We present an extension of the computational homogenisation theory to cases where different structural models are used at different scales and no energy potential can be defined at the small scale. We observe that volumetric averaging, that is not applicable in such cases unless similarities exist in the macro-and micro-scale models, is not a necessary prerequisite to carry out computational homogenisation. At each material point of the macro-model we replace the conventional representative volume element with a representative domain element (RDE). To link the large-and small-scale problems we then introduce a linear operator, mapping the smooth part of the small-scale displacement field of each RDE to the large-scale strain field, and a trace operator to impose boundary conditions in the RDE. The latter is defined based on engineering judgement, analogously to the conventional theory.A generalised Hill's condition, rather than being invoked, is derived from duality principles and is used to recover the stress measures at the large scale. For the implementation in a nonlinear finite-element analysis 'control nodes' and constraint equations are used. The effectiveness of the procedure is demonstrated for three beam-to-truss example problems, for which multi-scale convergence is numerically analysed.
Unbonded flexible pipes are a key technology in subsea production systems. Considering the trend towards production in greater depths and the introduction of novel designs, it is of increasing importance to have reliable analytical tools to assess the collapse capacity of flexible pipes under a variety of conditions. In this article, a finite element model for determining collapse pressure is described and used to investigate the effects of ovalisation and pipe curvature on pipe collapse pressure. The predictions of this model are compared to those of analytical formulations described in the literature for elastic and plastic collapse of flexible pipes.
Unbonded flexible risers are a key technology in existing and proposed offshore developments. With increasing water depth, the demands on risers increase and the design against hydrostatic and tension loads becomes more of a challenge. In addition, many existing subsea production systems are approaching the end of their design life and operators need to know if they can remain in-service. To enable the benefits from deepwater production and life extension projects to be realized while minimizing risks to life, property and the environment, accurate modelling and analysis tools are required to improve the prediction of failure modes and to develop a better understanding of the conditions leading to progressive failure. In this work, a multi-scale approach is adopted whereby a global dynamic analysis model is employed to determine the overall displacements of the riser and this is linked with a local model that can provide accurate forces and stresses for the prediction of collapse, fatigue damage and buckling of tensile armour wires. Firstly, we describe a nonlinear constitutive model for use in large-scale dynamic analysis of flexible risers based on an analytical homogenization of composite cylinders using the analogy between slip between pipe layers and plastic flow in continua. The model is able to reproduce the bending hysteresis behaviour observed in flexible pipes and its dependence on internal and external pressure. Secondly, we show a procedure for obtaining equivalent material parameters for this model from finite element local analyses of a flexible pipe. Finally, we show the implementation of this constitutive model in a riser system using two-dimensional co-rotational hybrid beam finite elements.
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