Table Of ContentSPRINGER BRIEFS IN APPLIED SCIENCES AND
TECHNOLOGY COMPUTATIONAL MECHANICS
Eduardo N. Dvorkin
Rita G. Toscano
Finite Element
Analysis of the
Collapse and
Post-Collapse
Behavior of Steel
Pipes: Applications
to the Oil Industry
SpringerBriefs in Applied Sciences and Technology
Computational Mechanics
Series Editors
Andreas Öchsner
Holm Altenbach
Lucas F. M. da Silva
For furthervolumes:
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Eduardo N. Dvorkin Rita G. Toscano
•
Finite Element Analysis
of the Collapse and
Post-Collapse Behavior
of Steel Pipes: Applications
to the Oil Industry
123
Eduardo N.Dvorkin
Rita G.Toscano
SIM&TEC
BuenosAires
Argentina
ISSN 2191-5342 ISSN 2191-5350 (electronic)
ISBN 978-3-642-37360-2 ISBN 978-3-642-37361-9 (eBook)
DOI 10.1007/978-3-642-37361-9
SpringerHeidelbergNewYorkDordrechtLondon
LibraryofCongressControlNumber:2013934726
(cid:2)TheAuthor(s)2013
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To my daughters Cora and Julia
Eduardo N. Dvorkin
To my mother, Elsa
Rita G. Toscano
Contents
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2 Shell Element Formulations for General Nonlinear
Analysis. Modeling Techniques. . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.2 The Standard A-I-Z Quadrilateral Shell Element
for Linear Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.2.1 Linear Analysis Kinematics . . . . . . . . . . . . . . . . . . . . . 10
2.2.2 Stress-Strain Relations. . . . . . . . . . . . . . . . . . . . . . . . . 13
2.2.3 The Locking Problem . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.2.4 Solving the Locking Problem. . . . . . . . . . . . . . . . . . . . 15
2.3 The MITC4 Quadrilateral Shell Element for Linear Analysis . . . 15
2.4 Nonlinear Analysis Using the MITC4 Element . . . . . . . . . . . . . 16
2.4.1 Infinitesimal Strains Problems: Total Lagrangean
Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.4.2 Finite Strains . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.5 Modeling Considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.5.1 The Nodal Director Vectors. . . . . . . . . . . . . . . . . . . . . 19
