Existing work on finite element result analysis

[feynman1]

Is there any existing work focusing on analyzing finite element visualized results and how they differ from analytical solutions, rather than on the method?

 

[FEAnalyst]

Well, that's something one should do whenever possible but it's usually not described in books/articles as it's the role of analyst to ensure that results are correct. And it's done not only by comparing with analytical values. Anyway, if you are looking for particular examples then check benchmark problems for various software (including open-source solvers like Code_Aster). They often include analytical solution as their purpose is to verify the correctness of FEA results.

 

[bigfooted]

You can also compute the analytical solution of the finite element discretization for simple problems and compare that with the analytical solution of the original differential equation. And probably any paper that introduces a new feature of a finite element method will show results for problems with analytical solutions.

 

[feynman1]

Well, that's something one should do whenever possible but it's usually not described in books/articles as it's the role of analyst to ensure that results are correct. And it's done not only by comparing with analytical values. Anyway, if you are looking for particular examples then check benchmark problems for various software (including open-source solvers like Code_Aster). They often include analytical solution as their purpose is to verify the correctness of FEA results.

thanks, is code_aster supported in windows?

 

[FEAnalyst]

thanks, is code_aster supported in windows?

Yes, there is a Windows version: https://code-aster-windows.com/download/

And here's an exemplary validation case with analytical solution used as reference: https://www.code-aster.org/V2/doc/default/en/man_v/v3/v3.01.103.pdf

 

[feynman1]

Yes, there is a Windows version: https://code-aster-windows.com/download/

And here's an exemplary validation case with analytical solution used as reference: https://www.code-aster.org/V2/doc/default/en/man_v/v3/v3.01.103.pdf

thanks a lot! Is there any way to know the name list of the examples without having to click each of them?
https://www.code-aster.org/V2/doc/default/en/man_v/v3/

 

[FEAnalyst]

thanks a lot! Is there any way to know the name list of the examples without having to click each of them?
https://www.code-aster.org/V2/doc/default/en/man_v/v3/

Yes, they are listed here: https://www.code-aster.org/V2/doc/default/en/index.php?man=cas-test
Unfortunately some are in French.

 

[FEAnalyst]

There is literature on validation. For example
https://www.amazon.com/dp/0521113601/?tag=pfamazon01-20
Oberkampf and Roy - Verification and Validation in Scientific Computing

Yeah, but it’s about mathematical methods of validating/verifying solutions of PDEs and general ways to check physics simulation results (another book like that: "Finite Element Analysis. Method, Verification and Validation" by Szabo and Babuska). Here the OP is looking for analytical solutions of simple FEA cases. Some books with examples of analyses in particular software feature analytical solutions but unfortunately it’s rare. One such book is "Analysis of Machine Elements Using SolidWorks Simulation 2021" by Nudehi and Steffen.

 

[feynman1]

Yeah, but it’s about mathematical methods of validating/verifying solutions of PDEs and general ways to check physics simulation results (another book like that: "Finite Element Analysis. Method, Verification and Validation" by Szabo and Babuska). Here the OP is looking for analytical solutions of simple FEA cases. Some books with examples of analyses in particular software feature analytical solutions but unfortunately it’s rare. One such book is "Analysis of Machine Elements Using SolidWorks Simulation 2021" by Nudehi and Steffen.

Thanks a lot and these are much needed really. I'm not necessarily looking for analytical solutions only, but explanations and verification of non-analytical ones.