LAB # 8
Finite Element Analysis Overview
Source: ANSYS documentation
What is Finite Element Analysis (FEA)?
Finite element method is a numerical analysis technique for obtaining approximate solutions to a
wide variety of engineering problems. Usually the problem addressed is too complicated to be
solved satisfactorily by classical analytical methods. The finite element method produces many
simultaneous algebraic equations, which are generated and solved on a digital computer. The finite
element method originated as a method of stress analysis. Today finite element methods are used
to analyze problems of heat transfer, fluid flow, lubrication, electric and magnetic fields, and many
others. Finite element procedures are used in the design of buildings, electric motors, heat engines,
ships, airframes and spacecraft.
The word finite element method was first coined by Clough in 1960 in a paper on plane elasticity
problems. In the years since 1960 the finite element method received widespread acceptance in
engineering. With the advent of the digital computer, it opened a new avenue for solving complex
plane elasticity problems. The first commercial finite element software made its appearance in
The finite element method works by discretizing (breaking a real object into a large number of
small elements). The behavior of each element is readily predicted by set mathematical equations.
Then the computer adds up all the individual behaviors to predict the overall behavior of the actual
object. The word "finite" in finite element analysis comes from the idea that there are finite
numbers of elements in a model. This is in contrast to the classical approach (differential equation
method) where an infinitesimal element is considered for derivation of the governing equations.
To summarize, the finite element method satisfies the governing equations in an approximate or
average sense whereas classical methods insist on validity of the solution at each and every point
in the domain. The finite element method is employed to solve almost all physical systems.
Structural mechanics (stress analysis)
Heat transfer - conduction, convection, radiation
Fluid Flow - both liquid and gaseous fluids