We are frequently asked here in techsupport what value of a load to apply when using symmetry to cut down on the
size of the overall problem that needs to be solved. As you will see, it is different for how you
handle Force and Pressure loads in Simulation FEA. We can even look into comparing this to the
mass and volume flow rates and velocity or pressure conditions in Flow
Simulation. You can use this blog post
as a guide to help you in modeling up your own problems when you want to use
the benefits of symmetry.
First off, let’s talk a little about when
you can use symmetry. Note that the true
determination of whether you can use symmetry or not depends on the final
results, but that seems a bit contradictory because your looking to solve the
problem and don’t have any results yet.
But there are 3 hints that can clue you into whether symmetry might be
feasible: 1) Obviously the geometry has to be symmetrical, but even if it is
not absolutely symmetrical, such as some details that don’t affect the overall
results and you can assumptively ignore those details . A typical example I recall is the screw for a
cap on the top of a bottle. 2) The
restraints and loads are symmetric. You
should look at this from the perspective of a free-body diagram (FBD), and the
example I use below will help to explain this better. 3) The material is symmetric; a rare case
when considering symmetry is where the materials are different, but it could be
an odd case when working with assemblies.
Again these 3 clues are not fail safe, and
the ultimate determination is in the final results. Using symmetry is a modeling assumption, and
for all analyses, you need to take note and manage your assumptions. If you have some experience with your model
and how it will behave, then this can also help to lead you to a decision if
symmetry is OK to use.
Let’s take the above example of a flat
plate with a hole in the center. It has
a fixed restraint on the left-hand side and a uniform Force applied on the
right-hand side face. When we check the
geometry using a SOLIDWORKS tool: Tools
> Symmetry Check, you can see that the part is symmetric about all three
directions showing that we can choose to keep a 1/8th section of the
original. Now when considering if the
loads and restraints are left-right symmetric, it initially doesn’t seem so
since we have a Force on one end but a Fixed restraint on the other. But from a FBD perspective, you will know
that the restraint will apply an equal and opposite reaction force, so it
actually is a symmetric loading case.
And it is the same material throughout the part, so no problem there.
Note that the face where the load is
applied is cut into four parts, so the question is: Do we need to change the
load? If we think about it, it makes
sense that if the same force were applied to only a quarter of the model, then
the results would be larger… exactly 4 times larger, in this linear test
case. So the conclusion can be made that
we should divide the original force by 4, or F/4. If the original load magnitude was 100, it
should now be 100/4 or 25.
Then, what happens in the case where we
have a Pressure load applied? Pressure
is defined as a force over unit area. If
the area is decreased by 4 times by the symmetry cuts, then the resulting force
that the Pressure exerts is automatically 4 times less. Thus, when we apply a Pressure in the context
of using symmetry, the magnitude of the load does not need to be adjusted.
There is a special case of symmetry that I
need to point out where both the Pressure and Force are unchanged. The special case is when we use the 2D
Simplification tool available in Simulation.
The full load, whether force or pressure, is applied to the edge of the
2D geometry as if it were to be applied to the entire model thickness (in the
case of a plane strain or plane stress problem) or the entire 360o revolve
(in the case of an axisymmetric problem).
In SOLIDWORKS Flow Simulation, currently
you can do a half or quarter symmetry solution by only changing the
Computational Domain options, i.e. you don’t actually cut the model but instead
change the bounding box where the calculation is performed. The values for Mass and Volume Flow Rate
boundary conditions are absolute (akin to a Force in FEA), So you will need to
reduce the flow rate by ½ or ¼ if you are using a half or quarter domain,
respectively. Pressure is the same as
pressure in a structural calculation, so no adjustment needed there. What about velocity? Velocity does not need to be changed either;
if you think about it from a flow rate perspective, where the rate needs to be
reduced because the amount of fluid moving through that opening changes, but
the velocity of the fluid will always be the same.
Important details not to forget when using
symmetry:
Make sure you apply the
appropriate symmetry conditions on all the faces that have been cut. There is a restraint type called Symmetry
(found under the Advanced restraint types), but this has the limitation that it
can only be applied to faces that are orthogonal (90o) to one
another, hence will not work on a pie sliver type of cut, for example. So it’s best to know that actual definition
of a symmetry restraint, in case that you need to apply manually using the Use
Reference geometry restraint type, is that the face can only translate on the
plane and cannot rotate out of plane. In
other words, the Normal translation and the other two directional Rotational
degrees-of-freedom are held to zero.
(Aside: Did you know that you can apply an Anti-Symmetric
restraint by applying just the opposite conditions as described above?)
Symmetry can be used for the
following study types: linear Static, Thermal and Nonlinear. It SHOULD NOT BE USED in a Frequency,
Buckling, Drop Test or Linear Dynamic study.
The results from all of these will most definitely have non-symmetric
responses. If you use symmetry in a
Frequency study, for example, you will only be able to extract the resonant
frequencies which are symmetric, and you would miss all of the non-symmetric
shapes.
For a Thermal study, when a
face has no condition set on it, it is defined as adiabatic, that is no heat
enters or leaves through this face, hence the symmetric condition is set by not
defining a condition to it. A Heat Power
load (in Watts) is absolute, so like a Force, has to be divided. A Heat Flux (in W/m2) is an
integrated over an area, so like a pressure does not need to be changed. Temperature is temperature, like a prescribed
value, so no need to change as well.
Final Stress Results from the plate with a hole using a proper symmetry loading conditions.
