Review
Finite elements in the analysis of pressure vessels and piping,
an addendum:A bibliography (2001–2004)
Jaroslav Mackerle *
Linko
¨ping Institute of Technology,Department of Mechanical Engineering,S-58183Linko ¨ping,Sweden Received 30November 2004;revised 13December 2004;accepted 31December 2004
Abstract
The paper gives a bibliographical review of finite element methods(FEMs)applied for the analysis of pressure vessel
structures/components and piping from the theoretical as well as practical points of view.This bibliography is a new addendum to the Finite elements in the analysis of pressure vessels and piping—a
bibliography [1–3].The listings at the end of the paper contain 856references to papers and conference proceedings on the subject that were published in 2001–2004.These are classified in the following categories:linear and nonlinear,static and dynamic,stress and deflection analyses;stability problems;thermal problems;fracture mechanics problems;contact problems;fluid–structure interaction problems;manufacturing of pipes and tubes;welded pipes and pressure vessel components;development of special finite elements for pressure vessels and pipes;finite element software;and other topics.q 2005Elsevier Ltd.All rights reserved.
Keywords:Finite element;Bibliography;Pressure vessels;pipes;Linear and nonlinear static and dynamic analysis;Fracture mechanics;Contact problems;Thermal problems;Fluid–structure interaction;Welding
1.Introduction
Pressure vessels and piping are widely used in reactor technology,the chemical industry,marine and space engineering.They often operate under extremes of high and low temperatures and high pressures,are becoming highly sophisticated and therefore also need advanced methods for their analyses.Advances are also made with materials applied for their fabrication.Concrete and composite materials are used more frequently in pressure vessels and their components to replace,in some cases,conventional steels.
During the last three decades considerable advances have been made in the applications of numerical techniques to
analyze pressure vessel and piping problems.Among the numerical procedures,finite element methods are the most frequently used.
Pressure vessel and piping analyses may have a variety of phases such as:elastic stress and deformation analysis
where both mechanical and thermal loads may be applied;heat transfer analysis;dynamic analysis;plastic and creep analysis;etc.There is in existence a large number of general purpose and special purpose finite element programs available to cope with each phase of the analysis.
This review on the subject is divided into the following parts and it concerns:
†linear and nonlinear,static and dynamic,stress and deflection analyses (STR)†stability problems (STA)†thermal problems (THE)
†fracture mechanics problems (FRA)†contact problems (CON)
†fluid–structure interaction problems (FLU)†manufacturing of pipes and tubes (MAN)
†welded pipes and pressure vessel components (WEL)†development of special finite elements for pressure vessels and pipes (ELE)
†finite element software (SOF)†other topics (OTH)
The status of finite element literature published between 1976and 2004,and divided into the categories described above,is illustrated in Fig.1.Data presented in this figure
International Journal of Pressure Vessels and Piping 82(2005)571–592
www.elsevier/locate/ijpvp
0308-0161/$-see front matter q 2005Elsevier Ltd.All rights reserved.doi:10.1016/j.ijpvp.2004.12.004
*Corresponding author.Tel.:C 4613281111;fax:C 4613282717.E-mail address:jarma@ikp.liu.se
include published technical papers in the primary literature;this means papers appearing in the various
general and specialized journals,conference proceedings as well as theses and dissertations.If we take the number of published papers as a measure of research activity in these various subjects,we can see the priority trend in research.
This paper is organized into two parts.In the first,each subject listed above is briefly described by keywords where current trends in application of finite element techniques are mentioned.The second part,Appendix A,is a listing of references on papers published in the open literature for the period 2001–2004,retrieved from the author’s database MAKEBASE [4,5].Readers interested in the finite element literature in general are referred to [6]or to the author’s Internet Finite Element Book Bibliography(www.solid.ikp.liu.se/fe/index.html ).The presented bibliography is an addendum to the author’s earlier bibliographies [1–3].Also the bibliography on creep and creep fracture/damage finite element modelling [7]may be of interest.
