Alternative analytical and finite element models for unbonded flexible pipes under axisymmetric loads

Abstract

The calculation of stress components in tensile armour wires of flexible pipes subjected to combined tension and bending is challenging given the intrinsic geometrical and physical nonlinearities. Mechanical loading simulation in finite element models yields heterogeneous curvature distribution, directly impacting stress evaluation. Addition of two auxiliary thermal layers internally and externally subjected to radial and longitudinal thermal expansions simulates equivalent axisymmetric loading, achieving relatively uniform curvature distribution. Calculation of equivalent thermal loads and expansion coefficients involves time consuming trial and error processes by running several finite element models. Therefore, a theoretical formulation that takes into consideration thermal sheaths with orthotropic thermal expansion coefficients and respective thermal loads is developed. A three-dimensional finite element model is also developed for direct application of axisymmetric mechanical or equivalent thermal loadings. A 6″ flexible pipe is employed in a case study to compare the finite element model results within themselves and with the analytical mechanical and thermal models. The analytical results are shown to be rigorously identical. The finite element models present small differences when compared to the analytical results allowing combined application of thermal and bending loading that results in constant curvature away from the boundaries.