PSI - Issue 37

A.F.F. Rodrigues et al. / Procedia Structural Integrity 37 (2022) 684–691 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

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Table 6. Parameters for the optimization problems of SP-1

Objective function No of frequencies, Number of search agents Tolerance Max. number of iterations Equation (3) 14 100 10 -6 1000

Table 7. Elastic constants computed, function values (Fval) and relative computational time (RCTime) for different numbers of search agents for PSO algorithm. 1 ( ) 2 ( ) 12 ( ) 12 Fval RCTime (Soares et al., 1993): 31.28 27.17 6.46 0.1659 Number of search agents 10 37.40 10.00 20.00 0.0500 2099.55 1.00 2 0 37.40 10.11 20.00 0.0500 2070.54 2.75 30 30.51 27.15 6.38 0.1673 45.67 17.05 40 37.40 10.11 19.73 0.0500 2039.11 4.42 50 30.51 27.15 6.40 0.1672 45.69 11.81 60 30.51 27.15 6.40 0.1674 45.65 11.92 70 30.51 27.15 6.37 0.1674 45.65 22.24 80 30.51 27.15 6.40 0.1672 45.69 22.43 90 30.51 27.15 6.38 0.1673 45.67 17.18 100 30.51 27.15 6.38 0.1673 45.65 17.50 4.3. Green Composites This section presents the results of the proposed method to green composites and wood specimens. The two specimens of are made of wooden strands bonded with adhesive (SP-2) and plywood of birch panels (SP-3). These specimens were studied, respectively, by (Larsson, 1997) using a dynamic test based on modal analysis and calculated numerical eigenvalues and by (Igea and Cicirello, 2020) using experimental data from the Chladni patterns and experimental modal analysis for the estimation of elastic constants with numerical optimization. The parameters for the optimization problems are listed in Table 8 and the design variable constraints are displayed in Table 3. Table 8. Parameters for the optimization problems of SP-2 and SP-3. Specimen Objective function No of frequencies, Number of search agents Tolerance Max. number of iterations SP-2 Equation (2) 7 50 10 -6 1000 SP-3 Equation (2) 5 50 10 -6 1000 4.3.1. Specimen SP-2 Table 9 lists the elastic constants computed with each one of the optimization algorithms and the relative differences. The Young's modulus, 1 , is the elastic constant that presents the closest values to the reference one for all algorithms, presenting a relative difference of around four per cent. The Young's modulus, 2 , presents a much higher relative difference of around forty per cent. The shear modulus, 12 , has lower values than the reference value, with a relative difference of around thirty-four per cent. It is interesting to note that the FA algorithm gives a Poisson's ratio closer to the reference value, with a relative difference of only around four percent. Table 10 presents the function value, the number of iterations, the number of function evaluations and the relative computational time for each algorithm. All the algorithms have similar values of the function value. However, the GWO needs one thousand iterations, which are the maximum number of iterations allowed. The algorithm that took the lowest number of iterations was the PSO and the one that took the longest time was the GWO. It can be concluded that the present