What is the Finite Element Method?

The finite element method (FEM) was independently developed by engineers, beginning in the mid-1950s. It approaches structural mechanics problems. The method started with promise in the modeling of several mechanical applications in the aerospace and civil engineering industries.

But What Exactly Is It?

WiseGeek describes FEM as:

“The finite element method is a tool for computing approximate solutions to complex mathematical problems. It is generally used when mathematical equations are too complicated to be solved in the normal way, and some degree of error is tolerable. Engineers commonly use the finite element method because they are concerned with designing products for practical applications and do not need perfect solutions. The finite element method can be adapted to varying requirements for accuracy and can reduce the need for physical prototypes in the design process.”

In short, FEM makes a numerical solution for a complex matter.

One example is the modeling of complex physical deformations in materials. After a collision, the damage on one end of the vehicle depends on what happened to the other areas.  The collision must be displayed through steps to see what the end result is. Because there are so many steps, it is impractical to model by hand. A computer using FEM can accurately solve the problem.

Boundaries define what conditions it needs for FEM to produce relevant results. In the case of a car collision, the boundary conditions would be the impact the outside object had on the car. The conditions can include point of impact, distributed forces, thermal effects (such as temperature changes or applied heat energy), or positional constraints.

The Advantage of Using FEM

A complete FEM model turns the information into a picture an engineer can analyze to intuitively identify weak points in a design and create a new plan, if needed. Visualization software is a crucial component of the finite element computer programs.

Exciting Prospects

The application of FEM is only now starting to reach its potential. It has a promising future in helping solve problems in areas such as: fluid-structure interaction, thermomechanical, thermochemical, thermo-chemo-mechanical problems, biomechanics, biomedical engineering, piezoelectric, ferroelectric, and electromagnetics.

Coming soon, Finite Element Method Courses from IEEE will provide a comprehensive and up-to-date account of FEM in photonics devices, with an emphasis on practical, problem-solving applications and real-world examples. Engineers will come away from this program with 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.

Resources

What is the Finite Element Method? wiseGeek.

Harish, Ajay. (21 Mar 2019). Finite Element Method – FEM and FEA Explained. SimScale.