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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.