Murilo Augusto Vaz

Post-buckling analysis of slender elastic rods subjected to terminal forces

Abstract This paper presents formulation and solutions for the elastica of slender rods subjected to axial terminal forces and boundary conditions assumed hinged and elastically restrained with a rotational spring. The set of five first-order non-linear ordinary differential equations with boundary conditions specified at both ends constitutes a complex two-point boundary value problem. Solutions for buckling, initial post-buckling (perturbation), large loads (asymptotic) and numerical integration are developed. Results are presented in non-dimensional graphs for a range of rotational spring stiffness, tuning the analysis from double-hinged to hinged–built-in rods.

Three-dimensional behaviour of elastic marine cables in sheared currents

Abstract This paper presents the formulation and solution of governing equations that can be used to analyse the three-dimensional (3D) behaviour of either marine cables during installation or the response of segmented elastic mooring line catenaries as used for floating offshore structures when both are subjected to arbitrary sheared currents. The methodology used is an extension of one recently developed for analyses of marine cables when being installed on the seabed or being towed. The formulation describes elastic cable geometry in terms of two angles, elevation and azimuth, which are related to Cartesian co-ordinates by geometric compatibility relations. These relations are combined with the cable equilibrium equations to obtain a system of non-linear differential equations, which are numerically integrated by fourth and fifth order Runga–Kutta methods. The inclusion of cable elasticity and the ability to consider arbitrary stored currents are key features of this analysis. Results for cable tension, angles, geometry and elongation are presented for three example cases—the installation of a fibre optic marine cable, the static analysis of a deep water mooring line and the response of a telecommunications cable to a multi-directional current profile.

A nonlinear formulation for the axisymmetric response of umbilical cables and flexible pipes

Abstract This paper presents formulations and a solution for the response of umbilical cables and flexible pipes subjected to monotonic loading of tension, torque, internal and external pressures. The homogeneous and helical wound layers are, respectively, described by Lames and Clebsch–Kirchhoffs formulations hence yielding nonlinear algebraic equations which are solved by an iterative algorithm. The model takes into account a number of features, such as material nonlinearity, gap formation and interwire contact and it may be applied to cross-section design and verification. The case studies illustrate the benefits of a nonlinear model.

THE TRANSIENT BEHAVIOUR OF MARINE CABLES BEING LAID - THE TWO- DIMENSIONAL PROBLEM

This paper presents a numerical model for the transient behaviour of marine cables during laying operations. The solution methodology consists of dividing the cable into n straight elements with equilibrium relationships and geometric compatibility equations satisfied for each element. The system of n non-linear ordinary differential equations is then solved by fourth- and fifth-order Runge-Kutta formulae. Results are presented for the cable element slope, cable-top tension, suspended length and required pay-out rate as functions of time and for the cable configuration when the cable ship accelerates or decelerates rectilinearly. The results indicate the necessity of considering the cable dynamics in such analyses, particularly for high cable laying speeds.

Analytical Formulation of Distributed Buoyancy Sections to Control Lateral Buckling of Subsea Pipelines

Subsea pipelines designed to operate under high pressure and high temperature (HP/HT) conditions tend to relieve their axial stress by forming buckles. Uncontrolled buckles can cause pipeline failure due to collapse, low cycle fatigue or fracture at girth welds. In order to control the lateral buckling phenomenon, a methodology was recently developed which consists of ensuring regular buckle formation along the pipeline. Distributed buoyancy is one of the most reliable initiation techniques utilized for this purpose which have been recently applied in some projects. The behavior of pipeline sections with distributed buoyancy is normally evaluated by Finite Element Analyses (FEA) even during preliminary design when analytical models could be adopted. FEA are also utilized in order to support reliability calculations applied within buckle formation problems. However, the referred analyses are usually time-consuming and require some experience to provide good results. This paper presents an analytical formulation for a pipeline section with distributed buoyancy, which can be utilized during preliminary design in order to evaluate the influence of buoyancy sections over buckle shape, feed-in length, tolerable Virtual Anchor Spacing (VAS), etc. Regarding buckle formation, this paper also presents a methodology to determine an expression for the critical buckling force to be used as part of the limit state function in reliability analyses, which combines the results obtained from the referred analytical formulation with Hobbs infinite mode.© 2010 ASME

Lateral buckling of bundled pipe systems

This paper presents an analytical formulation of the coupled buckling instability of a pipe-in-pipe system typical of that considered for high-temperature products in the oil and gas industry. The equations of bending for the inner and outer concentric pipes of a pipe-in-pipe system are coupled by imposing force equilibrium and lateral displacement compatibility for both regular and irregularly pitched spacers. An eigenvalue solution of the resultant equation gives an interesting insight into the coupled elastic stability of pipe-in-pipe systems and gives numerical data for local design.

