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This paper presents the simultaneous cost, standard sizes and rounded dimension optimization of a cantilever roof structure. Since the standard and rounded dimensions are proposed to be handled explicitly in the discrete type of the optimization, the mixed-integer non-linear programming (MINLP) is applied. The structure is built from the standard hot rolled steel I sections for columns, beams and struts, and from the reinforced concrete bases. The MINLP optimization model of the cantilever roof structure is developed. The model comprises the objective function of the structure’s self-manufacturing costs and the design, resistance and dimensioning (in)equality constraints. The latter are defined in accordance with the Eurocode 2, 3 and 7 specifications. The modified outer-approximation/equality- relaxation (OA/ER) algorithm is used. The MINLP optimization of a cantilever roof structure for a small football stadium near the city of Maribor in Slovenia is presented at the end of the paper. The obtained optimal result includes the minimal production costs of the structure, the optimal standard sections of steel elements and the optimal rounded dimensions of the concrete bases.
cost optimization, discrete optimization, mixed-integer non-linear programming, MINLP, roof structure
[1] Cicconi, P., Germani, M., Bondi, S., Zuliani, A. & Cagnacci, E., A design methodology to support the optimization of steel structures. Procedia CIRP, 50, pp. 58–64, 2016. https://doi.org/10.1016/j.procir.2016.05.030
[2] Kalanta, S., Atkočiunas, J. & Venskus, A., Discrete optimization problems of the steel bar structures. Engineering Structures, 31(6), pp. 1298–1304, 2009. https://doi.org/10.1016/j.engstruct.2009.01.004
[3] Hasançeb, O., Cost efficiency analyses of steel frameworks for economical design of multistorey buildings. JCSR, 128, pp. 380–396, 2017. https://doi.org/10.1016/j.jcsr.2016.09.002
[4] Mela, K. & Heinisuo, M., Weight and cost optimization of welded high strength steel beams. Engineering Structures, 79, pp. 354–364, 2014. https://doi.org/10.1016/j.engstruct.2014.08.028
[5] Zhang, Z., Pan, J., Fu, J., Singh, H.K., Pi, Y.L., Wu, J. & Rao, R., Optimization of long span portal frames using spatially distributed surrogates. Steel and Composite Structures, 24, pp. 227–237, 2017.
[6] Van Mellaert, R., Mela, K., Tiainen, T., Heinisuo, M., Lombaert, G. Schevenels, M., Mixed-integer linear programming approach for global discrete sizing optimization of frame structures. Structural and Multidisciplinary Optimization, 57(2), pp. 579–593, 2018. https://doi.org/10.1007/s00158-017-1770-9
[7] Eurocode 3. Design of steel structures, European Committee for Standardization, Brussels
2005.
[8] Eurocode 2. Design of concrete structures, European Committee for Standardization, Brussels 2004.
[9] Eurocode 7. Geotechnical design, European Committee for Standardization, Brussels 2004.
[10] Kravanja, Z. & Grossmann, I.E., New Developments and Capabilities in PROSYN—An Automated Topology and Parameter Process Synthesizer. Computers & Chemical Engineering, 18(11–12), pp. 1097–1114, 1994. https://doi.org/10.1016/s0098-1354(94)85027-5
[11] Kravanja, S., Kravanja, Z. & Bedenik, B.S., The MINLP optimization approach to structural synthesis. Part I: A general view on simultaneous topology and parameter optimization. International Journal for Numerical Methods in Engineering, 43(2), pp. 263–292, 1998. https://doi.org/10.1002/(sici)1097-0207(19980930)43:2<263::aid-nme412>3.0.co;2-u
[12] Kravanja, S., Kravanja, Z. & Bedenik, B.S., The MINLP optimization approach to structural synthesis. Part II: Simultaneous topology, parameter and standard dimension optimization by the use of the Linked two-phase MINLP strategy. International Journal for Numerical Methods in Engineering, 43(2), pp. 293–328, 1998. https://doi.org/10.1002/(sici)1097-0207(19980930)43:2<293::aid-nme413>3.3.co;2-f
[13] Kravanja, S., Soršak, A. & Kravanja, Z., Efficient multilevel MINLP strategies for solving large combinatorial problems in engineering. Optimization and Engineering, 4(1/2), pp. 97–151, 2003. https://doi.org/10.1023/a:1021812414215
[14] Kravanja Z., Challenges in sustainable integrated process synthesis and the capabilities of an MINLP process synthesizer, MipSyn. Computers & Chemical Engineering, 34(11), pp. 1831–1848, 2010. https://doi.org/10.1016/j.compchemeng.2010.04.017
[15] Drudd, A.S., CONOPT—A Large-Scale GRG Code. ORSA Journal on Computing, 6(2), pp. 207–216, 1994. https://doi.org/10.1287/ijoc.6.2.207
[16] CPLEX 11 User’s Manuals, ILOG inc., 2007.
[17] Brooke, A., Kendrick, D. & Meeraus, A., GAMS - A User’s Guide, Scientific Press, Redwood City, CA, 1988.
[18] Žula, T. & Kravanja, S., Cost optimization of a cantilever roof structure for the small football stadium in Limbuš. WIT transactions on the built environment, High Performance and Optimum Design of Structures and Materials III, WIT Press, 175, pp. 177–183, 2018.