9. Summary of results

Since this test does not have analytical reference solutions, but numerical solutions, the differences observed (less than 2% excluding one value) can be considered reasonable.

More precisely, for modeling A (mesh elbow in shells DKT and straight beams in TUYAU), it can be estimated that the solution obtained (2.7% difference in plane flexure, and 0.4% in out-of-plane flexure, compared to the reference: all-shell mesh from modeling D) makes it possible to validate the proper functioning of the shell_pipe connection.

For B modeling (elements TUYAU, 3 Fourier modes), the significant difference in plane flexure (6.8%) is due to the fact that the pipe is relatively thin, so that the ovalization in the elbow causes Fourier modes of order greater than 3 to appear.

In fact, the C modeling (TUYAU, 6 Fourier modes) is very close to the reference (0.01% in plane bending, and 2% in out-of-plane bending). The pipe element is therefore validated in terms of elasticity for these loads, compared to a shell solution (modeling D).

Modeling E (elements TUYAU with 4 nodes) gives results identical to modeling B, for a lower calculation cost due to a thinner mesh.