PSI - Issue 78

Alfonso Ferdinando Coniglio et al. / Procedia Structural Integrity 78 (2026) 1389–1395 1393 Equation 2 and 3 are both function of all the scenarios and independent variable considered and can be expressed in the form = ( , , ) and = ( , , ) , for each set of values collected in the vector is thus possible to calculate and for all the potential scenarios considered within the optimization problem. Based on this formulation, it is possible to define the objective function of the problem, called Working Index (WI) and expressed by equation 3. In such equation, are the number of scenarios considered, and the limits assumed respectively for the inter-story drift and the base shear, ( ) and ( ) assume the value of 1 if respectively ≤ and ≤ , zero in the other cases. = ∑ ( × ) = 1 (3) The optimization problem considered in this work is so represented by the following system of equations (equations 4). { WI = ∑ × = 1 = f (k, G, PGA) → = ( , 1 , . . . , ) → ∈ [ ; ], 1≥ 1 ≥ 2 . . .≥ > , T ≤ T → (4)

Fig. 4. (a) Pseudo-acceleration response spectrum; (b) Displacement response spectrum; (c) V B and Q represented on the bracing system.

3. Application to Case Studies For the purpose to show the advantage of using the methodology developed, many case studies, corresponding to different optimization problems (OP), are considered. Those lasts, reported in Table 1, are defined by specific sets of value related to the vectors , , and to the scalar 1 , 2 , ℎ , . This is for considering that the same set of modules sub-parts must be designed to build different types of modular building that must guarantee certain performance in as much as possible territories, as said before. As for the boundary conditions on , and are defined respectively equal to 1000 / and 50000 / , while is assumed equal to 0.5. Moreover, to each modular building different gravity loads, such as 1 , 2 , , are assigned to the inter-story levels ( ) and to the roof ( ), combined whit the seismic action at the SLV according to the seismic combination of loads. Analyses are performed using a MATLAB script, in which the optimization problem is implemented and solved by using the random search optimization technique. In the script, the independent variables are randomly generated for a defined number of combinations (100000 combinations), therefore, maximum values of is considered as the optimal values. For the non-optimized sets of module sub-parts, maximum values of the independent variables vector are considered.