2.Finite elements in the analysis of pressure vessels and piping
2.1.Linear and nonlinear,static and dynamic,stress and deflection analyses (STR)
The main topics included deal with the static and dynamic finite element analyses of pressure vessels,their components and piping,namely:stress and deformation analysis;2D and 3D linear elastic static and dynamic analysis;material and geometrical nonlinear static and dynamic analysis;seismic response analysis;impact analysis;response to detonation loading;damping charac-teristics;analysis of residual stresses;shakedown analysis;vibroacoustical analysis;mechanical behaviour studies;local mechanical behaviour studies;determining plastic and limit loads;stress concentration factors;stiffness evaluation;wrinkling;probabilistic studies.
Applications to:pipes;tubes;pipelines;tubesheets;piping elbows;pressure vessel components;containment vessels;pressure vessel heads;reactor vessel heads;nozzle models;thick-walled cylinders;reinforcing pads;tubular structures;saddle supports;anchorage.
Materials under consideration:steels;stainless steels;aluminium;composites;polymers;filament wound compo-sites;fibre-reinforced composites;polymer matrix compo-sites;titanium;foam filled aluminum tubes;steel reinforced plastics;structural foams.2.2.Stability problems(STA)
Stability problems are the main subject of this section Other topics included are:static and dynamic buckling;thermal buckling;inelastic buckling pressure;inelastic local buckling;buckling response to seismic loading;creep-induced buckling;critical,buckling strains;buckling of cracked components;post-buckling analysis;buckle propa-gation;bending instabilities;stability for cone–cylinder intersections.
Applications to:pipes;tubes;pipelines;linepipes;reeled pipe-in-pipe;pressure vessel components.
Materials:steels;low-alloy steels;aluminium;compo-sites;titanium.
2.3.Thermal problems (THE)
Heat transfer problems and thermomechanical finite element analyses are the main subjects of this se
ction.The following topics are also included:thermal loading and temperature cycling;temperature attenuation;thermal shock;pressurized thermal shock;heat transfer analysis;convective heat and mass transfer;turbulent forced convection and thermal radiation;thermal stratification;thermal striping;freezing problems;creep;local creep;high-temperature structural integrity procedures;design for elevated temperature service;thermal fatigue;fire perform-ance;thermal management studies;parametric studies.Applications to:pipes;tubes;pipelines;boiler tubes;banks of tubes;tube coolant piping systems;tube condenser;pressure vessels;reactor pressure vessels;cryogenic press-ure vessels;heat exchanger components;heated sterilizers;tube–fin exchangers;bellows;tanks;valves;subsea flowlines.
Materials:steels;concrete;composites;polymers;cer-amics;thermal insulations.
2.4.Fracture mechanics problems(FRA)
In this section fracture mechanics and fatigue problems are handled.The listing of references in the Appendix includes:linear and nonlinear 2D and 3D static and dynamic fracture mechanics problems;mechanical and thermal loading;macromechanical and micromechanical modelling;global/local analysis;crack tip opening;crack growth and propagation;delamination growth;cr
ack arrest behaviour;stress corrosion cracks;multiple cracks;microcracking;fracture toughness;strength;shear strength;cleavage fracture;burst pressure prediction;predicting the failure pressure;prediction of crack coalescence;progressive
Fig.1.Finite elements and various topics in pressure vessels and piping (1976–2004).
J.Mackerle /International Journal of Pressure Vessels and Piping 82(2005)571–592
572
crushing;limit load solutions;fracture mechanics par-ameters;stress intensity factors;J-integral;damage;damage tolerance;progressive damage;interlaminar and intralami-nar damage;fatigue problems;thermal fatigue;creep rupture;tearing failure;local failure modes;leak-before-break analysis;failure models for puncture;critical fracture energy;flow induced vibration failure;load capacity of corroded pipes;waveguide scattering by cracks;material fracture testing;NDT;flaw detection;pipe inspection; defect assessment at elevated temperature;fracture mech-anics in material processing;fracture mechanics in welding; life assessment;benchmark experiments;integrity evalu-ation methods;reliability analysis.
