The Finite Element Method (FEM) is a general mathematical and numerical method for finding approximate solutions to differential equations. Its strength is at solving partial differential equations from fields such as structural mechanics, since these equations are generally too complicated to solve using analytical methods from the basic math courses. The finite element method is especially good at dealing with complex 3D geometry and handling of boundary conditions.
In industry one usually talks about FE-computation or FE analysis.
In a nutshell the method takes a differential equation which is valid point-wise and extends it to a finite set of simple geometrical elements across the whole domain of interest. These elements are engineered specifically to be easy to handle by the computer. The elements are typically made of simple triangles or squares (2D and shells) and connected together with special points (nodes) in the corners or edges. Knowing the condition in the nodes, the behavior within the element can easily be described using interpolation. The complete set of elements of a structure is known as the mesh.
Video by The Efficient Engineer[1]
This website has support for annotation using Hypothesis. All pages should have a toolbar on the far right.
Hypothesis enables you to make and share public notes with the author and other readers or private notes and highlights, which are only visible to you.
To use this feature, just create a free account and you are up and running.
We encourage you to use this feature as much as possible, let us know if there are mistakes, if you do not understand something, etc.
We stand on the shoulders of giants. Thanks to prof Peter Hansbo.
This site is inspired by the Computational Thinking course given at MIT, as well as the Underactuated Robotics course.
This site uses the Pluto and PlutoSliderServer projects to enable the interactivity and Franklin as a static site generator, all built on the Julia language. Thanks to the community, who create amazing tools and propel us into an exciting future.
| [1] | Be sure to check out The Efficient Engineer's other content on mechanical engineering, the channel is a gold mine! |
