## Amazing Analyses

*FEA software is capable of more than ever, except engineering judgment.*

January saw the death of British mathe-matician Olgierd Cecil
Zienkiewicz, an early pioneer of the finite element method who pushed
for its computerization and who recognized the potential for using the
method to solve problems outside solid mechanics, purview of the famous
Euler-Bernoulli beam equation.

With his passing, we pause to
assess FEA’s past—looking at the pros and cons of the leap the method
has made into the software realm—and to look at what the future holds
for finite element analysis and its applications.

From its
inception in the 1940s until about a decade and a half ago, finite
element analysis had been performed exclusively by specialized analysts
who held Ph.D.s in the subject and had devoted their careers to the
discipline. But the FEA field has seen great change over the past 15
years, with a jump in the number of computer technologies available to
an increasing number of engineers. And like all changes, it has brought
risks and rewards.

In his lifetime, Zienkiewicz saw the finite
element method move from a powerful technique originally developed to
solve complex structural mechanical problems to its use today across
nearly all engineering fields, including bioengineering—and its stretch
into unrelated fields such as the simulation of weather patterns.
Beginning in the 1960s, FEA researchers began to extend the method
beyond linear structural analysis to nonlinear FEA and other
engineering disciplines such as fluid dynamics, heat transfer, soil
mechanics, wave propagation, and electromagnetics.

*Since
its inception in the 1940s, finite element analysis—originally
developed for numerical solution of complex problems in structural
mechanics—has become established in nearly all engineering fields,
including bioengineering, where it plays a role in studying many parts
of the body, such as nasal passages.*

Zienkiewicz himself sought to move the finite element method from a
research tool to a computer-based analysis method that could be called
upon by designers and engineers. And in 1968 he founded the first
journal dealing with computational mechanics, the *International Journal for Numerical Methods in Engineering*.

Today,
high-end FEA software packages are available to solve complex problems
across many disciplines. But they’re still not perfect; that is, the
engineers and researchers who use these tools can spend a lot of time
kitting them out and programming them for their own unique use.

Other
FEA packages introduced within the past 15 years are now commonly
integrated with computer-aided design applications, allowing product
developers to analyze as they design. The integration is intended to
speed up the design cycle because designers can analyze, then
immediately update, their designs.

**easy access**

Without a doubt FEA’s move to
the computer allowed it to become the widely used tool it is today,
said Samer Adeeb, an assistant professor in the department of civil and
environmental engineering at the University of Alberta in Edmonton. By
helping move the tool to the computer, Zienkiewicz enabled its
popularity and its growth, Adeeb added.

In the early 1970s, FEA
was run only on mainframe computers owned mainly by companies in the
aeronautics, defense, and nuclear industries. With the rapid decline in
the cost of computers and the concomitant increase in computing power,
today’s personal computers can now produce accurate FEA results. Adeeb
pointed out that many engineering technology vendors are currently
marketing simplified analysis programs, which walk users through a
series of steps that allow them to define the analysis they want to run
and then interpret the results.

“FEA has been around forever,
but it’s grown to be very powerful because of the computational power
that exists right now in computers,” Adeeb said.

“The problems
we’re now solving with FEA couldn’t have been done ten years ago
because you would have needed a mainframe,” he added. “Now a desktop
has enough computation power that anyone can run FEA.”

*FEA is now used by disparate industries for a range of applications. The packaging industry calls upon it to analyze designs for blow-molded products, including bottles, top. Bioengineers call upon the software for their own use, such as studying the growth of a human bone, bottom.*

That jump to the desktop makes for the packages that allow CAD users
to run more up-front analysis during design, but it can also mislead
untrained analysts, who may not fully understand the finite element
method and won’t exactly know how to best input information or how to
interpret results, Adeeb added.

“FEA is becoming so easy to run
and is so highly integrated with all the CAD software now, but the
output from the analysis is still the numbers a designer uses to
determine if the part is safe or not safe,” he said.

“It’s
sometimes too easy to toggle back and forth between CAD and FEA without
really knowing what you’re doing,” he said. “Some people abuse FEA
because it offers such a nice animation; so they try to get to the
animation they want rather than to actually solve a problem that
returns useful information.”

According to Adeeb, FEA software
shouldn’t be relied upon as a black box that spits out numbers.
Designers still need to know the proper inputs and to understand what
those numbers mean. The old adage holds true, he said: garbage in,
garbage out.

To get meaningful analysis results, designers
need to know how to identify the problem that needs solving in the
first place. That requires at least a basic understanding of the finite
method, he added. Before beginning analysis, designers will need to
simplify the problem at hand, to ask themselves whether the problem is
linear or nonlinear, and to identify the forces that need to be
analyzed.

As an instructor, Adeeb knows this line of
questioning doesn’t come intuitively to users who have little or no
understanding of the finite element method.

