**2. Method**

One of the difficulties with quantifying a geometric temperature coefficient is the complexity of the thermal expansion. Thermal expansion coefficients are nominally nonlinear, leading to different rates of expansion depending on how hot the geometry is in a given location. This leads to nonlinear thermal expansion. This is an important concept to understand because it drives the necessity for using more complex structural analysis techniques than first principles expansion. This is especially true when geometric expansion is mechanically restrained by other expanding materials.

The key to successfully quantifying a thermal expansion derived temperature coefficient is not the calculation of the coefficient itself, but more the mechanical model that is used to derive the geometry changes. To that end, finite element analysis is used to provide a high fidelity mechanical input into the Monte Carlo simulation [3]. **Figure 3** shows the generalized process for quantifying the temperature coefficient.

**Figure 3.** *General process flow.*

*Nuclear Reactor Thermal Expansion Reactivity Effect Determination Using Finite Element… DOI: http://dx.doi.org/10.5772/intechopen.93762*

#### **2.1 Finite element analysis**

Regardless of the source of the geometry information, whether an existing CAD model is defeatured or built from scratch, a simplified CAD geometry should be generated. The simplified geometry should contain enough information such that any complex expansion is captured, but simple enough to reduce the overall element count. A common example is removal of bolts and generally any small features from large geometries. FEA models in general run the risk of being too-large-to-compute without using resources unavailable to the typical engineer. Keeping total element count to a minimum is a driving factor when constructing an FEA model.
