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

2007 ◽  
Author(s):  
Marcelo Caire ◽  
Murilo Augusto Vaz
Keyword(s):  
Mathematical Formulation ◽  
Bending Stiffness ◽  
Radial Clearance ◽  
Flexible Pipe ◽  
Element Analysis ◽  
Linear Ordinary Differential Equations ◽  
Analysis And Design ◽  
Extreme Load ◽  
Non Linear ◽  
Pipe Bending

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.

Geometrical and Material Non-Linear Formulation for Bend Stiffeners

2004 ◽  
Author(s):  
Murilo Augusto Vaz ◽  
Carlos Alberto Duarte de Lemos
Keyword(s):  
Differential Equations ◽  
Constitutive Relations ◽  
Mathematical Formulation ◽  
Power Series Expansion ◽  
Constitutive Models ◽  
Bending Moment ◽  
Accurate Analysis ◽  
Linear Ordinary Differential Equations ◽  
Linear Elastic ◽  
Non Linear

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.

scholarly journals THERMAL POST-BUCKLING OF SLENDER ELASTIC RODS WITH DIFFERENT BOUNDARY CONDITIONS

2006 ◽  
Vol 5 (2) ◽  
pp. 50
Author(s):  
R. F. Solano ◽  
M. A. Vaz
Keyword(s):  
Boundary Conditions ◽  
Numerical Solutions ◽  
Mathematical Formulation ◽  
Different Boundary Conditions ◽  
Linear Ordinary Differential Equations ◽  
Linear Elastic ◽  
Buckling Behavior ◽  
Non Linear ◽  
Post Buckling ◽  
Complex Boundary

This paper presents mathematical formulation, critical buckling temperature and analytical and numerical solutions for the thermal post-buckling behavior of slender rods subjected to uniform thermal load. The material is assumed to be linear elastic, homogeneous and isotropic. Furthermore, large displacements are considered hence the formulation is geometrically non-linear. Three different boundary conditions are assumed: (i) double-hinged non-movable, (ii) hinged non-movable at one end, whereas at the other end longitudinal displacement is constrained by a linear spring, and (iii) double-fixed non-movable. The governing equations are derived from geometrical compatibility, equilibrium of forces and moments, constitutive equations and strain-displacement relation, yielding a set of six first-order non-linear ordinary differential equations with boundary conditions specified at both ends, which constitutes a complex boundary value problem. The buckling and post-buckling solutions are respectively accomplished assuming infinitesimal and finite rotations. The results are presented in non-dimensional graphs for a range of temperature gradients and different values of slenderness ratios, and it is shown that this parameter governs the rod post-buckling response. The influence of the boundary conditions is evaluated through graphic results for deformed configuration, maximum deflection, maximum inclination angle and maximum curvature in the rod.

Protective Barrier Wall Response to Sequential Blast and Fire Events

2021 ◽  
Author(s):  
Hunter Smith
Keyword(s):  
Thermal Loading ◽  
Structural Integrity ◽  
High Stress ◽  
Wall Structure ◽  
Element Analysis ◽  
Linear Dynamic ◽  
Extreme Load ◽  
Wall Panels ◽  
Non Linear ◽  
Barrier Wall

Abstract Blast and fire-resistant barrier walls are often required on offshore platforms to protect from accidental events. A wall structure designed for a probabilistic explosion event typically relies on inelastic response and plastic deformation to maintain a lightweight, efficient design. Design guides for such structures do not explicitly address how to account for the effects of interaction of blast and fire loading on structural performance and design acceptance criteria. If a wall assembly is required to provide rated fire and gas protection after an explosion event, it is generally assumed that structural integrity is maintained due to temperature increase limits (140°C) from the H-60/120 rated fire protection on the wall. This paper investigates the validity of this assumption for a typical offshore barrier wall designed to undergo permanent deformation during an initial blast event. The study was performed utilizing non-linear dynamic finite element analysis (FEA). FEA allows for design iteration, structural assessment, and validation against extreme load scenarios when testing of full-scale assembly may not be feasible. A typical wall structure was first analyzed for blast loading by non-linear dynamic structural analysis. Thermal loading from a subsequent hydrocarbon fire was then applied to observe the structural response in the post-blast damaged condition. Based on the rated temperature range, the resulting thermal expansion in the wall panels induces large stresses at the interface between wall panels and supporting steel. Non-linear FEA confirmed that yielding occurs which may increase existing plastic strains beyond design limits at locations of high stress concentration. Therefore, it is prudent to consider thermal performance in the design process, especially regarding connections and penetrations.

