Non-linear finite element analysis of flexible pipes for deep-water applications

This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University LondonFlexible pipes are essential components in the subsea oil and gas industry, where they are used to convey fluids under conditions of extreme external pressure and (often) axial load, while retaining low bending stiffness. This is made possible by their complex internal structure, consisting of unbonded components that are, to a certain extent, free to move internally relative to each other. Due to the product's high value and high cost of testing facilities, much e ort has been invested in the development of analytical and numerical models for simulating flexible pipe behaviour, which includes bulk response to various loading actions, calculation of component stresses and use of this data for component fatigue calculations. In this work, it is proposed that the multi-scale methods currently in widespread use for the modelling of composite materials can be applied to the modelling of flexible pipe. This allows the large-scale dynamics of an installed pipe (often several kilometers in length) to be related to the behaviour of its internal components (with characteristic lengths in millimeters). To do this, a formal framework is developed for an extension of the computational homogenisation procedure that allows multiscale models to be constructed in which models at both the large and small scales are composed of different structural elements. Within this framework, a large-scale flexible pipe model is created, using a two-dimensional corotational beam formulation with a constitutive model representative of flexible pipe bulk behaviour, which was obtained by further development of a recently proposed formulation inspired by the analogy between the flexible pipe structural behaviour and that of plastic materials with non-associative flow rules. A three-dimensional corotational formulation is also developed. The model is shown to perform adequately for practical analyses. Next, a detailed finite element (FE) model of a flexible pipe was created, using shell finite elements, generalised periodic boundary conditions and an implicit solution method. This model is tested against two analytical flexible pipe models for several basic load cases. Finally, the two models are used to carry out a sequential multi-scale analysis, in which a set of simulations using the detailed FE model is carried out in order to find the most appropriate coefficients for the large-scale model.EPSRC CASE studentship, with Lloyd's Register EME

Unloading of elastoplastic spheres from large deformations

The unloading behaviour of adhesion-free elastic-perfectly plastic spheres following contact presents complex non-linear features. Analytical models capable of accurately predicting this response have not yet been developed for an extensive range of material properties and initial deformation states, and consequently the use of semi-empirical models requiring calibration is widespread in the practical application of contact laws.In this work, we provide insight into contact behaviour during unloading by conducting a finite element study to characterise this response for a comprehensive range of material properties (1 ≤ E/σy ≤ 1000, 0.0 ≤ ν ≤ 0.45) and for particles that have undergone large deformation prior to unloading (0.01 ≤ d/R ≤ 0.5), leading to the following findings. Firstly, an empirical relation capable of accurately determining secant unloading stiffness from material properties and degree of initial deformation was formulated, which was expressed in non-dimensional form for maximum generality. An analytical model was also developed to help explain some of the contributing mechanisms identified from the finite element analysis. Secondly, the nonlinearity of the force-displacement curve in unloading was quantified and charted, and physical arguments were advanced to explain the trends revealed. Considering both stiffness and nonlinearity results, it was concluded that a single synthetic measure of initial particle deformation relative to deformation at first yield, which is currently used, is insufficient to characterise unloading response at large displacements.The unloading relations developed can be employed with static and dynamic multi-particle simulation approaches such as the Discrete Element Method (DEM) for more accurate simulation of compaction and flow of dense powder beds and problems reliant on accurate determination of contact areas after unloading between particles following large deformation.</div

Numerical derivation of a normal contact law for compressible plastic particles

A new contact law is proposed to describe the behaviour of plastically compressible particles. The law was derived from contact simulations in which a general continuum constitutive model, the von Mises Double Cap (VMDC) model, was introduced to represent the particle material behaviour, allowing distinct dilatory, shearing and densification plastic flow regimes. Elastic and plastic properties were prescribed as functions of density. Parametric studies were conducted covering the parameter space of published experimental data for a range of pharmaceutical powders and granules.The analysis showed plastic zones corresponding to the three flow regimes developing within the particle, with size, shape, location and onset conditions being dependent on the strength ratios of the constitutive model. The contact law established combines an initial quasi-linear region followed by an exponential hardening region, arising from the initiation, growth and hardening of plastic zones, and the development of dense and stable load-bearing structures.The outcome of these studies is a new contact law, relationships for predicting contact law parameters from material parameters for both loading and unloading, and guidelines for the analytical treatment of plastic compressibility in particle contact. The contact law can be employed in discrete element and homogenisation models to predict macroscopic properties of porous granular materials, while the analytical framework and qualitative findings can be used in the design of granules.</p