After Alfredo Gay Neto, Clóvis A. Martins, Paulo M. Pimenta,“Static analysis of offshore risers with a geometrically-exact 3D beam model subjected to unilateral contact”, Computational Mechanics (2013), doi:10.1007/s00466-013-0897-9.
- Against the author’s code
- 8 of 8 checks pass· see the checks
- Against the paper’s figures
- Not compared: the full text was not accessible to us
Research, not a design tool. Nothing here is an engineering result.
An 835 m line lies on the seabed, is pulled by its free end and lifted 186 m. Watch where it leaves the ground and how bending peaks there.
The model
A geometrically exact rod: each section moves and rotates freely, and the energy depends on stretch, shear, bending and twist measured in the section’s own frame. Three-node elements with two Gauss points. The seabed is a rigid plane that pushes back with a penalty spring at each node, with Coulomb friction.
We read the reference code’s own input files and solve the same three static steps: self-weight with contact, a 1 MN horizontal pull, then a 186 m lift of the free end. The solver is a new Rust crate, compiled to WASM for this page. Its tangent comes from differentiating the element energy twice, so Newton converges quadratically.
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At the end of step 3 we compare the bending moment and the shear force of all 134 elements with the values stored in the reference code’s tutorial guide. The touchdown point and the hanging shape are also checked against the elastic catenary. A 1 m cantilever (tutorial 1) checks the beam alone.
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Validation and sources
We did not compare the article’s figures: we had no access to the full text. The references are the results published with GIRAFFE, the author’s code, an independent exact solution for the cantilever and the analytical catenary for the riser. The difference is the largest over everything compared: the ten cantilever increments against the figure, the riser’s 134 elements for moment and shear, and the whole hanging part of the line.
| Quantity | Reference | Stabileo | Max. difference | Tolerance |
|---|---|---|---|---|
| Cantilever: tip X, Z at the end (m)GIRAFFE, Figure 1-6 of its guide | 0.8413, 0.4056 | 0.8414, 0.4056 | ✓ 0.000313 | 0.001 |
| Cantilever, 5 elements: tip X, Z (m)Exact rod solution, independent | 0.8416, 0.4055 | 0.8414, 0.4056 | ✓ 0.000165 | 0.001 |
| Cantilever, 40 elements: tip X, Z (m)Exact rod solution, independent | 0.8416, 0.4055 | 0.8416, 0.4055 | ✓ 0.0000000455 | 0.000001 |
| Riser: peak bending moment (N·m)GIRAFFE, tutorial 16 results | −294.3244 | −294.3244 | ✓ 0.0149 | 0.1 |
| Riser: peak shear force (N)GIRAFFE, tutorial 16 results | −91.9969 | −91.9962 | ✓ 0.0126 | 0.1 |
| Riser: touchdown (m along the line)GIRAFFE, tutorial 16 results | 216.7279 | 216.7279 | ✓ 0.0000112 | 0.05 |
| Riser: touchdown (m along the line)Analytical elastic catenary | 216.4460 | 217.1910 | ✓ 0.745 | 3.14 |
| Riser: hanging shape (m)Analytical elastic catenary | whole line | whole line | ✓ 0.000228 | 1.05 |
Statics only: no sea current, no wave or drag loads, no line-to-line contact. Agreement with the reference code is numerical; it is not an experiment and not a design check.
Reference code (BSD-3-Clause) · Input files
Cite this
Stabileo Research, “A riser lifted off the seabed”, reproduction of Alfredo Gay Neto, Clóvis A. Martins, Paulo M. Pimenta (2013), doi:10.1007/s00466-013-0897-9. Implementation: research/mechanics/gay-neto-2014 at commit cb671ed319d1. Engine: the Stabileo engine at the same commit.