Vol. 2
But how does FEA work?
Many legal professionals are exposed to Finite Element Analysis
(FEA) in the courtroom. Having a fundamental understanding of
how the method works can help an attorney (i) recognize when
FEA can strengthen a case, (ii) choose a capable expert and
(iii) develop meaningful challenges to the opposition's expert.
As discussed in the
last issue
of Courtroom FEA,
if a loss, injury or death is due to something bending or breaking,
FEA can help identify the cause of failure and hence the
responsible party. But how does it work?
But first, let's back up and discuss what is being conquered.
FEA is applied to many types of problems, such as temperatures
in consumer electronics, airflow around aircraft, and magnetic
fields in electric motors. By far the most common application
is structural FEA  determining how a solid body responds to
various forces.
The structural problem amounts to writing down some "governing
equations" that describe the material and how it behaves, and
then solving those equations for the physical part being analyzed
subject to how it is held and loaded. This can be done on paper
for some simple part shapes. The resulting "closed form solution"
is another equation that provides the answer in terms of the basic
variables, such as the part's dimensions.
But reality intervenes, and most parts are too complicated to solve
in closed form. FEA comes to the rescue by providing a "numerical
solution" for each individual problem. This is a large gathering
of numbers approximating the desired answers, such as displacements
and stresses, across the part. But each solution is unique to a
specific case; there is no simple answer in equation form.
Now then, how does FEA divide and conquer the problem to provide the
numerical solution? The answer lies in the name, "Finite Element
Analysis".
"Analysis" is obvious: the part is being analyzed under certain
conditions.
"Element" describes a small section of the part. In fact, the
governing equations mentioned above can generally be derived by considering
a small section, writing the equations for what's happening in that
section, and then mathematically allowing the size of the section to
become infinitesimal, or infinitely small. In FEA, each section is called
an "element", and the elements are not made infinitely small.
"Finite", then, refers to the countable number of elements
used to represent the structure. The elements are of finite, measurable
size. A computer can handle the computations on this finite number of
elements.
Each element acts on its neighboring elements. FEA assembles the equations
from all the elements into one large matrix equation, and the computer
is used to determine the numerical solution. A key concept of FEA is
this: if the elements are made small enough and are spread advantageously
across the part, the numerical solution can closely approximate
reality.
An experienced analyst can prepare the finite element model such that it
accurately predicts the part's behavior, and can ensure that the solution
algorithms do not interject significant errors. Results from the lessexperienced
are often suspect, and identifying them as so can be a tremendous advantage
in the courtroom.
Watch for the next issue of Courtroom FEA.
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