The finite element method (FEM) was independently developed by engineers, beginning in the mid-1950s, to address structural mechanics problems related to aerospace and civil engineering. It started with significant promise in the modeling of several mechanical applications in these areas.
But What Exactly Is It?
WiseGeek describes FEM this way:
“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 is a numerical technique used to perform finite element analysis of any given physical phenomenon.
One example is the modeling of complex physical deformations in materials, such as damage to a car resulting from a front end collision. Deformations in one area depend on deformations in other areas, so the collision must be modeled over several steps in time to see what the end result is. Because there are so many steps, it becomes impractical to model by hand, but a computer using FEM could solve the problem with a high degree of accuracy.
For FEM to produce meaningful results, a set of boundary conditions must be set up to define the conditions the model needs to respond to. In the case of a car collision, the boundary conditions would be the forces inflicted on the car by the external object. Boundary conditions can include point forces, distributed forces, thermal effects (such as temperature changes or applied heat energy), or positional constraints.
The Advantage of Using FEM
FEM makes it easy to produce detailed visualizations of a problem. Once a model has been fully solved, the information can be transferred into a picture. Visualizations allow engineers to intuitively identify weak points in a design, and this information could be used to create a new design. Visualization software is an essential part of many finite element computer programs.
The application of FEM is only now starting to reach its potential. One of the most exciting prospects is its application in coupled problems 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.
What is the Finite Element Method? wiseGeek.
Harish, Ajay. (21 Mar 2019). Finite Element Method – FEM and FEA Explained. SimScale.