# Breaking down FEA

12/12/2018

Finite element analysis (FEA) is the practical application of the finite element method (FEM) of solving engineering and mathematical physics problems that involve complex geometries, applied loads, and material properties that cannot be solved simply with partial differential equations. Compared to analyzing an entire part at once, FEM gives a more accurate representation of complex geometry, can be used on parts with dissimilar material properties, can be used to express local effects, and gives a simple representation of the overall solution.

The basic principle behind FEM, as you could maybe guess from the name, is that the part is broken up into smaller “finite elements” which are interconnected at distinct points called nodes. The number of elements and nodes is defined as the mesh. A finer mesh has more elements and nodes, which allows for more accurate results but takes longer to calculate. Using these elements and nodes, you can create an equation to express the effect of the neighboring pieces for each element in the structure. You can use these equations to create a matrix, which can then be used to solve for the effect on the whole structure. These calculations are nearly impossible to do by hand, which is why FEA software was developed.

FEM was originally developed as a way to solve complex problems in structural mechanics, primarily in aerospace applications. The first paper about FEM was published in the 1950s, though it initially was not taken seriously due to how impractical it was to do by hand. With the creation and development of computer technology, FEM started to become accepted and more widely used. NASA created the first FEA software called NASTRAN (NASA Structural Analysis) in the late 1960s. Many FEA programs have been created since, with some popular programs being ADINA, ANSYS, ABAQUS, DIANA FEA, LS-DYNA and SimScale.

FEA can be used to analyze a variety of problems, since it can be applied to problems expressed as partial differential equations. Some common applications include stress analysis, heat transfer, fluid flow, and electric and magnetic potential. Which software you want to use is heavily based on what applications you have. For example, DIANA is used primarily in civil and structural engineering while LS-DYNA is best known for explicit dynamics and crash analysis.

Image at top: Stress analysis on a part in ANSYS.

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