PSI - Issue 34

Riccardo Caivano et al. / Procedia Structural Integrity 34 (2021) 221–228 Riccardo Caivano et al./ Structural Integrity Procedia 00 (2019) 000 – 000

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algorithm the Method of Moving Asymptotes (MMA) is used (Svanberg 1987) which is considered one of the most efficient for solving topology optimisation problems. Instead, in HyperWorks, the Method of Feasible Direction (MFD), i.e. the software default one, is employed.

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Fig. 1 – Exanimated benchmarks from TopFat test cases: a) L-shape domain; b) Cantilever domain and c) Corbel domain In Table 1 the data related to the material properties and the defect population is reported. All the optimisations are carried out minimising the compliance, i.e. maximising the stiffness, with three constraints: a volume fraction constraint equal to 30%, a limit over the von Mises equivalent stress and the limit over the maximum first principal stress calculated thanks to Eq. (3) and (4). As already pointed out, in HyperWorks it is possible to set a constraint over the maximum first principal stress only and not over the alternate one such as in TopFat original algorithm.

Table 1 – Material properties, Fatigue, and defect population parameters from TopFat test cases (Gao et al. 2021) Parameter (Gao et al. 2021) Value Young modulus [ ] = 210 Poisson ratio = 0.3 Yield limit 02 [ ] 0 ℎ 2 = 580 0 2 = 620 0 2 = 660 Vickers hardness = 290 Superficial defect location parameters 1 1 = 1.41 LEVD location parameter √ [ ] √ = 16.96 LEVD scale location parameter √ [ ] √ = 2.389 Probability = 0.5 Stress ratio = 0 Reference volume 0 [ 3 ] 0 = 0.008 Initial volume [ 3 ] ℎ = 6400 = 20000 = 17700 Upper limit volume, ̅ ̅ = 0.3 ∙ Fatigue constraints ̄ , [ ] (Eq. 4) ̄ , = 510

The limit on the von Mises equivalent stress is set according to the supposed Yield stress, reported in Table 1. As for the fatigue constraint, by substituting the required values in Eq. (3) and (4), it results that the limit is around 510 MPa