Projection from gauss points to nodes

[Yijun Chen]

Dear Professors,

I have a small question about the projection procedure. In the quadrangle element 8 nodes 9 gauss points, Suppose I have a set of integral point values, as shown in figure 1. I referred to slcn3d.f file's projection rules, and the projection results in nodes as shown in figure 2. It looks like there's a strange node-value distribution. The ideal node values distribution would look like figure 3. Why is the distribution of nodes projected in figure 2 so strange?

Thank you very much in advance!

Yijun Chen

[Prof. S. Govindjee]

Which version of FEAP are you using?

[Yijun Chen]

Dear Prof. S. Govindjee,

Thank you very much for your reply.

 FEAP 8.3

Best wishes,

Yijun Chen

[Yijun Chen]

Meanwhile, I used the superconvergent patch recovery (SPR)  method in Matlab coding,  one element model in ABAQUS.
The gauss point values of ABAQUS as the Input set in the SPR method Matlab coding, and the output matches well with the node in ABAQUS.
The least-square method still has a strange projection.

[Prof. R.L. Taylor]

Feap has SPR for some options.  It is called command ZZHU in solutions.

[Yijun Chen]

Dear Prof. R.L. Taylor,

Thank you very much for your reply.

Best wishes,

[Prof. R.L. Taylor]

Sorry for not replying to your original e-mail.  I am confused by your referring to slcn3d.f for a 2-d problem.  In the figure 2 you show bad projections, I am not clear on how you got them. Did you use slcn2d.f in your program, or write your own routine.   We do not use a "row sum" projection for 8-node elements, indeed since ver8.3 we have looked for better schemes and currently, where appropriate we use a local least squares projection.  It seems to be quite good and in most instances gives better surface values.  I have not compared to SPR which uses extrapolated values at surfaces and thus always requires a mesh with internal nodes when properly implemented (in my view).  Normally, in 2-d problems we prefer to use the 9-node Lagrangian element type instead of 8-node Serendipity type.  This usually produces better projected values and allows for wider range of material properties in mixed forms.

[Yijun Chen]

Dear prof. Taylor,

thank you very much for your Valuable comments.

I checked the slcn1d.f, slcn2d.f, slcn3d.f, they all have the same projection rules. I built a user element elmt66.f and used the projection rules, and I monitored the gauss point values and projection node values for each element. I found the projection node values distribution is strange.

Meanwhile, I coded the slcn2d.f projection rule into Matlab code, method1.m, and other projection rules into method2.m and method3.m. I also build one element model in Abaqus, to explore the rationality of these projection methods. These attachments are attached above, see "Re: Projection from gauss points to nodes « Reply #4 on: May 25, 2020, 03:04:21 PM »". The results of the exploration show that the projection results of method 3 (spr projection rule) and Abaqus are very consistent.

In mixed form 2-d problems, your comment to use the 9-node Lagrangian element type is valuable. Thank you very much.

Best wishes,

Yijun Chen