Article
How the Finite Element Method (FEM) and Finite Element Analysis (FEA) Work Together
The finite element method (FEM) and finite element analysis (FEA) work together to give engineers insight into the structural behavior of designs. This combined approach helps them locate weak points and strengthen performance.
FEM
Engineers developed FEM in the mid‑1950s to provide numerical solutions for complex problems. In practice, FEM allows for some degree of error, making it useful when equations are too complicated to solve directly. Put simply, FEM breaks a large problem into smaller ones (“finite elements”), which makes the overall challenge easier to investigate. Engineers rely on FEM when they need to design adaptable solutions. Although practical, FEM does not always deliver perfect results for every application.
FEA
Engineers apply the mathematical equations behind FEM to create a simulation, known as a finite element analysis (FEA). Through these simulations, they can analyze how a product or design reacts under stress in real‑world conditions. The simulation divides the model into smaller elements within a mesh. By doing so, engineers test how different parts of a design interact and perform under simulated stressors.
In other words, FEA provides a virtual model that lets engineers experiment with structural designs using software. Together, FEA and FEM predict the structural behavior and integrity of a design.
Trevor English explains in Interesting Engineering:
Complex mathematics is required in order to understand the physical phenomena that occur all around us. These include things like fluid dynamics, wave propagation, and thermal analysis…Yet, in complex situations where multiple highly variable equations are needed, Finite Element Analysis is the leading mathematical technique.”
Trevor English, Interesting Engineering
Benefits of FEM and FEA
Improved accuracy and enhanced design: FEM and FEA allow for enhanced accuracy of structural analysis. They give insight into how the various elements of a design interact in minute detail. Engineers can investigate both the interior and exterior of a design.
Faster and inexpensive testing: Because FEM and FEA allow engineers to create virtual simulations, they reduce the need for physical prototypes and testing. This saves time and reduces costs.
Applications of FEM and FEA
Traditionally, FEM was used to test designs within aerospace and civil engineering. However, it is now expanding to other disciplines. These include biomechanics, thermomechanical, fluid-structure interaction, biomedical engineering, ferroelectric, thermo-chemo-mechanical problems, piezoelectric, and electromagnetics.
The mathematical principles behind FEM can also be applied to other areas. These include computational fluid dynamics (CFD) and the thermal dynamics of a structure.
“For example, if you know the temperature at one point in an object, how would you determine the exact temperature at other points of the object, dependent upon time?” writes Trevor English in Interesting Engineering. “Utilizing FEA, an approximation can be made for these points using different modes of accuracy. There’s a square approximation, a polynomial approximation, and a discrete approximation. Each of these techniques increases in accuracy and complexity.”
Learn the Finite Element Method (FEM)
The new course program from IEEE Educational Activities, Finite Element Method for Photonics, provides a comprehensive and up-to-date account of FEM in photonics devices. It emphasizes practical, problem-solving applications and real-world examples. Engineers will gain an understanding of how mathematical concepts translate to computer code finite element-based methods.
Connect with an IEEE Content Specialist today to learn how to get access to this program for your organization.
Interested in the course for yourself? Visit the IEEE Learning Network (ILN).
Resources
Gigantic, Michael. (10 September 2020). What Is Finite Element Analysis? Learning Hub.
English, Trevor. (7 November 2019). What Is Finite Element Analysis and How Does It Work? Interesting Engineering.
Harish, Ajay. (21 Mar 2019). Finite Element Method – FEM and FEA Explained. SimScale.
The Benefits of Finite Element Analysis in Manufacturing. Manor Tool.
Thursday, 7th May 2020