PSI - Issue 78

Enrico Bernardi et al. / Procedia Structural Integrity 78 (2026) 599–606

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For OPT1 results, β reaches 0.75, as higher values lead to damping ratios greater than 1 (as is explain in Bernardi et al. 2023a). Furthermore, for OPT2 and β >0, the value of μ was considered up to 1, as for higher values the multi objective approach becomes meaningless, as seen in Figure 3.

a)

b)

Fig. 3. Optimization results (in terms of Pareto fronts) for μ =0.5, 1 and 1.5, referring to OPT1 (a) and OPT2 (b) .

Fig. 4. Multi-objective design model proposed.

4. Case study The retrofit technique and the reliability of the model were evaluated through time history analyses on a lumped mass model of a reinforced concrete (RC) structure (floor mass m i =350 t and story stiffness k i =780 kN/mm were