2.5.2 Number of d.o.f. per Node. . . . . . . . . . . . . . . . . . . . . . 19
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
3 Collapse and Post-Collapse Behavior of Steel Pipes. Finite
Element Models. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
3.2 Two Dimensional Finite Element Models
of Very Long Pipes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
3.2.1 Formulation of the 2D Models . . . . . . . . . . . . . . . . . . . 24
3.2.2 Two Dimensional Finite Element Results
Versus Experimental Results . . . . . . . . . . . . . . . . . . . . 24
3.2.3 Strain Hardening Effect. . . . . . . . . . . . . . . . . . . . . . . . 27
3.2.4 Effect of Ovality, Eccentricity and Residual Stresses. . . . 28
vii
viii Contents
3.3 Three Dimensional Finite Element Model
of Very Long Pipes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
3.3.1 Formulation of a 3D Model for Very Long Pipes. . . . . . 29
3.3.2 Validation of the Finite Element Model. . . . . . . . . . . . . 32
3.3.3 Pipes Under Bending Plus External Pressure . . . . . . . . . 33
3.4 Three Dimensional Finite Element Model of Finite Pipes. . . . . . 39
3.4.1 Residual Stresses . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
3.5 Main Observations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
4 Experimental Validation of the Finite Element Models.
Applications: Slotted Pipes and Axial Loads. . . . . . . . . . . . . . . . . 43
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
4.2 The Experimental Validation Program. . . . . . . . . . . . . . . . . . . 43
4.2.1 Full-Scale Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
4.3 Validation of the Finite Element Results . . . . . . . . . . . . . . . . . 49
4.3.1 Numerical Results. . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
4.4 Application: Validation for Slotted Pipes . . . . . . . . . . . . . . . . . 56
4.4.1 Numerical Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
4.4.2 Numerical Results. . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
4.5 Application: Collapse of Steel Pipes Under External Pressure
and Axial Tension. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
4.6 Main Observations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
5 Collapse and Post-Collapse Behavior of Deepwater Pipelines
with Buckle Arrestors: Cross-Over Mechanisms. . . . . . . . . . . . . . 71
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
5.2 Experimental Results. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
5.2.1 Experimental Set-up . . . . . . . . . . . . . . . . . . . . . . . . . . 72
5.2.2 Geometrical Characterization of the Tested Samples. . . . 74
5.2.3 Mechanical Characterization of the Tested Samples . . . . 75
5.3 The Finite Element Model . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
5.4 Validation of the Finite Element Results . . . . . . . . . . . . . . . . . 79
5.4.1 Exploring the Finite Element Model . . . . . . . . . . . . . . . 79
5.4.2 Comparison Between the Finite Element
and Experimental Results. . . . . . . . . . . . . . . . . . . . . . . 81
5.5 Main Observations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
6 Conclusions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
6.1 The Usage of 2D and 3D Models . . . . . . . . . . . . . . . . . . . . . . 87
6.2 Nonlinearities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
6.3 Follower Loads. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
Contents ix
6.4 Material Modeling. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
6.5 Modeling of Residual Stresses . . . . . . . . . . . . . . . . . . . . . . . . 89
6.6 Code Verification and Model Validation . . . . . . . . . . . . . . . . . 89
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
Appendix: Imperfections Measuring System. . . . . . . . . . . . . . . . . . . . 91
Chapter 1
Introduction
Theproductionofoilandgasfromoffshoreoilfieldsis,nowadays,moreandmore
important.Asaresultoftheincreasingdemandofoil,andbeingtheshallowwater
reserves not enough, the industry is being pushed forward to develop and exploit
more difficult fields in deeper waters.
As aconsequenceofthe extremelysevereworkconditions,the constructorsof
deep-water pipelines need tubular products with enhanced resistance to withstand
alltheloadsthatwillbeappliedtothepipeline,bothduringitsconstructionandin
operation. Among them: internal and external pressure, bending, tension, com-
pression,concentratedloads,andthermalloadcombinedwithimpact andfatigue.
Averyimportantissuetotakeintoaccountisthebucklingphenomenon[1,2].
Thepipelinemaybuckleglobally,eitherdownwards(inafreespan),horizontally
(‘snaking’ on the seabed), or vertically (as upheaval buckling) (Fig. 1.1); global
buckling implies buckling of the pipe as a bar in compression (column mode). If
the internal pressure is higher than the external one, it introduces a destabilizing
effect. It was demonstrated in [3, 4] that the pressurized pipe buckling load is
lower than the Euler buckling load for the same pipe but under equilibrated
internal/externalpressures;ontheotherhand,whentheexternalpressureishigher
than the internal one, the resultant pressure has a stabilizing effect.
Steel pipesunderexternalpressure mayalsoreach their load carryingcapacity
due to a second failure mode: the localized collapse [5, 6]; in this case the pipe
structure collapses with its sections losing their round shape (Fig. 1.2). The local
buckling failure mechanism is most common during pipelay, due to excessive
bending at the sagbend in conjunction with external overpressure. This book is
focused on the collapse failure mode, considering pipes under external pressure
only and external pressure plus bending.
Inthedesignofmarinepipelinesitisveryimportanttobeabletodeterminethe
collapse pressure of steel pipes subjected to external hydrostatic pressure and
bending.Itisalsorequiredtobeabletoquantifytheeffectofshapeimperfections,
such as ovality and eccentricity, and of residual stresses on the collapse strength.
Theinvestigationofthepost-collapseequilibriumpathisalsorequiredtoassesson
the stability of this regime; that is to say, in order to assess if a collapse will be
E.N.DvorkinandR.G.Toscano,FiniteElementAnalysisoftheCollapse 1
andPost-CollapseBehaviorofSteelPipes:ApplicationstotheOilIndustry,
SpringerBriefsinComputationalMechanics,DOI:10.1007/978-3-642-37361-9_1,
(cid:2)TheAuthor(s)2013
2 1 Introduction
Fig.1.1 Globalbuckling
Fig.1.2 Localbuckling
localized in a section or will propagate along the pipeline. Therefore, it is also
importanttobeabletoquantifytheeffectofthegeometricalimperfectionsandof
the residual stresses on the post-collapse regime.
