# Computing displacements and factors of safety

After a validation or an optimization step completes, SmartSlice returns values of maximum displacement and minimum safety factor. This section provides an overview of how these values are computed.

The short explanation is that SmartSlice constructs a finite element model (FEM) based on the part geometry, print settings, and data provided by the slicer after the part is sliced. This model is sent to our finite element analysis (FEA) solver where the solution is solved, and the displacement and safety factor results are computed.

Here is the more elaborate explanation. One of the most common methods for simulating the behavior of a part is called the finite element method (FEM). The FEM is a numerical method used to compute solutions to many problems in areas such as heat transfer, structural analysis, and vibrations and it is used in every industry imaginable from aerospace and automotive to consumer goods. There are many resources available for learning about the FEM and a good place to start is on Wikipedia.

In general, FEM models are built “by-hand” using commercial FEA preprocessor software. For many parts, this process is relatively straightforward but it becomes very arduous and challenging for parts manufacturing using 3D printing techniques such as fused-filament-fabrication because such parts contain spatially varying micro-structures and material properties. To overcome these obstacles, SmartSlice automatically constructs, solves, and processes a FEM using data from the slicer and material property data derived from experimental testing. The general steps in this process are as follows:

• The part geometry (.stl file) and the print settings (layer width, infill density, etc.) are sent to the  slicing engine to be sliced and the engine returns a set of “sliced data”.

• Then, this data is used to construct a finite element mesh of the part.

• Additionally, this sliced data is used to assign material properties that correspond to each region of the part. There are 3 types of regions: walls, infill, and top/bottom layers. Click here to learn how the material properties are computed.

• The mesh is constrained using the anchor and load surfaces that users defined in SmartSlice.

• Next, the model is sent to our FEA solver and the solution to the FEM is computed.

• From this solution, the maximum displacement and minimum safety factor are calculated.

The net result is that SmartSlice constructs and solves a high-fidelity FEM in a matter of seconds or minutes compared to hours or days for a hand-built FEM of the same part. And this all happens in the cloud so it does not demand any local machine resources.