Finite element analysis (FEA) is a computerized method for predicting how a component/assembly will react to environmental factors such as forces, heat, and vibration. Though it is called “analysis,” in the product design cycle, it is used as a virtual prototyping tool to predict what is going to happen when the product is used.

Finite element analysis, as related to the mechanics of solids, is the solution of a finite set of algebraic matrix equations that approximate the relationships between load and deflection in static analysis and velocity, acceleration, and time in dynamic analysis.

In 1678, Robert Hooke set down the basis for modern finite element stress analysis as Hooke’s Law. Stated simply, an elastic body stretches (strain) in proportion to the force (stress) on it. Mathematically, the formula is as follows:

**F=kx**

Where:

**F** = force

**k** = proportional constant

**x **= distance of stretching

This is the only equation one needs to know to understand linear finite element stress analysis.

The finite element method works by breaking a real object down into a large number of elements (1000s or 100,000s of cubes), as shown in the following graphic. The behavior of each little element, which is regular in shape, is readily predicted by a set of mathematical equations. The summation of the behavior of each individual element produces the expected behavior of the actual object.

The finite element is a small, but not infinitesimal, part of the mechanical structure being modeled. The mechanical structure applied complex strength of materials formulations on simple geometric shape. The simplest examples are rods, beams, and triangular plates. More complicated elements include quadrilateral plates, curved shells, and 3D solids such as hexahedrons (bricks).

The word “finite” in “finite element analysis” indicates that there are a finite number of elements in a model, such as a piston. Prior to the development of FEA tools, engineers employed integral and differential calculus techniques to solve engineering analysis problems. These techniques break down objects into an infinite number of elements for problem solving.