## 3 Results and Discussion
### Results of the Experimental Validation  
To validate the developed FRep CAD/CAM system, we printed the part shown in Figure 6(a) left, and conducted its mechanical testing. Dimensions of the printed part (Figure 8(a)) are \(86\times 25\times 20\) mm. The part was cut from the substrate and tested in the three-point bending mode (Figure 8(b)) at the Instron 5969 testing machine.  
Results of the experimental validation are presented as load-displacement curves for several control points. The vertical component of displacement is used in these curves. The obtained load-displacement curve for point P3 (Figure 8(c)) is presented as red dots in Figure 8(f). Computed results for the same load are presented as the solid red line. One can clearly see the disagreement between computational and experimental data.  
This discrepancy between the analytical and experimental results of the red lines can be attributed to flutes (Figure 8(c)) manufactured to increase the stability of the part during the test. A sagging was observed in their areas (Figure 8(d)) during the testing process. It influenced the load-displacement curve with the displacement value of the whole printed part. The vertical displacement of point P3 was calculated relative to point P0 (Figure 8(c)) for subtracting the influence of sagging from the load-displacement test curve. Figure 8(f) shows the load-displacement curves relative to point P0 as green patterns. The correlation between the experimental and predicted results holds up to a load of 15 kN.  
During the compression test, it was possible to achieve local plastic deformations. Depending on the distance from P0, the contribution of plastic deformation to the vertical displacement differs. Therefore, additional points, P1 and P2 (Figure 9c), were considered. The computational results for those points are presented in Figure 9e. The correlation between the experimental and computational results for the point P2 is preserved up to the load of 10 kN. For the point P1 the correlation with computational results can be observed up to the load of 5 kN.  
We can conclude that the contribution of plastic deformation is the highest in the vicinity of the point P0. The deflection from the elasticity is observed for point P1. It influences the vertical displacements of points P2 and P3. We can conclude that mechanical testing results repeat the theoretical results within the elastic field region, where the computational model was applied. At the loads exceeding 15 kN, the contribution of plasticity starts to grow, and it becomes impossible to compare the computational and experimental results obtained during optimization. At the same time, this experimental validation showed that the proposed approach can be freely used for 3D printed parts that are made up of ceramics [34] and other materials without plastic deformation.  
Moreover, we can compare the experimental value of the work done by the applied force and the theoretical values of elastic deformation energy. The upper limit of elastic deformations was observed at the point P3 at the load of 15 kN. This point lies in the vicinity of the loaded point of the body. Therefore, we can calculate an approximate value of the work done by the applied force as follows:  
\[A=\frac{Fd}{2} \tag{20}\]  
where \(F\) is the load and \(d\) is the deformation at a given point. The load equals 15 kN, \(d\) equals 0.053 mm. Thus, the work \(A\) equals 0.4 J. The FEM routine of Algorithm 1 provides the same value of elastic energy at these load and dimensions of the printed part.