Possible bug in 8-node quad element in transient explicit problems

[Camilo Valencia]

Dear all:

I am performing some explicit analysis. Please, have a look at the attached file, I have a 2D bar with the boundary conditions showed in.

I made these analyses using 4, 8, and 9-node quad elements. The results for the 4 and 9-node elements are as expected, but when I use the 8-node element, I don't have convergence.

I don’t know if there is a problem with my FEAP compilation, with the FEAP implementation, or maybe there is an inherent problem with the lumping process for this type of element. Could you help me with that problem please?

Thank you in advance.


Camilo Valencia

P.S. I made the analyses with a Windows and a Linux compilation and I have the same results.

[FEAP_Admin]

Please post your input files and results which you feel are correct and those which you feel are wrong.

[Camilo Valencia]

Hello, thank you for your answer.

There are two groups of files. The files named as ‘*9N’ correspond to the 9-node analysis and those named as ‘*8N’ correspond to the 8-node analysis. I attached the input file and a screenshot from FEAP with the displacement in the X direction for each case (9 and 8 node).

As you can see, in the 9-node figure, we have the wave propagating through the bar. And in the 8-node case the displacements go to infinite. 

I am applying a displacement load on the edge showed in my post above. 

I am attaching the files in two different posts because they exceed the maximum size allowed.

Thank you.

Camilo Valencia

[Camilo Valencia]

And the second group of files.

[Camilo Valencia]

Hello FEAP developers

Do you have any comments about the problem I told you?

Thank you, cordially
Camilo Valencia

[FEAP_Admin]

The problem you are seeing is due to the well-known problem with the 8-node serendipity shape functions.
If you look at the mass matrix it has negative masses on the off diagonal and in the lumped case even
the diagonal mass has negative values!  If you time step explicitly with this type of mass, you will just get garbage.

Bottom line: only use the 8-node serendipity element if you really know what you are doing.

[Camilo Valencia]

Yes, I know the 8-node serendipity shape functions. But I had curiosity about the lumping procedure used in FEAP.
In the reference [1] (page 569) there are three different lumping procedures for the mass matrix. In the case of 8-node elements, there exists a lumping process that doesn't lead to negative masses, the so-called "Diagonal scaling procedure".

[1] The Finite Element Method: Its Basis and Fundamentals, Sixth Edition. O. C. Zienkiewicz, R. L. Taylor , J.Z. Zhu. Elsevier

Cordially
Camilo Valencia

[FEAP_Admin]

Have a look in elements/solid2d/mass2.f for the details of the lumping method.

Also you can print the mass matricies in FEAP form the Macro prompt:  "show,cmas1" and "show,lmas1" (assuming you have formed them already).

[Camilo Valencia]

Ok, thank you for your time.

Camilo Valencia