The Finite Element Method: A Four-Article Series - Part 1
The following four-article series was published in a newsletter
of the American Society of Mechanical Engineers (ASME).
It serves as an introduction to the recent analysis discipline
known as the finite element method. The author is
an engineering consultant and expert witness specializing in
finite element analysis.
FINITE ELEMENT ANALYSIS: Introduction
by Steve Roensch, President, Roensch & Associates
First in a four-part series
Finite element analysis (FEA) is a fairly recent discipline
crossing the boundaries 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 conditions, (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 available.
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.
Next month's article will go into detail on the pre-processing
phase of the finite element method.