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Reference solutions as well as solutions from existing modeling methods are available in this page for the experiment of an elastic beam under gravity, fixed on one side. Concerning the beam geometry, the beam cross-section is circular with a radius R and L is the length of the beam. Its density is called ρ, its Young Modulus E and its Poisson ratio ν. The experiment and parameter values are reported in the following table:
| L(m) | 0.178 |
| R(m) | 0.019 |
| ρ(kg.m-3) | 1,070 |
| E(Pa) | 60,000 |
| ν | 0.49 |
| g(m.s-2) | 9.81 |
The Bernouilli-Euler theory of beams provides a formulation of the beam deflection. Please refer to the paper in ISBMS'08 proceedings for more details.
Available data in SOFA examples:
The experimental solution proposed in this validation environment is a cylindrical beam made of silicone gel. The estimated Young Modulus is equal to 60,000 Pa and the Poisson ratio has a value of 0.49. The beam was glued at one extremity to an inverted T-shaped vertical support made of plexiglas, and submitted to its own weight. It was then scanned in a helical CT scanner. The shape of the deformed beam is available in SOFA.
Available data in SOFA examples:
Data are available in the SOFA release in the examples directory (sub-directory:./Benchmark/Accuracy/). Different SOFA scenes are ready to be used with the right coefficients. The "WriteState" attribute allows to record data from the simulation. Accuracy measurements (distance and surface) can be performed by using the commands at the end of each file.
For the moment, solutions of 5 different modeling methods are available. Users of the validation environment are welcome to contribute to this database with new solutions. Final meshes of the different modeling methods will be available soon!