PSI - Issue 37

Iulian Constantin Coropețchi et al. / Procedia Structural Integrity 37 (2022) 755 – 762 Coropetchi et al./ Structural Integrity Procedia 00 (2019) 000 – 000

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and E y = 3989.024 MPa. The best solutions that ensure equal values for the effective stiffness for the two orthogonal directions are the four solutions presented in the lower left corner of fig. 4 with E x = E y = 3953.66 MPa. These are also the maximum values being equal on both directions.

Fig. 4. Pareto frontier – intersection with isotropic solutions.

Choosing the best solution in this case is a difficult task for the algorithm, as the formulation of the objective function can lead to different results. 3.2. Greedy algorithm A Greedy algorithm, as its name suggests, is an algorithm that takes the local optimal solution at each stage. In our case the algorithm starts from a random initial distribution of soft and hard elements. The first step is to evaluate the objective function of the initial configuration. In the next step, the algorithm changes the material of one element with its opposite material and, after that, it searches the next best element to change its material so that the imposed material fraction is kept constant. For example, if the first element is a soft material, the algorithm will change it to a hard material and will look for the best element with hard material that must be changed to soft so that the objective function will have a greater value. The algorithm does this process for all elements in the domain and determines the objective function for each switch. From all the possible switches, the one that has the highest value for the objective function is kept and used for the next iteration. If the new objective function value is higher than the last one, the whole process of switches is redone and if it is not higher than the last it exists the loop (Gu et al., 2016) and the iteration is aborted. The overall methodology of the Greedy algorithm is depicted in Fig. 5a and an example of how the algorithm works is presented in Fig. 5b.