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Robust and reliability-based design optimization of steel beams
DOI:
https://doi.org/10.24425/ace.2023.147651Abstract
In line with the principles of modern design a building structure should not only be safe but also optimized. In deterministic optimization, the uncertainties of the structures are not explicitly taken into account. Traditionally, uncertainties of the structural system (i.e. material parameters, loads, dimensions of the cross-sections) are considered by means of partial safety factors specified in design codes. Worth noticing, that optimal structures are sensitive to randomness design parameters and deterministic optimal solutions may lead to reduced reliability levels. It therefore seems natural to extend the formulation of deterministic optimization with the random scatter of parameter values. Such a formulation is offered by robust optimization and reliability-based design optimization. The applicability of RBDO is strongly dependent on the availability of the joint probability density function. A formulation of non-deterministic optimization that better adapts to the design realities is robust optimization. Unlike RBDO optimization, this formulation does not require estimation of failure probabilities. In the paper using the examples of steel beams, the authors compare the strengths and weaknesses of both formulations.References
[1] P. Szeptyński and L. Mikulski, “Preliminary optimization technique in the design of steel girders according to Eurocode 3”, Archives of Civil Engineering, vol. 69, no. 1, pp. 71-89, 2023, doi: 10.24425/ace.2023.144160.
[2] R.H. Lopez and A.T. Beck, “Reliability-based design optimization strategies based on FORM: a review”, Journal of the Brazilian Society of Mechanical Sciences and Engineering, vol. 34, no. 4, pp. 506-514, 2012, doi: 10.1590/S1678-58782012000400012.
[3] Y. Aoues and A. Chateauneuf, “Benchmark study of numerical methods for reliability-based design optimization”, Structural and Multidisciplinary Optimization, vol. 41, no. 2, pp. 277-294, 2010, doi: 10.1007/s00158-009-0412-2.
[4] A.T. Beck, W.J.S. Gomes, R.H. Lopez, and L.F.F. Miguel, “A comparison between robust and risk-based optimization under uncertainty”, Structural and Multidisciplinary Optimization, vol. 52, no. 3, pp. 479-492, 2015, doi: 10.1007/s00158-015-1253-9.
[5] N. Kuschel and R. Rackwitz, “Two basic problems in reliability-based structural optimization”, Mathematical Methods Operational Research, vol. 46, no. 3, pp. 309-333, 1997, doi: 10.1007/BF01194859.
[6] B.D. Youn and K.K. Choi, “A new response surface methodology for reliability-based design optimization”, Computers & Structures, vol. 82, no. 2-3, pp. 241-256, 2004, doi: 10.1016/j.compstruc.2003.09.002.
[7] I. Doltsinis and Z. Kang, “Robust design of non-linear structures using optimization methods”, Computer Methods Applied Mechanics and Engineering, vol. 194, no. 12-16, pp. 1179-1795, 2005, doi: 10.1016/j.cma.2004.02.027.
[8] W. Chen, W. Fu, S.B. Biggers, and R.A. Latour, “An affordable approach for robust design of thick laminated composite structure”, Optimization and Engineering, vol. 1, no. 3, pp. 305-322, 2000, doi: 10.1023/A:1010078107194.
[9] Y.Q. Li, Z.S. Cui, X.Y. Ruan, and D.J. Zhang, “CAE-based six sigma robust optimization for deep-drawing sheet metal process”, The International Journal of Advanced Manufacturing Technology, vol. 30, pp. 631-637, 2006, doi: 10.1007/s00170-005-0121-y.
[10] K.H. Hwang, K.-W. Lee, and G.-J. Park, “Robust optimization of an automobile rearview mirror for vibration reduction”, Structural and Multidisciplinary Optimization, vol. 21, no. 4, pp. 300-308, 2001, doi: 10.1007/s001580100107.
[11] M. Rosenblatt, “Remarks on a multivariate transformation”, The Annals of Mathematical Statistic, vol. 23, no. 3, pp. 470-472, 1952.
[12] M. Hohenbichler and R. Rackwitz, “Non-normal dependent vectors in structural safety”, Journal of the Engineering Mechanics Division, ASCE, vol. 107, no. 6, pp. 1227-1238, 1981.
[13] M. Hohenbichler, S. Gollwitzer, W. Kruse, and R. Rackwitz, “New light on first and second order reliability methods”, Structural Safety, vol. 4, no. 4, pp. 267-284, 1987.
[14] A. Der Kiureghian and M. De Stefano, “Efficient algorithm for second-order reliability analysis”, Journal of Engineering Mechanics, vol. 117, no. 12, pp. 2904-2923, 1991, doi: 10.1061/(ASCE)0733-9399(1991)117:12(2904).
