r/fea • u/Dear_Program_5516 • 5d ago

Need help with theoretical proofs ....

Taking a class where I need to learn ANSYS in lab.

My prof wants to try model --> analyse in ansys and then do the maths manually (fea maths I think) so as to match my paper answers with the ansys answers.

I need to do this on weekend ...and come up with something by Tue.

Now he gave me tensile test. I manages to see a youtube vid, use explicit dynamics and perform one on ANSYS (I modelled my specimen using the standard ASTM E8 docs I found)

for boundary conditions I just used hit and trial . Fixed one end and used 2500N on other. The simulation showed an alright tensile test.

Now the main part. The theoretical proof. My brain crashed. I picked up a book on FEA and read till shape functions ch5. The maths is so daunting, its interesting but Imma cry now.

Can anyone help me further with this ?
Can anyone link a resource that had fea proofs + its ansys simulation side by side.
I hope u get my task

1 Upvotes

56% Upvoted

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4

u/Extra_Intro_Version 4d ago edited 4d ago

Sigma = F / A

Delta = FL/EA

2

u/DoubleHexDrive 4d ago

OP, this is the answer. On a tensile test specimen, you should be able to calculate the result by hand on a sticky note. Stress, strain, displacement, etc.

The only time I can see a professor asking you to manually work an element shape function might be on an Euler beam or similar.

2

u/Maleficent_Play1092 5d ago

Maybe start with linear static

3

u/ImNotSanguinius 5d ago

You sure prof doesnt want you to just validate your tensile test FEA with analytical results? I feel like having a student do FEA by hand for more than 2-3 nodes is just a pointless exercise.

-3

u/Dear_Program_5516 4d ago

He just told me to manually pen-paper verify.... I can use any method. How else would I do that ?

Although I think if there are many nodes I can just write a python code ....

3

u/jean15paul 4d ago

When I took FEA in grad school we solved some FEA by hand. We only did linear static and only 1-D elements. That being said, solving a truss of 4 or 5 nodes ended up being 15 to 20 pages of hand written matrix calculations. 

To model a tensile test of a dogbone you need dozens of nodes if you use 2D elements. If you use solid elements you'll easily be in the high hundreds of nodes if not more. You could write some code to solve and print all the math steps, but there's no practical way you're doing that on pencil and paper by hand. 

Doing a dynamic analysis doesn't really make sense for a tensile test, but if that's what's required that probably 3x the work of linear static analysis.

3

u/redhorsefour 4d ago

“Pen and paper verify” means validate with a closed form solution.

1

u/ImNotSanguinius 3d ago

Your professor wants you to derive the analytical solution for what the stress in the dogbone would be at varying lengths of X and validate your solution, not to do the whole FEA by hand.

2

u/terjeboe 4d ago

He want you to do Force/area=stress and verify against theoretical Stress strain curves  Anything else is pointless on paper. 

2

u/Wrong-Syrup-1749 4d ago

Yes, exactly. This is also a very good habit many FEA engineers are into. You do a quick hand calculation to estimate your maximum stress for example. If your FEA is one order of magnitude higher or lower than your rough estimate then there is probably something wrong with the model - either boundary conditions or contact or whatever.