## 4 Results and Discussion
### Effect of Boundary Conditions on Beam-Based Model Results  
An important practical detail present in many prints is de-bonding the part from the bed during the print process. To explore the significance of this, a second beam-based model was created. This model included self-weight and the elliptical cross-section of the beads with otherwise identical properties to the first beam-based model. There were two cases for boundary conditions, one which implemented a fixed boundary condition like in the first beam-based model and one which used the BBOEF elements derived previously to simulate de-bonding and part lift-off. Table 2 presents a summary of the results of the  
Figure 16: Comparison of vertical stress at corner between wall and brim throughout print.  
Figure 15: Comparison of axial stress throughout printing at wall centerline (beam-based solution denoted by solid lines, continuum solution denoted by dashed lines).  
comparison with BBOEF results termed \"Spring\" and the fixed results denoted \"Fixed.\" Detailed results and a discussion are presented in the remainder of this section.  
A comparison between final displacements predicted by the two beam-based models is shown below in Figure 17.  
For both \(x\)- and \(y\)-direction displacements, the two models have similar patterns of variation with the BBOEF model having larger magnitudes in general. This is consistent  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Type** & **Max-Spring** & **Max-Fixed** & **Min-Spring** & **Min-Fixed** & **Max Diff** & **Min Diff** \\ \hline X-displacement (mm) & 0.174 & 0.1744 & \(-0.171\) & \(-0.171\) & \(-0.229\%\) & \(-0.467\%\) \\ Y-displacement (mm) & 0.232 & \(1.03\times 10^{-5}\) & \(-0.330\) & \(-0.355\) & \(2260000\%\) & \(-6.91\%\) \\ Axial Stress (Mpa) & 1.50 & 2.60 & \(-1.52\) & \(-1.12\) & \(-42.5\%\) & \(35.4\%\) \\ Vertical Stress (Mpa) & 1.25 & 5.09 & \(-1.87\) & \(-1.80\) & \(-75.4\%\) & \(4.29\%\) \\ \hline \hline \end{tabular}
\end{table}
Table 2: Summary of comparison of boundary conditions of the beam-based model.  
Figure 17: Comparison of displacements between two beam-based models with different boundary conditions.  
with the boundary conditions, where the BBOEF model is freer to move than the fixed one. It also makes sense that the largest differences are near the bottom of the wall, close to the boundary. Interestingly, though the bottom corners of the BBOEF part lift off \(\sim\)0.2 mm, this deformation does not significantly affect vertical displacements in the upper half of the wall.  
Figure 18 shows significant differences in magnitude and pattern of stresses between the two models. Both axial and vertical stresses are much lower for the BBOEF model, and in particular the high 5.3 MPa vertical stress near the bottom corners of the model with the fixed base is completely relieved in the BBOEF model, which predicts no stress at those locations. Such vertical stresses are a major contributor to inter-layer de-bonding during or following printing, which highlights the importance of accurately simulating boundary conditions. We also emphasize the relative ease of incorporating such boundary conditions with the beam-based modeling framework developed here.  
Figure 18: Stresses after cooldown for both beam-based models.