Finite Element Analysis
FEA
An Introduction to Application
Brian Maynard
Outline
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Terminology
Overview
WHO USES IT!
Why is this useful for YOU?
What type of analysis is it capable of?
What industries is it used in?
Some Terminology
• Mesh- splitting a model up into small pieces (elements) that make
analysis possible (in this case tetrahedral meshing)
• Element- base unit that is created by the mesh (the tetrahedrons)
• Node- on the surface of the element (green), where the analysis
takes place (I,J,K,L,M,N,O,P)
• Loads- physical forces acting through the nodes
FEA in a Nutshell
• Finite Element Analysis (FEA) is used for finding numerical solutions
for complicated geometries by dividing the pieces of the geometry
into small elements and then coming up with approximate solutions
to PDEs at the nodes. This is an iterative process. These solutions
are then integrated along the whole geometry to come up with a
steady state solution that may evolve with time. A model is solved
when all local nodes retain a certain degree of accuracy after a
certain iteration.
For more on theory see:
http://www.comlab.ox.ac.uk/kathryn.gillow/femtutorial.pdf
Next 3 slides are taken from
Kathryn Gillows talk
After creating a geometry and defining the
material properties, one must MESH!
This is done in the top figure. Meshing
can be done in a variety of ways, it is good
practice to create smaller element sizes
(finer meshing) in areas of greater
complexity. This ensures greater
accuracy in analysis.
After meshing, you want to put some
boundary conditions on your model (add
loads). Then you are ready to solve your
complicated problem FEA style!
Here we see a cylindrical magnetic shield
modeled.
APPLICATIONS!
• The applications of this type of analysis is boundless in industry and
engineering fields ranging from automotive crash analysis to
calculating thermo-mechanical deformation in a pipe to calculating
forces in nasal respiration. The types of loads applied to the model
can be mixtures of mechanical, electrical, thermal, gravitational,
inertial, etc… making its applicability and usefulness obvious for
anyone in engineering.
Is FEA Used for Research in Our
Group?
• Well, Zhou and I use it! It helps Zhou figure out charge
collecting characteristics of pixels, and it helps me figure
out if our pixel VELO is going to experience thermal
runaway (an effect brought on by the irradiated silicon’s
leakage current). This in turn acts as an exponentially
temperature dependent heat source, which under
insufficient cooling and/or high power chip, can cause
some serious damage to the detector!
YIKES!
Other people?
• It is also used for medical imaging research by another
group (Lipson) here at SU in collaboration with SUNY
Upstate Medical (Department of Radiology).
• FEA is also used in other major experiments at CERN for
thermal analysis of the detector (ATLAS, CMS, ALICE)
(below is the ATLAS thermal modeling)
A Quick Walkthrough
• We want to see what
the thermal profile of a
piece of aluminum with
three 1 W heaters
placed on it is. The
cooling will be applied
to areas A and B. The
first step is to create
the geometry and to set
the material properties.
Both are given at the
right.
B
A
Material
Aluminum
Glue
Heater
κ (W/mK)
200
1
150
Pick a Mesh and Mesh
• Does this figure display
my meshed model?
How can you tell?
What do the elements
look like?
Why are the elements
smaller by the base of
the heaters?
How was the pizza?
The Solution
• Here is the complete
nodal solution of all the
input heat loads and
cooling.
Piece of pizza! er…
I mean cake!
Should YOU Use FEA?
• You must first talk with your advisor to make sure that
FEA is right for you. Using FEA for an extended period
of time may cause successful research, contact your
advisor immediately. FEA should not be used with
alcohol and may cause undesirable results. Contacting
your advisor when under the influence is ill advised. For
more information on FEA, search the web or ask
questions to people who have used FEA.
Some Useful References
• Schaum's Outline of Finite Element
Analysis
• http://www.comlab.ox.ac.uk/kathryn.gillow/
femtutorial.pdf