Leilei Dong

An Analytical Model to Predict the Bending Behavior of Unbonded Flexible Pipes

Analytical formulations are presented to determine the bending moment-curvature relationship of a helical layer in unbonded flexible pipes. Explicit expressions describing the variation of both bending stiffness and moment as a function of the applied curvature are given. The approach takes into account the nonlinearity of the response caused by the interlayer slip. The contribution of local bending and torsion of individual helical elements to the bending behavior of helical layers is included. Theoretical results for a typical unbonded flexible pipe using the nonlinear formulation for helical layers are compared with experimental data from the available literature. Encouraging correlations are found and the importance of the initial interlayer pressures is seen. The influence of local bending and torsion of individual helical elements on the bending behavior of the entire pipe is also evaluated. The results show that the inclusion of this local behavior significantly influences the full-slip bending stiffness.

Taper design and non-linear analysis of bend stiffeners at the riser–vessel interface

The connection of a flexible riser to the floating production system is identified as a critical area with respect to extreme deformation and fatigue damage. Bend stiffeners are designed to provide a gradual stiffness transition at the riser–vessel interface, protecting the riser against overbending and from the accumulation of fatigue damage. Thus, they are of vital importance to deep-water oil and gas production systems. A methodology for the bend-stiffener taper design is firstly outlined in this paper. The exact expression of the angle at the tip of the bend stiffener required for the design is derived. Then, a mathematical formulation and the numerical solution procedure for the geometrical and material non-linear analysis of the riser-stiffener system are developed. The governing differential equations are obtained from geometrical compatibility, equilibrium of forces and moments, and non-linear material constitutive relations. An analytical approach to predict the bending moment versus curvature relation for each cross-section is presented assuming that the bend-stiffener material is non-linear symmetric, while for asymmetric materials the constitutive relation is calculated numerically. A numerical solution procedure is implemented in MATLAB code to solve the boundary value problem. Furthermore, the flexible pipe structure exhibits an approximately bi-linear hysteretic bending moment against curvature relation. The effect of the bending stiffness bi-linear behaviour on the bend-stiffener response is evaluated for the non-linear material case. A case study is carried out and the results show the potential influence of the material non-linearity on the stiffener response and the need to incorporate the effect of non-linear bending of the pipe in bend-stiffener analyses.

The tensile armour behaviour of unbonded flexible pipes close to end fittings under axial tension

An analytical model is given to investigate the tensile armour behaviour of unbonded flexible pipes close to end fittings under axial tension with no friction. The deviation from the initial lay angle is taken to describe the path of the single armour wire and is determined by minimisation of the strain energy functional using the Euler equation. The obtained simultaneous differential equations are transformed into a boundary value problem which is solved numerically. An analytical solution is found by neglecting the twist of the wire cross-section with respect to the wire centre-line. The developed model is verified with a finite element simulation. Good agreement of armour wire path and maximum lateral bending moment is observed between the model predictions and the finite element results. The discrepancies in the bending and twisting moment distributions are attributed to the twisting constraint assumed in the analytical solutions. The verified model is then applied to typical flexible pipe designs to find the level of the greatest increases in stress. Inclusion of the cross-section twist decreases the lateral bending stress. The potential effect of friction on the results is also discussed.

An Element-Free Galerkin Method Based on Complex Variable Moving Kriging Interpolation for Potential Problems

The moving Kriging interpolation (MKI) is an accurate approximation method that has the interpolating property. However, it is rarely used in meshless methods because of its low efficiency. In this paper, we proposed an efficient MKI method, the complex variable moving Kriging interpolation (CVMKI) method, for “domain” type meshless method. Further, we proposed the CVMKI-based element-free Galerkin (CVMKIEFG) method for 2D potential problems. CVMKIEFG is an efficient meshless method and can impose the essential boundary conditions directly and easily. We proposed two formulations for CVMKIEFG: the conventional formulation and the cell-based formulation. The latter formulation is proposed for higher efficiency. Three 2D example problems are presented to demonstrate the efficiency and accuracy of CVMKIEFG.