In another post (https://forum.freecadweb.org/viewtopic. ... &start=100) I raised a concern about the accuracy of the results obtained with the CalculiX 3-node beam element. Here some further notes and considerations.

I analysed the problem of a simply supported beam under uniform load and found that for a coarse mesh (1 three-noded element) the mid-span displacement is 20% lower than that obtained with classical beam theory (i.e. 59.5393 mm versus a theoretical value of 74.4048 mm):

It is only with a very fine mesh that a good agreement with theory is achieved (73.7716 mm, which is 0.9% below the theoretical value).

My initial suspicion was that the uniform load was inconsistently applied and upon close inspection I found that there is indeed a difference between the nodal load values exported to INP file and what is obtained by integrating the Hermitian shape functions for a three-node beam (e.g. https://pdfs.semanticscholar.org/12be/d ... 87f271.pdf):

However, manual correction of the *CLOAD card did not give any improvement of the results.

To demonstrate that a normal 3-node Hermitian element (i.e. with displacement and rotational degrees of freedom) should give very accurate results, I generated the stiffness matrix for a single element and multiplied its inverse with the above consistent load vector:

This shows that a single three-noded element can reproduce the theoretical value for the maximum displacement of a simply supported beam under uniform load to within 0.0000512%.

It is therefore worth further investigating why the CCX beam gives such large errors for this simple case.