**3. Results and Discussion**

The stress-strain state for the initial (solid) and the structurally designed beam were compared. The maximum stress did not change significantly, but the distribution of stress inside the product decreased (see Figure 3). The algorithm showed fast convergence; it was about 38 iterations. The maximum stress was localized in the zones of kinematic constraints for the initial geometry. In addition, for the structurally designed beam the maximum stress was localized in the zones of kinematic boundary conditions (see red regions in Figure 3). On the other hand, zones of stress reduction appeared for the structurally designed beam (see blue regions in Figure 3).

The distribution of the received porosity and ellipticity coefficients is shown in Figure 4. The zones of high porosity are localized where the von Misses stress was minimal (red zones in Figure 4a). In the same zones, the pore's ellipticity coefficient is close to 1 (red zones in Figure 4a), which means that in this region the pore is almost spherical.

The 3D geometry was restored for the following manufacturing (see Figure 5a). The initial and structurally designed samples were manufactured in two ways: longitudinal and transversal printing. After the manufacturing, the samples were scanned by CT (see Figure 5b,c). The deviations of pore geometry in the manufactured samples were noted. They were caused by the cooldown speed of the printing material drop. However, the distribution of the porosity was close enough to the design (deviations about 5%).

In the three-point bending experiments for the initial geometry, which was longitudinally printed, the maximum force was 1675 N, and the maximum displacement was 3.35 mm. For the structurally designed geometry, which was longitudinally printed, the maximum force was 1825 N, and the maximum displacement was 3.56 mm. A crack appeared in the middle, in the longitudinal direction between the kinematics constraints and the applied force (see Figure 6a). In the three-point bending experiments for the initial geometry, which was transversally printed, the maximum force was 7196 N, and the maximum displacement was 10.73 mm. For the structurally designed geometry, which was transversally printed, the maximum force was 6271 N, and the maximum displacement was 4.76 mm. A crack appeared under the applied force. The stress-strain curves for all the cases are shown in Figure 6b,c. The ultimate force deviation for the initial and structurally designed cases was about 10%, and it could be decreased by improving the manufacturing of the samples. A significant difference was noted for the displacements in the case of the transversal printing. The structurally designed sample became more rigid (4.76 mm vs. 10.73 mm).

Comparing the slope (for the longitudinal printing), a 25% increase was noted for the structurally designed sample (1184 N/mm and 1491 N/mm, respectively). The slope in the case of the transversal printing decreased by 20% for the structurally designed sample (710 N/mm and 894 N/mm, respectively).

**Figure 3.** Von Mises stress distribution for initial (**a**) and structurally designed (**b**) beam.

**Figure 4.** Distribution of porosity(**a**) and ellipticity coefficient (**b**).

**Figure 5.** Restored 3D geometry (**a**), CT scans for longitudinal printing (**b**), and transversal printing (**c**).

**Figure 6.** Three-point bending scheme (**a**), a stress-strain curve for longitudinal printing (**b**), and transversal printing (**c**); black lines—initial geometry, red lines—structurally designed geometry.