As a numerical
technique, FEA allows engineers to find approximate solutions of
partial differential and integral equations. FEA software simulates
where structures bend or twist and indicates the distribution of
stresses and displacements. The software uses a complex system of
points to form a grid, or mesh, across a model. The engineer assigns
nodes at a particular density throughout the material, often depending
on the expected stress levels of a certain area. The mesh contains the
material and structural properties that define how the part will react
to certain load conditions.

“The first question I ask my
students on exams is: what is FEA and why do you need it?” Adeeb said.
“If people can’t offer the correct definition of what it is I don’t
trust them using FEA. Within the definition itself lies the
understanding of what they’re doing.”

Companies that hire designers to perform both CAD and FEA should offer new employees an introductory course to FEA, Adeeb said.

“Otherwise
what they’re doing is just an animation, and that doesn’t differ from a
computer scientist who is just drawing on the computer,” he said.

**the simple stuff**

Though desktop FEA has come
a long way in the past few decades, everyday users—even those well
trained in FEA—still face everyday problems when trying to analyze
designs and behaviors as part of their jobs, said Rick James, vice
president of consulting at the SimuTech Group of Rochester, N.Y.

One
problem is that while many FEA applications are integrated with CAD
systems today, many of these calculate what James called “the simple
stuff”; that is, they perform relatively basic stress and fatigue
analyses. Users will need to purchase a third-party analysis
application to run advanced fatigue analysis or other types of analyses
on top of the simple stuff, he said.

“Most FEA desktop software
doesn’t do the niche stuff like crack-growth propagation, where you’re
watching a crack form and move on the screen,” James said.

And advanced FEA add-ons require that users have much more information to hand.

According
to James, “This advanced fatigue stuff asks for this load history and
that load history and then this residual stress from welding.”

Thus,
the everyday CAD users will likely need advanced training to best use
advanced packages. Training costs and software costs can quickly add
up. According to James, extra analysis software on top of the already
existing FEA application can run companies anywhere from $30,000 to
$60,000 depending on the package, the number of packages needed, and
user needs.

But the companies that really need advanced FEA capabilities simply can’t get by with everyday FEA software alone, he said.

**already here**

But the good news is that for
many uses the everyday FEA software of the type integrated with CAD
systems has advanced enough to be of great help. In fact, according to
Adeeb, the software is very user friendly and—when properly programmed
by the user—adept at analyzing most FEA engineering problems.

“For
certain applications, like analyzing engineering structures that behave
according to theories developed one hundred years ago, FEA software
doesn’t need advancing,” he said.

But the story differs when
high-end FEA packages are used for applications not strictly related to
engineering, such as biomedical problems, he said. The human body,
after all, is nonlinear in behavior. So not only is defining the
complex problems related to the body a challenge for a researcher, so
is determining how to call upon FEA software to best solve them, Adeeb
said.

For example, as part of his research, Adeeb needed to
create and analyze a model of a human bone as it grew. For this, he
used Abaqus, software marketed by Dassault Systèmes of Paris, a
powerful, high-end package used to solve complex physical problems.

Software
for complex simulations isn’t plug and play, Adeeb said. The software
programs meant to model complex or unusual problems are built to allow
their users to configure the software—to a certain degree—to their own
unique needs.

“I can do the analysis, but it takes me a lot of
trying to fool the software and coming up with workarounds; it’s not
something I can directly model, and it takes me a long time to try to
model something like that,” he said.

Researchers can be assured
the vendors of these customizable, high-end systems like Abaqus and
Ansys of Canonsburg, Pa., will be stepping up with software to suit
specialized needs in the future. But for new and specialized
applications like biomedical software, development takes time, James
said.

“But FEA software has proven to be very lucrative so it’s worth it for these guys to work on development,” he added.

Still,
whether researchers and engineers call upon FEA software to solve
complex problems or to analyze fairly straightforward structures as
they design, they’ll need to bring their own judgment to the problem at
hand, James said.

“FEA is never going to be the ultimate
decision-making tool, nor should it be,” he said. “It’s still used for
mathematical equations and modeling physics, and you still have to use
engineering judgment when calling out a result you don’t think is true,
even if your software can do amazing feats.”

But the mix of
engineering know-how, engineering judgment, and amazing feats of
software make for analysis and design never dreamed possible before the
age of FEA.

In 1998, upon acceptance of the Timoshenko Medal
from ASME, Zienkiewicz speculated about the future of FEA by referring
to Charles Duell, commissioner of the U.S. Office of Patents in 1899,
who famously speculated that everything that could be invented had
already been invented.

“I do not share this pessimistic view,
and I think we shall see many exciting developments in the coming
years,” Zienkiewicz said. “It is evident that both applied mechanicians
and mathematicians will continue to contribute to the numerical
analysis field.”

He said that more than a decade ago, and it still stands.