The Finite Element Method: A Four-Article Series
FINITE ELEMENT ANALYSIS: Introduction
First in a four-part series
Finite element analysis (FEA) is a fairly recent discipline
crossing the boundaries geometric series of mathematics, physics, engineering
and computer science. The method has wide application and
enjoys extensive utilization in the structural, thermal and
fluid analysis areas. The finite element method is
comprised of three major phases:
(1) pre-processing, in
which the analyst develops a finite element mesh to divide
the subject geometry into subdomains for mathematical
analysis, and applies material properties and boundary
(2) solution, during which the program derives
the governing matrix equations from the model and solves for
the primary quantities, and
(3) post-processing, in which
the analyst checks the validity of the solution, examines
the values of primary quantities (such as displacements and
stresses), and derives and examines additional quantities
(such as specialized stresses and error indicators).
The advantages of FEA are numerous and important. A new
design concept may be modeled to determine its real world
behavior under various load environments, and may therefore
be refined prior to the creation of drawings, when few
dollars have been committed and changes are inexpensive.
Once a detailed CAD model has been developed, FEA can
analyze the design in detail, saving time and money by
reducing the number of prototypes required. An existing
product which is experiencing a field problem, or is simply
being improved, can be analyzed to speed an engineering
change and reduce its cost. In addition, FEA can be
performed on increasingly affordable computer workstations
and personal computers, and professional assistance is
It is also important to recognize the limitations of FEA.
Commercial software packages and the required hardware,
which have seen substantial price reductions, still require
a significant investment. The method can reduce product
testing, but cannot totally replace it. Probably most
important, an inexperienced user can deliver incorrect
answers, upon which expensive decisions will be based.
FEA is a demanding tool, in that the analyst must be
proficient not only in elasticity or fluids, but also in
mathematics, computer science, and especially the finite
element method itself.
Which FEA package to use is a subject that cannot possibly
be covered in this short discussion, and the choice involves
personal preferences as well as package functionality.
Where to run the package depends on the type of analyses
being performed. A typical finite element solution
requires a fast, modern disk subsystem for acceptable
performance. Memory requirements are of course dependent on
the code, but in the interest of performance, the more the
better, with 512 Mbytes to 8 Gbytes per user a representative
range. Processing power is the final link in the
performance chain, with clock speed, cache, pipelining and
multi-processing all contributing to the bottom line.
These analyses can run for hours on the fastest
systems, so computing power is of the essence.
One aspect often overlooked when entering the finite element
area is education. Without adequate training on the finite
element method and the specific FEA package, a new user will
not be productive in a reasonable amount of time, and may in
fact fail miserably. Expect to dedicate one to two weeks up
front, and another one to two weeks over the first year, to
either classroom or self-help education. It is also
important that the user have a basic understanding of the
computer’s operating system.