## 5 Conclusions  
A beam-based finite element framework for the simulation of the fabrication of large 3D-printed polymer parts was developed. Because the model is beam-based, it has the potential to use many fewer DOFs than existing continuum models which typically use brick elements. Not only do brick elements have more DOFs per element, but the size of the bricks is limited by layer height whereas the beam elements are not. Fewer DOFs suggests the model is faster than a comparable continuum model. Additionally, using beam elements allows for the simulation of part lift-off with relative ease. Finally, the use of beams allows for more accurate modeling of the ellipse-shaped bead cross-section, which is normally modeled as rectangular in a continuum model.  
The framework is tested by comparing resulting stresses and displacements to a continuum model made with ABAQUS AM modeler. Reasonable agreement is observed, with the beam-based model also extended to allow separation of the part from the bed during printing. Specific conclusions are highlighted below.  
* Spatial and temporal convergence studies showed generally smooth and adequate convergence of the beam-based model. Run times for the beam-based model were much less than for the ABAQUS AM model. Although the ABAQUS AM model was not optimized for solution efficiency, the beam-based model was developed using the MATLAB programming language, which is interpreted and relatively inefficient. Overall, convergence and run-time studies indicate that beam-based models have potential to be substantially more computationally efficient than widely available continuum modeling tools.
* The beam-based model and ABAQUS AM predicted very similar patterns of displacements and stresses. While the beam-based model tends to predict smaller displacements and somewhat larger stresses than the ABAQUS AM continuum model, these discrepancies are likely due in part to the simplified model of the brim necessitated by the two-dimensional nature of the current beam-based model.
* Simulations clearly show that simulating the practical boundary condition where part-bed separation is allowed during the print results in significantly reduced residual part stresses, indicating that accurately modeling boundary conditions is critical to accurate predictions. Part-bed separation is challenging to simulate with available continuum models, highlighting the value of this particular feature of the beam-based model developed here.  
Despite its advantages, the beam-based model requires significant further development to make it a broadly useful tool for simulating the development of residual stresses and deformations in large, 3D-printed polymeric parts. Future efforts should focus on extending the beam-based model to 3D to allow the simulation of complex 3D-printed parts, obtaining experimental temperature and displacement information during the printing of large 3D polymeric parts to validate the model, and incorporating more complex phenomena like inter-layer slip, viscoelasticity and progressive fracture between printed layers.  
Conceptualization, W.G.D. and I.B.H.; methodology, W.G.D. and I.B.H.; software, I.B.H.; validation, I.B.H. and W.G.D.; formal analysis, I.B.H.; investigation, I.B.H. and W.G.D.; resources, W.G.D.; data curation, I.B.H.; writing--original draft preparation, I.B.H.; writing--review and editing, W.G.D.; visualization, I.B.H.; supervision, W.G.D.; project administration, W.G.D.; funding acquisition, W.G.D. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the US Department of Defense, grant number C5-23-1003.  
Not applicable.  
The original contributions presented in the study are included in the article, further inquiries can be directed to the corresponding author.  
**Acknowledgments:** The authors thank [PERSON] and [PERSON] for their assistance with the use of their continuum model.  
**Conflicts of Interest:** The authors declare no conflicts of interest.