PSI - Issue 34

Atefeh Rajabi Kafshgar et al. / Procedia Structural Integrity 34 (2021) 71–77 Atefeh Rajabi Kafshgar et al./ Structural Integrity Procedia 00 (2021) 000 – 000

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2.3. Multi-objective optimization

Multi-objective optimization can be used when we are faced with several conflicting goals and it is intended to study and optimize them simultaneously. For our case, the single objective optimization of stress and toughness provides different levels of printing factors. Both responses can be considered in a multi-objective optimization model to achieve different alternatives (Pareto front) that are not dominated by other levels. The results help decision-makers to review different choices and select the appropriate values. NSGA-II algorithm is used to optimize the following optimization model. If there are other constraints, they can be considered in this model. Fig. 2 illustrates Pareto front of multi-objective optimization obtained from the analyses of results in Matlab. Pareto solutions and Pareto front can be used to choose a configuration of process parameters. For example, UTS of 26.520 MPa and toughness 1.034 J is obtained by infill density of 59.852%, extrusion temperature of 207.912 o C, raster angle of 46.622 o and layer thickness of 0.191mm. Another solution with higher UTS of 29.039 MPa and lower toughness of 0.802 J is obtained by infill density of 59.889%, extrusion temperature of 218.868 o C, raster angle of 61.597 o and layer thickness of 0.115mm. Now, one can choose between these Pareto solutions (given in Eqs. (7) and (8)) for any desired preferences and possible conditions.

(7) (8)

Max

8.13 0.1876 0.1204 0.0166 12.48 A B C D = − + + + −

Stress

Max 1.897 0.008250 0.00650 0.004889 1.167 Thoughness A B C D = + − − +

: 20 60; where A   200

220; B   45

90; C   0.1 0.2 D  

Fig. 3. Pareto front suggesting the optimize values of toughness-UTS for different printing parameters.

3. Conclusions The influence of process parameters on the mechanical properties of the FDM processed parts with PLA were investigated by the means of ANOVA and the Taguchi method. The subsequent conclusions were extracted from the present work. Three of the mechanical properties i.e. UTS, modulus of elasticity, and yield strength had the same behavior when changing the levels of process parameters, and the highest level of them was noted at infill density of 60%, extrusion temperature of 220 o C, raster angle of 90 o and layer thickness of 0.1mm. on the other hand, elongation at break and toughness had the same behavior, too. The highest levels of these two mechanical properties were obtained at an infill density of 60%, extrusion temperature of 200 o C, raster angle of 45 o, and layer thickness of 0.2mm. Two of the conflicting responses i.e. UTS and toughness were considered simultaneously in the multi-objective model and Pareto solutions were obtained. Indeed, regression equations were extracted from the multi-objective analyses to obtain optimum values of both UTS and toughness in terms of the input parameters. The approach and the results of this paper can help in understanding the influence of the process parameters on five important mechanical properties of