## October 9, 2014

### Symmetry in SOLIDWORKS Simulation - Guide to Applying Loads & Restraints Appropriately

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.