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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 ...

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 re...

Anthraquinone [1, 2-C] methylisoxazole is synthesized from 2-ethylanthraquinone through nitration and treating with oleum. The different methods of 2-ethylanthraquinone nitrated were discussed. The optimum conditions were determined. The structure of the product was confirmed by MS and 1H NMR.