PSI - Issue 81

Artem Bilyk et al. / Procedia Structural Integrity 81 (2026) 177–183

182

Direct selection from existing ranges of welded I-beams gives a cross section of 80B2. Advanced evolutionary search method (Alhijawi and Awajan (2024); Avramenko et al. (2021)) on discrete sets of sheets taking into account real rolling (production limitations) – gives a 30% lower metal consumption, which is explained by both optimization and significant discreteness of existing assortments of welded beams. The difference between the results obtained by the evolutionary search method and the proposed directed selection method is small at first glance, but at large lengths and with the widespread use of beams of the same type, it is noticeable. The comparison shows the effectiveness of the proposed method, which additionally takes into account the technological and production limitations of factories, and the maximum waste-free cutting of sheets. With an increase in the dimensions and quantitative parameters of the problems, the proposed method will demonstrate an even greater difference due to a significant natural reduction in the FPS, and faster calculation time and the absence of possible accumulation of errors due to a decrease in the number of operations will also be noticeable (Table 4).

Table 4. Comparative results of optimization calculations of steel beams

Method b f , cm t f , cm t w , cm H w , cm H, cm

Direct selection Evolutionary search method

Proposed method

28 2.2 1.4

23.8

11.1

2.5 0.6

1.4 1.2

75.4 79.8 179.6 100%

66.4 71.4 124.7 69.4%

98.9 101.7 117.6 65.5%

Linear weight, kg/m 2

Difference

4. Conclusions The present study develops and validates a method of directed selection of design solutions for optimal design problems of welded steel I-beams. The proposed method combines a guaranteed attainment of the global optimum with a significant reduction in computational effort. It is based on the staged formation and sequential reduction of discrete feasible solution region while accounting for model, technological, production, and regulatory constraints. The transition from continuous models to discretization that corresponds to real structural elements and available product assortments prevents the generation of impractical or non-manufacturable optimal solutions. This ensures the practical applicability of the optimization results under real design conditions. The effectiveness of the proposed method is demonstrated through a case study involving the selection of steel beam cross section for protective structure of critical infrastructure facility. Comparative analysis with direct selection and evolutionary optimization methods shows the advantage of the proposed approach in terms of minimizing the linear mass of the beam. Consideration of realistic sheet-cutting options and technological constraints associated with the fabrication of welded beams reduces the feasible solution space by several orders of magnitude. This reduction enables a guaranteed search for the globally optimal solution. The obtained results confirm the suitability of the proposed method for high-dimensional optimization problems and its strong potential for implementation in engineering practice related to the design of steel structures. References Aykut, K., 2019. Topology Optimization Applications on Engineering Structures. Alhijawi, B., Awajan, A., 2024. Genetic algorithms: theory, genetic operators, solutions, and applications. Evol. Intel. 17, 1245 – 1256. Avramenko, S.E., Zheldak, T.A., Koriashkina, L.S., 2021. Guided hybrid genetic algorithm for solving global optimization problems. Radio Electronics, Computer Science, Control, (2), 174 – 188. Banychuk, N.V., Kobelev, V.V., 1983. On the optimal non-uniform cross-sectional shapes of beams. Mechanics of Solids 5, 162 – 167. Bazhenov, V.A., Granat, S.Ya., Shishov, O.V., 1999. Construction Mechanics. Computer Course: Textbook. K.: KNUCA, 584. Belsky, G.E., Tamarchenko, V.S., 1990. Cross-section optimization is an important reserve for reducing material consumption in steel beams. Construction mechanics and construction engineering 1, 83 – 88. Bilyk, A.S., 2014. Optimal selection of structures with discretely variable loading scheme. Collection of scientific works of the V.M. Shymanovsky Institute of Industrial Research 14, 70 – 78. Bilyk, A.S., Adamenko, V.M., 2012. Fundamentals of optimal design of steel rod structures: Methodological recommendations for practical classes in the discipline of targeted training. K.: KNUBA, 20. Bilyk, A.S., Koval, M.V., Koval, V.V., Kotsyuruba, V.I., Kubrakov, O.M., 2023. Fundamentals of engineering protection of critical infrastructure facilities of the energy sector of Ukraine against enemy air attack: monograph; edited by A.S. Bilyk. Kyiv: General Staff of the AFU, 194 p. Bilyk, A.S., Kotsyuruba, V.I., et al., 2022. Calculation methodology and justification of requirements for engineering protection of critical national infrastructure facilities from UAVs. Strength of Materials and Theory of Structures, 109, 164 – 183. Bilyk, S.I., 2008. Rational steel I-beams with variable wall height. Resource-saving materials, structures, buildings and structures 17, 73 – 78. Burke, E.K., Kendall, G., 2006. Search Methodologies - Introductory Tutorials in Optimization and Decision Support Techniques. Springer Science & Business Media, 620. Chorney, N., Chorney, R., 2005. Systems Theory and Systems Analysis: Textbook for Students of Higher Education. Kyiv: MAUP, 256. DBN V.2.6-198, 2014. Steel structures. Gordeev, V.N., 2009. Elementary problems of I-beam optimization. Collection of scientific works of the Ukrainian Research and Design Institute of Steel Structures named after V.M. Shymanovsky 3, 27 – 48. Horev, V.V., Uvarov, B.Yu., Filippov, V.V., 1997. Metal constructions. In 3 vol., T.1. Elements of steel structures. Higher School, 527. Lobanov, L.M., Shimanovsky, V.N., Gordeev, V.N., 2003. Welded construction structures. In 3 vols., T.3. Kyiv: IES named after E.O. Patona.