Weakness of 1st order shell tri elements against other codes

Analysis issues
1

1st order shell should be calculated internal with extra nodes. Tri is here the weak part.

So a tri3 should have the option be expanded to a wedge15 and quad4 to a hex20. Quad4 is here ok, but in mixed mesh with tri an Expansion is also necessary to hex20.

An alternative is expansion to 2 wedge6 with zero phase at tri3 and to two hex8 with zero phase at quad8 position. Than only double calculation effort with doubled internal elements.

Node Results can be reduced to tri3 and quad4.

See report in Adapy tool:

See also

2

reduced abaqus shell elements at 1st order are also significant better than reduced 1st order calculix quad elements.

3

That is to be expected. From the “golden rules” section in the CalculiX User’s Manual (emphasis mine):

USE QUADRATIC ELEMENTS (C3D10, C3D15, C3D20(R), S8, CPE8, CPS8, CAX8, B32), except for explicit dynamic calculations. The standard shape functions for quadratic elements are very good. Most finite element programs use these standard functions. For linear elements this is not the case: linear elements exhibit all kind of weird behavior such as shear locking and volumetric locking. Therefore, most finite element programs modify the standard shape functions for linear elements to alleviate these problems. However, there is no standard way of doing this, so each vendor has created his own modifications without necessarily publishing them. This leads to a larger variation in the results if you use linear elements. Since CalculiX uses the standard shape functions for linear elements too, the results must be considered with care.

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4

Diamant rule: Yes to golden rule, but do not forget improvement with expanding possibilities.

The shell elements are here expanded to solid elements for better results.

So why should tri3 not expanded internal to two wedge6 or one wedge15 instead of one wedge6?

An option to this will improve result without more size of result data.

5

If you want to use second order expanded elements, you can use the second order 1D/2D counterparts. For example, S6 expands to wedge15.

By the way: 1D/2D elements are not expanded for better results, but to be able to handle them in a 3D finite element framework.

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6

Let’s also keep in mind that CalculiX has the user element US3 which is also 1st order triangular shell, but true one (not expanded to solid). It would be interesting to compare its performance with S3.

Abaqus has some comprehensive benchmarks comparing various element types. They usually don’t include S3, but the 3DNLG-10: Elastic-plastic behavior of a stiffened cylindrical panel under compressive end load NAFEMS benchmark includes it:

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7

S3.and S3R are in abaqus in your table the same.
My summary: also calculix should calculate with tri3, here S3, like other codes and not 50% or 100% away.
So an improvement is necessary here to be at same level of abaqus and others.
The way to improve is the decision of the developers here.
But there are more things in the roadmap, which are more important. So it can wait.

Here is the workaround to go to quad4 or second order s6 or s8.
A warning should be in docu and log text using tri3 in calculix with to high stiffness of s3 elements.

8

as mentioned before, it’s a nature limitation of linear solid element expands from shell in CalculiX. There’s no solution to improved currently like linear tetrahedral also, but add more integration point along the thickness for linear solid of wedge and hexahedral element maybe. Quadratic shell element with composite options activated shown perform better in large deformation and plasticity.

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