The Effect of Flexible Pipe Non-Linear Bending Stiffness Behavior on Bend Stiffener Analysis

Bend stiffeners are critical components for flexible risers and umbilical cables employed to ensure a safe transition at the riser-vessel interface, avoiding overbending and accumulation of high cyclic fatigue damage. The analysis and design of bend stiffeners usually consider the system as a unique beam, in which the pipe bending response is linear. However, the structural mechanics of these complex layered structures is governed by internal friction mechanisms that yield non-linear moment versus curvature relationship. In fact, the pipe structure exhibits an approximately bi-linear hysteretic bending moment against curvature relationship arising from the progressive activation of friction and consequential slipping between adjacent layers. The flexible pipe bending stiffness substantially reduces after a given critical curvature (i.e., after slip between adjacent layers) is reached. In this paper, the effect of this flexible pipe non-linear response on the bend stiffener design is evaluated. The mathematical formulation and the solution methodology are presented. A set of four non-linear ordinary differential equations is obtained from geometrical compatibility, equilibrium of forces and moments and constitutive equations and a numerical solution is obtained using the shooting method. A finite element analysis is developed to validate the analytical model and to assess the effect of the radial clearance between the structures on the bend stiffener response. A case study is presented for some static loading conditions and it is observed that the bending stiffness bi-linear behavior may not affect the bend stiffener extreme load design results, but it may significantly influence the fatigue analysis.Copyright

Geometrical and Material Non-Linear Formulation for Bend Stiffeners

A mathematical formulation and a numerical solution for the geometrical and material non-linear analysis of bend stiffeners — employed to protect the upper terminations of flexible risers and subsea umbilical cables — are presented in this paper. The differential equations governing the problem result from geometrical compatibility, equilibrium of forces and moments and material constitutive relations, which can be linear elastic symmetric or non-linear elastic asymmetric. In this latter case, the bending moment versus curvature for each cross-section is calculated and then expressed by a polynomial power series expansion. Hence, a set of four first order non-linear ordinary differential equations is written and boundary conditions are defined at both ends. A one-parameter shooting method is employed and results are presented for a case study where linear elastic symmetric and non-linear elastic asymmetric constitutive models are compared and discussed. It is shown that an accurate analysis of bend stiffeners depends on a precise assessment of the material constitutive property.© 2004 ASME

Viscoelastic Analysis of Bend Stiffeners

Bend stiffeners are polymeric structures employed to ensure a smooth and safe transition in the upper connection of risers and umbilical cables, protecting them against accumulation of fatigue damage and excessive curvatures. Recent failures have stimulated a better understanding of the mechanical response in order to increase the reliability in design and analysis of bend stiffeners. This work presents a mathematical formulation that represents the system riser/bend stiffener considering geometric non linearity and polyurethane with viscoelastic behaviour, an inherent characteristic to polymers. The following assumptions are considered: cross-sections remain plane after deformation, large deflections are accepted but it is a small strain bending problem, the self-weight and external forces are disregarded and the material is assumed with linear viscoelastic behaviour. The curves that represent the viscoelastic response of the material have been raised by means of creep tests, whose specimens were cut from actual bend stiffeners. The time dependent data obtained in the experimental tests were well approximated by a third order Prony series which describes the creep function. The set of four first order non linear ordinary differential equations results from geometrical compatibility, equilibrium of forces and moments and linear viscoelastic constitutive relations. The numerical solution of the problem is obtained using a one-parameter shooting method. The results are then compared with the consolidated numerical solution for linear elastic material. It is concluded that the viscoelastic phenomena can lead to excessive curvatures on the upper terminations of risers and umbilical cables if the polymeric structure were designed considering elastic behaviour. The correct characterization of the viscoelastic properties of polyurethane used on bend stiffeners must be taken into account when accurate analysis is desired.Copyright

Dynamic tests in a steel catenary riser reduced scale model

ABSTRACT Experimental investigations were conducted on a steel catenary riser (SCR) with different stiffness seafloor models both in dry and wet conditions. The motion oscillator and cell load connect the riser model in a tank, and forced motions with different amplitudes and frequencies were studied. Model tests are conducted in air and a small scale factor (1/435) is used. This model has been built having as reference a riser prototype in 900 m water depth and the numerical analysis is carried out in time domain using the developed CABLE3D. Results demonstrate the influence of the platform in-plane motion on the dynamic response of the riser model, and both of them are consistently good. This study provides a novel and simple experimental tool developed for testing of the SCR global dynamic analysis, and discusses the results including motion response, top tension and dynamic curvature near touchdown zone.