## 4 Results and Discussion
### Comparison between Beam-Based Model and ABAQUS Structural Model  
To verify the model formulation and predictions, the results of the beam-based model were compared to those of the ABAQUS continuum model. It is important to note here that at present, neither model has been validated with experimental data and so this comparison is not a validation of model accuracy. However, the previous review of the literature shows that many researchers have used continuum models incorporating ABAQUS AM Modeler, which makes it a reasonable benchmark against which to assess the beam-based model predictions. Because the two modeling approaches differ significantly (element type, dimensionality, etc. ), some variation between the two sets of results is expected. The  
Figure 10: Simulation time versus time step and mesh density. Figure 9: Difference in average vertical displacement versus time step and mesh density. continuum results displayed are the average through the wall thickness. Table 1 offers a summary of the results of the comparison of the final state of the part between the two models, where \"Beam\" denotes the beam-based model and \"Cont\" the continuum model. A more detailed full-field comparison of quantities follows. Shown in Figure 11 are the full field displacements in the horizontal and vertical directions for both models at the end of simulation, after the part has cooled to ambient room temperature. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Type** & **Max-BB** & **Max-Cont** & **Min-BB** & **Min-Cont** & **Max Diff** & **Min Diff** \\ \hline X-displacement (mm) & 0.174 & 0.173 & \(-0.171\) & \(-0.172\) & 0.803\% & \(-0.583\%\) \\ Y-displacement (mm) & \(1.03\times 10^{-5}\) & 0 & \(-0.355\) & \(-0.361\) & 100\% & \(-1.89\%\) \\ Axial Stress (Mpa) & 2.60 & 1.99 & \(-1.12\) & \(-1.21\) & 23.4\% & \(-7.57\%\) \\ Vertical Stress (Mpa) & 5.09 & 3.97 & \(-1.80\) & \(-1.25\) & 22.0\% & 30.6\% \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Summary of comparison of modeling approaches. Figure 11: Comparison of final displacements (mm) between beam-based and continuum models. The spatial variation of the displacements in both directions is very similar between the two models, with the beam-based model having less displacement overall. In the case of the \(x\)-displacements (Figure 11a), the maximum difference was roughly 0.03 mm, about 20% of the maximum displacement. The largest differences are in the first third of the layers, which suggests the simplified, single-element width brim at the base of the beam-based model may be playing a significant role in the discrepancies. Examining the \(y\)-displacements (Figure 11b), there is a maximum difference of 11% of the maximum displacement or 0.04 mm. The small differences between the models in the lowest part of the wall suggests that the simplified brim discretization used in the beam-based model might not impact vertical \(y\)-displacements as significantly. Finally, the pattern of results is nearly symmetric about the wall centerline in both models, showing that the effect of the un-symmetric printing pattern is small. Figure 12 shows \(x\)-displacements of the right edge of the wall at six points in time: four during printing, at the end of printing and at the end of cool down. At a given time step, Figure 12 shows that the shape of the curves of the two models are very similar. Though the displacements are different in the bottom of the wall between the two models, they converge at a height of roughly 300 mm and stay close after this for all but the first time step where the wall height is less than 300 mm. Figure 13 shows the vertical displacement throughout time at one point, located where the magnitude of displacement after cooling is maximum, indicating that both the trend and magnitude of \(y\)-displacements at the location shown match very well for both models. Overall, displacements in both directions for both models match well, but stresses still must be examined.