## 1 Introduction  
With recent advances in technology, 3D printing for structural applications has become increasingly popular. One type of 3D printing is material extrusion, or fused deposition modelling (FDM). A computer model of the desired part is created, and a program called a slicer converts the geometry into instructions for the printer, called G-code. The printer uses the G-code to construct the part layer by layer, where molten polymer is pushed out of a moving nozzle and deposited in a bead or raster. Depending on the part geometry, a single layer can consist of several beads. After the layer cools for a predetermined amount of time, the next layer is printed on top in the same fashion. FDM allows for creation of complex parts with relative ease and low labor requirements [1]. Originally, FDM printers were quite small, with build volumes allowing part sizes on the scale of inches [2]. Within the last decade, researchers have begun working with large-scale printers with print volumes on the order of meters. Furthermore, these printers can use short-fiber reinforcing material which can increase strength and stiffness [3], enabling the applicability of FDM in construction. Large-scale 3D printers have been used to produce concrete form work [4; 5],a culvert diffuser [6], a mold for a vacuum-infused prototype FRP bridge girder [7] and even a small house [8]. These examples show the potential of large-scale 3D printing. However, because of the manufacturing process which induces repeated heating and cooling of the polymer, there are some unique pitfalls to navigate when 3D printing. If the part cools too much between the placement of layers, this can cause warping and poor inter-layer adhesion. However, printing another layer on an excessively hot part can cause collapse [9]. Furthermore, due to the directional nature of the printing process, the strength of these parts is highly anisotropic. Both the strength and unwanted distortions are dependent on the printing parameters, e.g., print speed, layer height, raster direction, bed temperature and chamber temperature to name a few [10]. It is not usually clear a priori which combination of settings produces a successful print, and this can cause an inefficient trial and error manufacturing process that wastes time and materials [11]. In order to remedy this, some researchers have turned to computational models to help predict the behavior of 3D-printed parts. Many different computational models of the FDM printing process have been created. Laminate analysis, typically used for fiber reinforced composites, has been applied to 3D-printed specimens. Each layer of the part is assumed to be a linear elastic orthotropic lamina with a direction of reinforcement, in this case the printing direction. Layers are typically assumed to be perfectly bonded together. Researchers have looked at Acrylonitrile Butadiene Styrene (ABS) [12; 13; 14; 15; 16; 17] or Polylactic Acid (PLA) [14; 15; 18; 19], either neat [12; 14; 15; 16] or reinforced with short carbon fiber [13; 17; 18], long carbon fiber [20] or wood flour [19], obtaining their material properties from either their own uniaxial coupon testing [12; 13; 14; 16; 18; 19; 20] or from existing published literature [15]. Many have focused on using classical lamination theory (CLT) [12; 13; 14; 17; 18; 19; 20], first-order shear deformation theory [15] and/or homogenization [15; 16; 17] to predict the stiffness of uniaxial coupons or multi-layered plates and some have predicted failure using the Azzi-Tsai [16], Hill [13], Tsai-Hill [12; 19] or Tsai-Wu [20] failure criterion. Comparisons of predicted to experimental stiffness and yield strength are typically within 10%. Though laminate analysis shows promise for simple parts made of unidirectional layers, many FDM parts have complex geometry and infill, which cannot be modeled using this method. As a result, some researchers have used beam [21; 22; 23] or shell [24] elements to model the infill of small-scale FDM parts.