Numerical spring model – ANSYS

ANSYS is a general finite element package that can be used to carry out numerical calculations on a wide range of complex problems. In this thesis is has been used to calculate if the TP will deform enough to influence the force distribution of the jacks.

4.5.1 Build-up of the model

The model is build up out of two cylinders, one with a diameter of 5 m and one with a diameter of 4 m. These are respectively the TP and the seafastening tubular. Both cylinders are built up out of Shell181 elements. In between the cylinders are link elements, called Combin14 elements, to represent the hydraulic cylinders. These are the springs. In figure 4.6 half of the cylinder model is displayed.

Figure 4.6: Build-up of the model

Only a 6 m part in axial direction of the TP is modeled. It is always a goal in numerical analysis to keep the model as small as possible, so as to keep computation time to a minimum.

The outer cylinder, representing the TP, has a local wall thickness of 85 mm. In this model it is the only part that has a density, so that when an acceleration load is applied, only this part will be forced to translate. The inner cylinder has no density.

The inner cylinder is restrained in all directions. The outer cylinder is restrained in axial direction over the entire circumference of both outer edges of the cylinder. The same edges are restrained on two discrete locations in y-direction, so the model cannot rotate around the x-axis. No restrained is applied in z-direction other than the springs. This means that the outer cylinder can translate in only in z-direction.

The springs have a spring stiffness and an initial force. In ANSYS this is modeled by giving the Combin14 elements an initial length that differs from the length given in the geometry. ANSYS then calculates itself what the force in the spring is. It should be noted that the model shows local

53 deformation because of the spring force, even before the acceleration load is applied. This local deformation cause the spring to relax a little. A small iteration was done to make sure the springs have the right spring force after the cylinder deformed locally. For a detailed overview of the results, see Appendix I.

4.5.2 Model validation

The model is validated against the hand calculated model proposed in section 4.1. This is done by giving both cylinders an infinite stiffness, i.e., E=2e14. The springs have their normal stiffness and initial length to provide the required pretension force.

The first check is done with zero acceleration applied. No change in spring force should occur, and this is the case.

The second check is done with the occurring acceleration. This should produce the force distribution as given in figure 4.2 and 4.3. This is also the case.

From this it is concluded that the model behaves as expected. Now the stiffness parameters can be changed to realistic values and its effect observed.

4.5.3 Realistic values of stiffness

If for the outer cylinder a realistic value of the stiffness is used, i.e. E=2e5, the force in the springs will change, due to local deformation, the spring is relaxed a little. In reality the hydraulic cylinders will also elastically deform the TP locally, but they continue to exert a force until the required pretension force is achieved. To also realize this in the numerical model, the initial length of the springs needs to be increased, so that after local deformation the correct spring force remains.

The value of the local deformation, DMX = deformation = 1.41 mm. This corresponds with the loss in pretensioning force. After compensating for this loss, the initial force is 1433 kN and the local deformation is 1.66 mm.

When also the acceleration is applied, the total deformation plus displacement is 3.77 mm.

Furthermore, the heaviest loaded spring now has increased its force with 337 kN

To see if the TP would deform under the influence of the spring force, also a model with only two springs opposite to each other was made. A clear ovalization was observed. As was stated in section 4.3, there was reason to believe that the stiffness of the TP was of the same order as the stiffness of the jacks. Adding more jacks stiffens the TP and makes the systems response much more like the kettle formula.

Figure 4.7 shows the displaced TP.

54 Figure 4.7: Displaced TP ring. The displacement is exaggerated trough a scaling factor so it is better

visible.

4.5.3.1 Linear analysis

If a linear analysis is performed, the results show no difference with the model proposed in section 4.1. This means the TP reacts much stiffer than expected, namely close to infinitely stiff. It will not deform enough change the force distribution.

4.5.3.2 Nonlinear analysis

If a nonlinear analysis is performed, the result show only a difference of less than 1% with the model of section 4.1. This analysis make a series of linear analysis, where the outcome of a previous step is input for the next step. Since each step greater than 1 takes the deformed geometry into account, a slightly different result is expected, due to the extra component present in springs with a slight angle.

The difference is small enough to conclude that a nonlinear calculation is not necessary.

4.6 Conclusion

The goal of the analysis in this chapter was to find out the force distribution on the TP. A simple model consisting of two infinite stiff rings with springs in between is suitable for determining the force distribution. An numerical calculation done in ANSYS showed no significant difference. So, the TP will not deform enough to change the force distribution.

The local stresses in the TP follow only from the local spring forces and follows a linear relation, i.e., if a spring force is doubled, then so will the stresses.

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