On the multi-scale computation of un-bonded flexible risers

The purpose of this paper is to model the detailed effects of interactions that take place between components of un-bonded flexible risers, and to study the three-dimensional motion responses of risers when subjected to axial loads, bending moments, and internal and external pressures. A constitutive law for un-bonded flexible risers is proposed and a procedure for the identification of the related input parameters is developed using a multi-scale approach. A generalized finite element structural model based on the Euler–Bernoulli beam theory is developed in which the constitutive law is embedded. The beam theory is enhanced by the addition of suitable pressure terms to the generalized stresses to account for the internal and external pressures, and it can therefore be efficiently used for large-scale analyses. The developed nonlinear relationship between generalized stresses and strains in the beam is based on the analogy between frictional slipping between different layers of a flexible riser and frictional slipping between micro-planes of a continuum medium in non-associative elasto-plasticity. The merit of the present constitutive law lies in its ability to capture many important aspects of the structural response of risers, including the energy dissipation due to frictional slip between layers and the hysteresis response.