Deepwater Flexible Risers and Pipelines. Yong Bai

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Figure 4.8 Pressure armor’s load and boundary conditions.

Material properties and other parameters needed for the computation are listed in Table 4.1. The pressure armor is considered as linear elastic. Based on the formulations illustrated in Section 2.1, the radial stiffness could be calculated as 253.08 MPa/mm.

      Due to the intricate shape of the imported cross-section and potential contacts a contact of type “General contact” is employed to simulate the interactions between the two parts. In ABAQUS environment such contact typology is not related to any specific configuration but is able to relate two surfaces of general shape (even of complex shape as in the present case). In order to assume that surfaces in contact slide freely without friction “Frictionless” tangential behavior is selected, while in order to carry out the contact pressure analysis “Hard contact” normal behavior with “Allow separation after contact” is chosen. This means that ABAQUS is able to put in contact two surfaces by indicating “Hard contact” option and the two surfaces during simulation might not be in contact according to the algorithm “Allow separation after contact” as discussed in [16]. The latter is defined by (p-h) model, which relates the contact pressure p among surfaces and the overclosure h between contact surfaces. When h < 0, it means no contact pressure, while for any positive contact h is set equal to zero, as discussed in [21].

Table 4.1 Parameters for pressure armor layer.

The external pressure supposed as constant along the width of the ring and applied directly on the external surface. Kinematic is governed by the boundary conditions, and symmetric boundary condition with respect to the xy plane is exploited. The pitch length is kept unchanged during the simulation. U1 displacements are allowed at the bases of the ring (z = 0), while U2 displacements are allowed in the middle surface of the ring (x = 0), as shown in Figure 4.8.

C3D8R element (eight-node continuum linear brick elements with reduced integration and hourglass control) is used for the mesh of the two parts, as shown in Figure 4.9. These elements can be used for linear and complex non-linear analysis producing high accuracy results when contacts and non-linear geometry are considered, as discussed by Kim et al. [22].

Due to the frictionless contacts of this case, “Dynamic implicit” simulation is activated to obtain the radial displacements, thanks to the possibility of applying larger increments and achieve higher accuracy compared to a Dynamic explicit analysis. Large strains are activated automatically by ABAQUS environment and implementation within its FE analysis because the flag “Nonlinear geometry” has been activated during the ABAQUS simulation. Moreover, material is considered as elastic in this case, with properties shown in Table 4.1. In order to achieve relatively accurate quasi-static analysis results from the dynamic analysis, the ratio between kinetic energy (ALLKE) and strain energy (ALLSE) for the whole model should be low enough during its whole process, and their corresponding energies are illustrated in Figure 4.10, which shows that the numerical results are reliable.