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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for all three benchmarks. Accordingly, in the TopFat original test cases the alternate first principle stress limit is set to 255 MPa which corresponds to a limit of 510 MPa with a stress ratio equal to zero by Eq. (4). It is worth noting that, to visualize better the final topologies in HyperWorks TO, the command ‘Iso’ is used. Basically, this command discards from the final visualisation all the elements with a density inferior to a certain threshold, in the following cases 0.505. In Fig 2a and in Fig. 2b the final topology obtained in TopFat and the one obtained with HyperWorks are reported, respectively. The original TopFat solution requires around 1000 iterations whereas the HyperWorks 4090. As it can be noticed the topologies are quite different especially in the lower-left portion of the domain. Moreover, the HyperWorks solution is 7% stiffer and the maximum stresses are conservatively smaller than the corresponding limit stresses. However, the re-entrant corner is partially included in the final topology whereas it is excluded in the original TopFat solution. Anyway, in both the topologies a feasible solution is found, guarantying the structural safety according to the employed discretization model.

a)

b)

= 1080  = 580 MPa 1 = 510 MPa = 1003 = 479 MPa 1 = 470 MPa Fig. 2 - L-shape benchmark: a) final topology obtained in TopFat and data; b) final topology obtained in HyperWorks and data. Notation : : compliance; : maximum von Mises equivalent stress; 1 : maximum first principal stress As for the cantilever domain, almost the same considerations highlighted for the L-shape domain can be carried out. Fig. 3a shows the solution obtained in the original TopFat while Fig. 3b shows the one obtained via HyperWorks TO. The HyperWorks solution converges in 554 iterations while the original TopFat final topology is reached in roughly 750 iterations. In this case, the final topologies are remarkably different, but both belong to the feasible design regions of the optimisation. The HyperWorks solution is 10% stiffer and the stresses are well below the imposed limits. However, the HyperWorks solution partially includes the upper and lower edge in the final topology. These are the most stressed zones for the cantilever structure and for this reason they are excluded in the original TopFat result. Lastly, the Corbel structure optimisations reported in Fig. 4a and 4b are obtained with the original TopFat algorithm and the HyperWorks TO, respectively. In this case, the HyperWorks TO algorithm has not been able to reach a feasible design. The stresses result to be higher than the imposed limits and the final topology is badly and poorly connected even if the convergence has been reached after 2119 iterations (450 in TopFat).

a)

b)

= 5380  = 620 MPa 1 = 510 MPa = 4805 = 429 MPa 1 = 449 MPa Fig. 3 - Cantilever benchmark: benchmark: a) final topology obtained in TopFat and data; b) final topology obtained in HyperWorks and data. Notation : : compliance; : maximum von Mises equivalent stress; 1 : maximum first principal stress This phenomenon can be addressed to the extreme characteristics of this geometry. Indeed, this case is analyzed in