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Finite Element Analysis (FEA)
Finite Element Analysis (FEA)
Finite Element Analysis is essentially a generated simulation based on known physical properties of a given object or test.
More specifically, FEA makes use of a mathematical technique called Finite Element Method, a system of basic equations that can be combined to model complex systems.
3D printing
3D printing
3D printing poses a challenge to finite element analysis because the pieces are not uniformly manufactured.
Since finite element method relies on building complexity from simplified equations, it cannot model the way printing orientation effects a piece.
My goal is to explore how accurately finite element analysis can predict the deformation of 3D printed objects
Elasticity: Stress and strain
Elasticity: Stress and strain
Stress is an internal force defined by: force/area
Strain is a measurement of deformation, defined by: change in dimensions/the original dimension (before a force is applied)
Shown to the right is a stress-strain curve. Stress-strain curves are measured from real materials by slowly applying a force and tracking the deformation. Using this data, predictions about the behavior of similar materials under load can be made.
There are several elements that are key to understanding a stress-strain curve. The first is plastic vs elastic deformation.
Plastic Deformation
Plastic Deformation
Although the name may at first seem counter-intuitive, plastic deformation is when a material has deformed past the point of "snapping back into place."
When you bend a fork enough, it stays bent instead of springing back
Elastic deformation
Elastic deformation
Elastic deformation is when a materials springs back into its starting place after a force has been applied to it
With either a spring or a rubber band, they will snap back to their original size, even after being deformed
How do we analyze this?
When a material has enough force applied to it, it reaches its elastic limit
Once this happens, the relationship between stress and strain are no longer necessarily linear
Because of this, its much harder to analyze an object past its elastic limit, so keeping the force in the linear zone is important
Testing predictions
Testing predictions
I wanted to analyze a piece with relatively simple geometry, so that force modeling wouldn't get too complex
Although the CAD model was fairly simple, I still needed to accurately recreate the forces acting on the test piece
SolidWorks Simulation Overview.mp4Simulation Demo
Simulation Demo
Here you can see the brief process I went through to run a basic simulation in SolidWorks
Reality
Reality
This was the deformation of the test piece when I had filled the weight of the water bucket up to 10 pounds
The piece started to deform overall much faster than I predicted, so I increased in smaller increments to remain in the elastic region for as long as possible
Prediction
Prediction
Although this picture looks initially promising, it was actually the prediction at the point where 3x the amount of force would be applied.
I expect a large amount of error comes from the way the piece is manufactured, but I will expand on this in my sources of error
Sources of Error
Sources of Error
I didn't have a clear idea of when the piece moved from elastic to plastic deformation
Since analysis becomes much more difficult outside of the linear relationship between stress and strain, I needed to do a few tests to gain a better understanding of where the elastic limit was
3D printing structure
Although the piece had 100% infill, it's unclear to what extent the fabrication method effected the final result
Work Cited
Work Cited
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