Definition of Finite Element Analysis

In mathematical terms, Finite Element Analysis (FEA), also known as the Finite Element Method (FEM), is a numerical technique for describing physical phenomena in terms of partial differential equations. Finite element analysis is widely used in many engineering disciplines for solving structural mechanics, vibration, heat transfer, fluid flow, electromagnetics, and other problems.

For a video that introduces the basics of FEA, see Basics of Stress and Strain for 3DEXPERIENCE.

You use the FEM to predict the behavior of mechanical, thermal, electrical, and chemical systems under their operating conditions, to reduce the design cycle time, and to improve overall system performance.

The basic steps in any FEA process are as follows:

Geometric representation
Creates the geometric features of the system to be analyzed stored in a CAD database.
Discretization of geometry
Splits the geometry into relatively small and simple geometric entities, called finite elements. This discretization process is better known as mesh formulation. The elements are called “finite” to emphasize the fact that they are not infinitesimally small, but only reasonably small in comparison to the overall model size.
Element formulation
Develops the equations that describe the behavior of each element. Material properties for each element are considered in the formulation of the governing equations. This involves choosing a displacement function within each element. Linear, quadratic, and cubic polynomials are frequently used functions.
Assembly
Obtains the set of global equations for the entire model from the equations of individual elements. The loads and support (boundary) conditions are applied to the appropriate nodes of the finite element mesh.
Solution of equations
Provides the solution for the unknown nodal degrees of freedom (or generalized displacements).
Postprocessing
Obtains visualization plots for quantities of interest, such as stresses and strains.

Note: FEA is not the only tool available for numerical analysis. Other numerical methods used in engineering include the Finite Difference Method, Boundary Element Method, or Finite Volumes Method. However, due to its versatility and high numerical efficiency, FEA has come to dominate the software market for engineering analysis, while other methods have been relegated to niche applications. Using FEA, you can analyze models of complex shapes under their operating load environment and predict their behavior within the desired accuracy.