Modelling and co-simulation of a permanent magnet synchronous generator

2019 ◽  
Vol 38 (6) ◽  
pp. 1904-1917 ◽  
Author(s):  
Roberto Eduardo Quintal-Palomo ◽  
Maciej Gwozdziewicz ◽  
Mateusz Dybkowski
Keyword(s):  
Permanent Magnet ◽  
Synchronous Generator ◽  
Simulation Method ◽  
Electrical Machine ◽  
Permanent Magnet Synchronous Generator ◽  
Element Analysis ◽  
Content Type ◽  
Analysis And Design ◽  
Non Linear ◽  
Linear Circuits

Purpose The purpose of this paper is to obtain an accurate methodology for modelling and analysis of the permanent magnet synchronous generator connected to power electronic components. Design/methodology/approach This paper presents the methodology of the co-simulation of a permanent magnet synchronous generator. It combines Simulink, Maxwell and Simplorer software to demonstrate the electrical machine behaviour connected with the power electronics’ circuit. The finite element analysis performed on the designed machine exhibit a more accurate behaviour over simplified Simulink models. Results between both simulation and co-simulation are compared to measurements. Findings The co-simulation approach offers a more accurate depiction of the machine behaviour and its interaction with the non-linear circuits. Research limitations/implications This paper focuses on the interior permanent magnet type of PMSG and its interaction with a passive rectifier (nonlinear circuit). Practical implications The advanced capabilities of the co-simulation method allow to analyse more variations (geometry, materials, etc.), and its interaction with non-linear circuits, than previous simulation techniques. Originality/value The co-simulation as a tool for analysis and design of systems interconnected with unconventional and conventional electrical machines and prototypes, and the comparison of the obtained results with classical analysis and design methods, against measurements obtained from the prototype.

Pipe Bending and Running Forces in Medium to High-Curvature Wells Using Finite Element Analysis

1998 ◽  
Vol 120 (4) ◽  
pp. 263-267 ◽  
Author(s):  
A. C. Seibi ◽  
A. M. Al-Shabibi
Keyword(s):  
Finite Element ◽  
Horizontal Wells ◽  
General Purpose ◽  
Bending Stiffness ◽  
Radius Of Curvature ◽  
Element Analysis ◽  
Finite Element Program ◽  
Hole Radius ◽  
Element Program ◽  
Pipe Bending

The present paper describes the running process in horizontal wells and studies the effect of some factors on running forces required to push pipes through curved holes with short to medium radii of curvatures. Estimation of the running forces was performed using a general-purpose finite element program called ANSYS. The effect of pipe bending stiffness, hole radius of curvature, and hole clearance are investigated. Finite element results showed that the pipe bending stiffness becomes insignificant for medium curvatures (i.e., radius of curvature greater than 80 m). It was also found that the running force at the kick-off point (k.o.p) increases as the radius of curvature shortens (severe doglegs) and as the pipe stiffness increases. In addition, FE results revealed that the effect of hole clearance on the running force is negligible.

Dynamic Response of an Unbalanced Rotor Supported on Bearing With Outer Race Waviness

2013 ◽  
Author(s):  
P. K. Kankar ◽  
Satish C. Sharma ◽  
S. P. Harsha
Keyword(s):  
Dynamic Response ◽  
Chaotic Behavior ◽  
Mathematical Formulation ◽  
Rotational Frequency ◽  
Hertzian Contact ◽  
Radial Clearance ◽  
Outer Race ◽  
Unbalanced Rotor ◽  
Non Linear ◽  
Rolling Elements

The paper investigates the non-linear dynamic response of an unbalanced rotor supported on ball bearings with outer race waviness. The excitation is due to unbalanced force and waviness on outer race. The sources of non-linearities are both the radial clearance as well as the Hertzian contact between races and rolling elements. The nonlinear responses due to unbalanced rotor supported on bearings are investigated. The combined effects like non-linear stiffness and non-linear damping for unbalanced rotor with bearing waviness have been considered and analyzed in detail for a rotor bearing system. In the mathematical formulation, the contacts between the rolling elements and the races are considered as an oscillating spring-mass-damper system. The appearance of regions of periodic, sub-harmonic and chaotic behavior is seen to be strongly dependent on the number of waves in the outer race. The results show the appearance of instability and chaos in the dynamic response as the number of waves in the outer race is changed. The study indicates that the interaction of ball passage frequency (ωbp) due to outer race waviness and rotational frequency (X) due to the unbalanced rotor force. Poincaré maps and frequency responses are used to elucidate and to illustrate the diversity of the system behavior.