[15] A. Hasofer and N. Lind, “Exact and invariant second-moment code format”, Journal of the Engineering Mechanics Division, ASCE, vol. 100, no. 1, pp. 111-121, 1974.
[16] R. Rackwitz and B. Flessler, “Structural reliability under combined random load sequences”, Computers & Structure, vol. 9, no. 5, pp. 489-494, 1978, doi: 10.1016/0045-7949(78)90046-9.
[17] A. Dudzik and U. Radoń, “The evaluation of algorithms for determination of the reliability index”, Archives of Civil Engineering, vol. 61, no. 3, pp. 133-147, 2015, doi: 10.1515/ace-2015-0030.
[18] K. Kubicka and U. Radoń, “Proposal for the assessment of steel truss reliability under fire conditions”, Archives of Civil Engineering, vol. 61, no. 4, pp. 141-154, 2015, doi: 10.1515/ace-2015-0041.
[19] K. Kubicka and U. Radoń, “Influence of the buckling coefficient randomness on the reliability index value under fire conditions”, Archives of Civil Engineering, vol. 64, no. 3, pp. 173-179, 2018, doi: 10.2478/ace-2018-0037.
[20] P. Zabojszcza, U. Radoń, and W. Szaniec, “Probabilistic approach to limit states of a steel dome”, Materials, vol. 14, no. 19, art. no. 5528, 2021, doi: 10.3390/ma14195528.
[21] P. Zabojszcza and U. Radoń, “The impact of node location imperfections on the reliability of single-layer steel domes”, Applied Science-Basel, vol. 9, no. 13, art. no. 2742, 2019, doi: 10.3390/app9132742.
[22] A. Dudzik and B. Potrzeszcz-Sut, “Hybrid approach to the first order reliability method in the reliability analysis of a spatial structure”, Applied Science-Basel, vol. 11, no. 2, art. no. 648, 2021, doi: 10.3390/app11020648.
[23] I. Enevoldsen and J.D. Sørensen, “Reliability-based optimization in structural engineering”, Structural Safety, vol. 15, no. 3, pp. 169-196, 1994, doi: 10.1016/0167-4730(94)90039-6.
[24] N. Kuschel and R. Rackwitz, “Optimal design under time-variant reliability constraints”, Structural Safety, vol. 22, no. 2, pp. 113-127, 2000, doi: 10.1016/S0167-4730(99)00043-0.
[25] H. Streicher and R. Rackwitz, Reliability-oriented optimization for time-invariant problems with optimization algorithm JOINT 5, research report. Technical Report Project 28159. 2001.
[26] H. Streicher and R. Rackwitz, “Structural optimization - a one level approach”, in AMAS Workshop on Reliability-Based Design and Optimization - RBO’02, S. Jendo, K. Doliński, and M. Kleiber, Eds.,Warsaw, 2002.
[27] G. Cheng, L. Xu, and L. Jiang, “A sequential approximate programming strategy for reliability-based structural optimization”, Computer & Structure, vol. 84, no. 21, pp. 1353-1367, 2006, doi: 10.1016/j.comp struc.2006.03.006.
[28] J. Ching and W.C. Hsu, “Transforming reliability limit state constraints into deterministic limit-state constraints”, Structural Safety, vol. 30, no. 1, pp. 11-33, 2008, doi: 10.1016/j.strusafe.2006.04.002.
[29] http://www.Strurel.de. [Accessed: 27.11.2022].
[30] http://numpress.ippt.gov.pl/. [Accessed: 27.11.2022].
[31] M.J. Sasena, et al., “Improving an ergonomic testing procedure via approximation-based adaptive experimental design”, ASME Journal of Mechanical Design, vol. 127, no. 5, pp. 1006-1013, 2005, doi: 10.1115/1.1906247.
[32] M. Liefvendahl and R. Stocki, “A study on algorithms for optimization of Latin hypercubes”, Journal of Statistical Planning and Inference, vol. 136, no. 9, pp. 3231-3247, 2006, doi: 10.1016/j.jspi.2005.01.007.
[33] R. Stocki, K. Kolanek, J. Knabel, and P. Tauzowski, “FE based structural reliability analysis using STAND environment”, Computer Assisted Mechanics and Engineering Sciences, vol. 16, pp. 35-58, 2009.
[34] P. Zabojszcza, U. Radoń, and P. Tauzowski, “Robust optimization of a single-layer lattice dome”, Modern Trends in Research on Steel, Aluminium and Composite Structures, 2021, doi: 10.1201/9781003132134.
[35] R. Stocki, P. Tauzowski, and J. Knabel, “Reliability analysis of a crashed thin-walled s-rail accounting for random spot weld failures”, International Journal of Crashworthiness, vol. 13, no. 6, pp. 693-706, 2008, doi: 10.1080/13588260802055213.
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