PSI - Issue 81

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

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3. Reduction of the set of discrete solutions of the object by imposing variable constraints, a reduced FRS of the object is obtained: S red =S \{ 1 ∪ 2 ∪…∪ } . 4. Direct search in the obtained FRS by the characteristic target criterion (decision rule) and determination of the globally optimal solution: : =arg min ∈S red ( ) . In fact, taking into account all the restrictions in the form of reduction translates the problem into an unconditional comparison of the residual points of the discrete FRS. An illustrative graphic example of the application of the proposed method is shown in Fig. 1.

a

b

c

Fig. 1. An illustrative example of the proposed method usage in the Feasible region of solutions: (a) FRS and constraints with a linearized goal function; (b) when imposing additional constraints in discrete FRS; (c) taking into account technological and production constraints and rarefaction of discrete FRS. The globally optimal option is shown in red point Discretization, unlike approximation of the FRS, allows you to reduce the amount of calculations and provides an accurate solution, since each discrete value corresponds to a realistic object. Let us consider the applicability of the method to the specific problem of selecting the optimal cross-section of steel welded beams. Building structures always have certain dimensions, which are determined by the functional features of the structure, building, and type of structure (Bilyk and Adamenko (2012)). The model constraints (system boundaries) in the case considered in this article are set as follows: beams are assumed to have an I-section, equal-flange, welded, operate according to a hinge scheme, vertically loaded; transverse ribs are assumed to be structural and do not affect the calculation or are absent, longitudinal ribs are absent; steel grade is fixed, the same for the wall and flanges; the compressed flange is always the upper one; only 1 stress class is considered according to DBN V.2.6-198; functional restrictions on the height of the I-beam accepted as: h w +2t f ≤ 1500 mm; beam support along t he entire length, local stresses in the flanges do not require verification; there is no structural up of a beam.

Fig. 2. Welded I-beam cross-section

The variable parameters are the thickness and width of the flange, as well as the thickness and width of the I-beam wall. Technological and production limitations are variable, as they depend on the specific manufacturer of metal structures. The following principles were applied in determining these limitations: • Minimizing waste when cutting sheets; • Taking into account production constraints of factories; • Taking into account technological features of manufacturing (trimming, gaps for plasma cutting of sheets, etc.); • Consideration of regulatory checks, which are crucial when selecting a cross-section. Let's consider the technological limitations of manufacturing metal beams and sheet metal processing. 1) Technological limitations of sheet grades. The following assumptions are made: 1. Minimum width of the required sheet b f ≥ 100 mm. 2. Maximum width of the sheet required h w ≤ 1500 mm. 3. The principle of zero waste – dividing the workpiece into equal, albeit not rounded parts to 10 mm, but without scraps (number of divisions).