A Simplified Design Model for Modular Steel Buildings Subject to Vapor Cloud Explosions (VCEs)

2020 ◽  
Vol 14 ◽  
Author(s):  
Osama Bedair
Keyword(s):  
Dynamic Response ◽  
Minimum Cost ◽  
Design Parameters ◽  
Front Wall ◽  
Steel Buildings ◽  
Element Analysis ◽  
Analysis And Design ◽  
Vapor Cloud ◽  
Building Components ◽  
Analytical Expressions

Background: Modular steel buildings (MSB) are extensively used in petrochemical plants and refineries. Limited guidelines are available in the industry for analysis and design of (MSB) subject to accidental vapor cloud explosions (VCEs). Objectives: The paper presents simplified engineering model for modular steel buildings (MSB) subject to accidental vapor cloud explosions (VCEs) that are extensively used in petrochemical plants and refineries. Method: A Single degree of freedom (SDOF) dynamic model is utilized to simulate the dynamic response of primary building components. Analytical expressions are then provided to compute the dynamic load factors (DLF) for critical building elements. Recommended foundation systems are also proposed to install the modular building with minimum cost. Results: Numerical results are presented to illustrate the dynamic response of (MSB) subject to blast loading. It is shown that (DLF)=1.6 is attained at (td/t)=0.4 for front wall (W1) with (td/T)=1.25. For side walls (DLF)=1.41 and is attained at (td/t)=0.6. Conclusions: The paper presented simplified tools for analysis and design of (MSB) subject accidental vapor cloud blast explosions (VCEs). The analytical expressions can be utilized by practitioners to compute the (MSB) response and identify the design parameters. They are simple to use compared to Finite Element Analysis.

Behaviour of Axially Loaded Composite Wall Panel by Using Finite Element Analysis

2015 ◽  
Vol 815 ◽  
pp. 49-53
Author(s):  
Nur Fitriah Isa ◽  
Mohd Zulham Affandi Mohd Zahid ◽  
Liyana Ahmad Sofri ◽  
Norrazman Zaiha Zainol ◽  
Muhammad Azizi Azizan ◽  
...  
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Composite Structures ◽  
Element Analysis ◽  
Steel Sheets ◽  
Linear Behavior ◽  
Non Linear ◽  
Composite Wall ◽  
Experimental Values ◽  
Civil Engineering Infrastructure

In order to promote the efficient use of composite materials in civil engineering infrastructure, effort is being directed at the development of design criteria for composite structures. Insofar as design with regard to behavior is concerned, it is well known that a key step is to investigate the influence of geometric differences on the non-linear behavior of the panels. One possible approach is to use the validated numerical model based on the non-linear finite element analysis (FEA). The validation of the composite panel’s element using Trim-deck and Span-deck steel sheets under axial load shows that the present results have very good agreement with experimental references. The developed finite element (FE) models are found to reasonably simulate load-displacement response, stress condition, giving percentage of differences below than 15% compared to the experimental values. Trim-deck design provides better axial resistance than Span-deck. More concrete in between due to larger area of contact is the factor that contributes to its resistance.

In-Place FE Modeling of Unbonded Flexible Pipelines Capturing Pressure Stiffening and Decoupled Axial/Nonlinear Bending Stiffness

2010 ◽  
Author(s):  
Edvin Hanken ◽  
Evelyn R. Hollingsworth ◽  
Lars S. Fagerland
Keyword(s):  
Water Injection ◽  
Bending Stiffness ◽  
Axial Stiffness ◽  
Fe Model ◽  
Nonlinear Bending ◽  
Upheaval Buckling ◽  
History Effects ◽  
System Integrity ◽  
Non Linear ◽  
Bending Behaviour

For fast track pipeline projects the need for costly installation vessels and sophisticated materials for rigid pipeline water injection systems, have made flexible pipelines a competitive alternative. They can be installed with less costly construction vessels, provide a competitive lead time and a corrosion resistant compliant material. Flexible pipelines have relative high axial stiffness and low non-linear bending stiffness which is a challenge to model correctly with FE for in-place analyses of pipelines. Whilst some FE programs can model the non-linear bending behaviour of a flexible pipeline at a given pressure, current FE tools do not include the effect of increased bending resistance as the system is pressurized. Therefore, a 3D FE model in ANSYS was developed to simulate the decoupled axial and nonlinear bending behaviour of a flexible, including the bend stiffening effect for increasing pressure. A description of the model is given in this paper. It will be demonstrated how the FE model can be used to simulate the 3D nonlinear catenary behaviour of an high pressure flexible pipeline tied into a manifold during pressurization. Due to high manifold hub loads during pressurization it is essential that such a model is capable of capturing all effects during pressurization to achieve an acceptable confidence level of the system integrity. It is also described how the FE model is used for upheaval buckling design, capturing non-linearities and load history effects that can reduce the conservatism in the design.

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