FEA is a numerical modeling tool used for the prediction of how a part or assembly behaves under specific loading conditions.

FEA involves the summation of finite elements by the finite element method. Finite elements can be thought of as small regions broken down from the original part to ease in calculations.

The finite element method takes a numerical approach toward an approximate solution of partial differential equations. The individual finite elements represent an approximation of a partial differential equation used to solve a specific boundary condition.

These finite elements are summated through the body of a part and are represented as a mesh of polygons. The end result is a more usable set of simultaneous algebraic equations which can be more easily manipulated to a desired result.

Why all this emphasis on mathematical theory? Having a greater understanding of how FEA works allows the designer to have a better idea of how to read and interpret the FEA results. This allows for greater part optimization and allocation of material to satisfy loading conditions, making FEA a fantastic and invaluable tool in a designers' toolbelt.