## 4 Results and Discussion
### Comparison between Beam-Based Model and ABAQUS Structural Model
Figure 14 shows axial and vertical stress over the entire wall after cooldown and indicates that the largest discrepancies in stress between the two models are concentrated in the lowest third of the wall. Though the spatial variations are very similar, the magnitudes of the beam-based model are significantly higher, with the largest difference in the axial direction of 0.9 MPa being around 32% of maximum stress. In the case of vertical stresses, the largest difference of roughly 1.7 MPa coincides with the maximum  
Figure 12: Comparison of \(x\)-displacement of right edge of wall throughout print (beam-based solution denoted by solid lines, continuum solution denoted by dashed lines). stress in the beam-based model of 5.1 MPa, corresponding to a 33% difference. These discrepancies could be caused by the use of the simplified brim in the beam-based model. Larger magnitudes of stresses in the beam based versus continuum models are consistent with the smaller magnitudes of displacements observed previously. Figure 15 shows axial (\(x\)-direction) stress at the vertical centerline of the wall as a function of height for multiple discrete times. Comparison of axial stresses shows a similar trend as \(x\)-displacements where the shapes of the curves are very similar between the models and the magnitudes match very well for portions of the wall higher than 300 mm for all time shown. The worse agreement for heights below 300 mm could be due to the beam element model's simplified discretization of the brim. The post-cooldown maximum vertical stress in the beam-based model occurs at the interface between the brim and the second layer. Stress versus time at this location is shown in Figure 16 for both the beam-based and continuum model. Examination of Figure 16 shows that though the shapes of the two curves are very similar, at almost all times the stress in the beam-based model is larger than that of the continuum model, with a final difference of roughly 33%. It is important to note that the locations of maximum final stress of the two models do not coincide: the maximum vertical stress in the continuum model is 4 MPa and is located one bead higher, between the second and third layers. Again, these discrepancies between the magnitudes and locations of maximum vertical stress may be due to the beam-based model's simplified representation of the brim. It is important to stress that because the two modeling strategies are significantly different, discrepancies between the models are not in themselves cause for concern and without experimental data the relative accuracy of the two models cannot be compared. Overall, temporal and spatial trends for both displacement and stresses matched well between the two models. The magnitudes of peak displacements and stresses from the two models did not match as well, especially in the lower part of the wall. However, this could be due in part to the simplified discretization of brim in the beam-based model. It is also important to note that the results of the continuum thermal model showed a significant  
Figure 13: Comparison of \(y\)-displacement throughout print at location of final maximum. variation in temperature through the thickness of the brim, which could not be captured in the two-dimensional beam-based model. Comparisons were further complicated by the fact that certain algorithms in ABAQUS are not explained in documentation. For example, in the beam-based model, elements are only included in the stiffness matrix after they are activated, but inactivated elements in ABAQUS have very small non-zero stresses, suggesting they are included in the stiffness matrix before activation to some extent. This makes it impossible to determine how differences in element activation schemes impact the comparison between model results. Further, a part made using FDM is not a continuum but rather a pattern of discrete beads, which implies that a continuum FE model itself is not an ideal representation.