Description du projet
Cet exemple de vérification est une modification de VE0064 - récipient à paroi épaisse, où la seule différence est que le matériau du réservoir est incompressible. A thick-walled vessel is loaded by inner and outer pressure. The vessel is open-ended, thus there is no axial stress. The problem is modeled as a quarter model and described by the following set of parameters. While neglecting self-weight, determine the radial deflection of the inner and outer radius ur(r1), ur(r2).
| Matériau | Elastic Incompressible | Module d'élasticité | E | 1.000 | MPa |
| Poisson´s Ratio | ν | 0.499 | |||
| Géométrie | Inner Radius | r1 | 200.000 | mm | |
| Outer Radius | r2 | 300.000 | mm | ||
| Load | Inner Pressure | p1 | 60.000 | kPa | |
| Outer Pressure | p2 | 0.000 | kPa | ||
The aim of this verification example is to show the phenomenon of volumetric locking of finite elements. This problem can occur in incompressible material cases when the Poisson ratio ν is approaching 0.5 (rubber materials, materials in plastic state). In this case, the finite element displacements tend to zero. The volumetric locking cannot be avoided by the mesh refinement. All fully integrated elements will lock when the incompressible material is used. The simplest way to avoid locking is using reduced integration. In this case the number of integration points is reduced. The integration scheme is one order less accurate than the standard integration scheme. In RFEM the reduced integration is used so the result will be correct, as seen bellow.
Solution analytique
The analytical solution is the same as in the case of VE0064 - Thick-Walled Vessel. Desired radial deflection of the inner and outer radius of the open-ended vessel ur(r1), ur(r2) can be determined using the following equations:
Paramètres RFEM
- Modeled in RFEM 5.06 and RFEM 6.06
- The element size is lFE = 2.000 mm
- Isotropic linear elastic material model is used
résultats
| Quantity | Solution analytique | RFEM6 | Ratio | RFEM5 | Ratio |
| ur(r1) [mm] | 29.988 | 29.986 | 1.000 | 29.987 | 1.000 |
| ur(r2) [mm] | 22.497 | 22.495 | 1.000 | 22.495 | 1.000 |
