm optimization for constrained engineering design problems, Engineering Applications of Artificial Intelligence, vol. 20, no. 1, pp. 89–99, Feb. 2007, doi: https://www.doi.org/10.1016/j.engappai.2006.03.003.
22. K. Deb, Optimal design of a welded beam via genetic algorithms, AIAA Journal, vol. 29, no. 11, pp. 2013–2015, Nov. 1991, doi: https://www.doi.org/10.2514/3.10834.
23. K. M. Ragsdell and D. T. Phillips, Optimal Design of a Class of Welded Structures Using Geometric Programming, Journal of Engineering for Industry, vol. 98, no. 3, pp. 1021–1025, Aug. 1976, doi: https://www.doi.org/10.1115/1.3438995.
24. T. Ray and K. M. Liew, Society and civilization: an optimization algorithm based on the simulation of social behavior, IEEE Trans. Evol. Computat., vol. 7, no. 4, pp. 386–396, Aug. 2003, doi: https://www.doi.org/10.1109/TEVC.2003.814902.
25. V. K. Mehta and B. Dasgupta, A constrained optimization algorithm based on the simplex search method, Engineering Optimization, vol. 44, no. 5, pp. 537–550, May 2012, doi: https://www.doi.org/10.1080/0305215X.2011.598520.
26. S.-F. Hwang and R.-S. He, A hybrid real-parameter genetic algorithm for function optimization, Advanced Engineering Informatics, vol. 20, no. 1, pp. 7–21, Jan. 2006, doi: https://www.doi.org/10.1016/j.aei.2005.09.001.
27. M. G. H. Omran and A. Salman, Constrained optimization using CODEQ, Chaos, Solitons & Fractals, vol. 42, no. 2, pp. 662–668, Oct. 2009, doi: https://www.doi.org/10.1016/j.chaos.2009.01.039.
28. M. Zhang, W. Luo, and X. Wang, Differential evolution with dynamic stochastic selection for constrained optimization, Information Sciences, vol. 178, no. 15, pp. 3043–3074, Aug. 2008, doi: https://www.doi.org/10.1016/j.ins.2008.02.014.
29. M. Mahdavi, M. Fesanghary, and E. Damangir, An improved harmony search algorithm for solving optimization problems, Applied Mathematics and Computation, vol. 188, no. 2, pp. 1567–1579, May 2007, doi: https://www.doi.org/10.1016/j.amc.2006.11.033.
30. A.-R. Hedar and M. Fukushima, Derivative-Free Filter Simulated Annealing Method for Constrained Continuous Global Optimization, J Glob Optim, vol. 35, no. 4, pp. 521–549, Aug. 2006, doi: https://www.doi.org/10.1007/s10898-005-3693-z.
31. Introduction to Optimum Design, Elsevier, 2004. doi: https://www.doi.org/10.1016/B978-0-12-064155-0.X5000-9.
32. H. Raj, R. Sharma, G. S. Mishra, A. Dua, and D. C. Patvardhan, An Evolutionary Computational Technique for Constrained Optimisation in Engineering Design,
33. J.-F. Tsai, Global optimization of nonlinear fractional programming problems in engineering design, Engineering Optimization, vol. 37, no. 4, pp. 399–409, Jun. 2005. https://www.doi.org/10.1080/03052150500066737.
34. A. D. Belegundu and J. S. Arora, A study of mathematical programming methods for structural optimization. Part I: Theory, in International Journal for Numerical Methods in Engineering, Sep. 1985, pp. 1583–1599. doi: https://www.doi.org/10.1002/nme.1620210904.
Published
2024-12-31
How to Cite
Azbah, A. (2024). APPLICATIONS OF MONTE CARLO SIMULATION TO STRUCTURAL ENGINEERING PROBLEMS. Nonconventional Technologies Review, 28(4). Retrieved from https://www.revtn.ro/index.php/revtn/article/view/490
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