Applications to:pipes;tubes;pipelines;elbows;line-pipes;pipe bends;pressure vessels;reactor pressure vessels; heat exchangers;power plant components;tube-to-tube-sheets;pressurized cylinders;deep-water pipelines;branch junctions;dents;perforated plates;drainage systems.
Materials:steels;stainless steels;aluminium;titanium; composites;braided composites;sandwich composites; polymers;rubber;cladding materials;foamfillings.
2.5.Contact problems(CON)
2D and3Dfinite element studies of static and dynamic contact problems dealing with pipes and pressure vessels are included in this section.Other subjects under consideration are:behaviour of joints to static,dynamic and thermal loading;junctions under pressure and bending;creep induced contact and stress evolution;contact pressure due to thermal loading;stress concentration factor;lateral contact stiffness;flexibility analysis;externalflange loads; moment resistance;estimation of sealing performance;bolt-up and disassembly process;stick-slip and stick-slip-separation;study of gaps between components.
Applications to:pipes;tubes;pressure vessels;pipe flange connections;gasketed and non-gasketedflanged pipes;flanged connections for high-temperature appli-cations;piping branch junctions;
tube-to-tubesheet joints; tube–gusset plate connections;stub–flange joints;shear joining;lapped shear joints;boltedflanged joints;tubesheet-to-channel connections;nozzle–shell junctions;nozzle–sphere connections;ferrule strap connections;bonded connections;joining by curing.
Materials:steels;stainless steels;aluminium;polymers; composites;concrete.
2.6.Fluid–structure interaction problems(FLU)
The main topics include:coupledfluid–structure response analyses;fluid induced vibration problems; dynamic analysis offluid-filled pipes;analysis of pipes conveyingfluids;radial–axial deformations of pipes con-veyingfluid;instability analysis in shells conveying fluid;modal vibration suppression;wave–seabed–pipe interaction.
Applications to:pipes;tubes;pipelines;pressure vessels; tube bundles;submerged pipes.
Materials:steels;composites;fluids.
2.7.Manufacturing of pipes and tubes(MAN)
Thefinite element simulation of manufacturing pro-cesses is the subject of this section.The main topics
listed are:material characteristics and formability;determination of the coefficient of friction;determination of forming limit; study of forming parameters;flow stress determination; bending problems;cold bending;laser tube bending;bulge forming;hydrostatic tube bulging;electromagnetic bulging; drawing;cold drawing;bend-stretching forming;tubular hydroforming;dual hydroforming;planetary rolling;hot roll sizing milling;roller levelling;rotationally molding; extrusion;semi-solid extrusion;tubeflaring;tube-nosing process;outward curling;cold pilgering;casting;necking and bursting;fold formation;lubrication mechanisms;fixtures design.
Applications to manufacturing of:pipes;tubes;line-pipes;pipelines;seamless tubes;T-shape tubes;elbows; bellows;pressure vessels.
Materials:steels;stainless steels;microalloyed steels; aluminium;titanium;zircaloy;steel reinforced plastics; polymers;composites.
2.8.Welded pipes and pressure vessel components(WEL)
The subjects in the simulation of welding processes included here are:2D and3D thermomechanical analysis; heat transfer analysis;residual stresses caused by welding; temperature distribution;determination of welding pressure; prediction of welding parameters;creep behaviour of we
lds; local stress effect;fracture behaviour of welds;weld fatigue; life prediction;weld testing;structural integrity assessment.
Welding of:pipes;tubes;gas pipelines;pressure vessel components;pressure vessels;tubesheet assembly;long seam welds;girth welds;butt welds;friction welding; ultrasonic welding;multi-pass welding;prepregs welding; sleeve repair welding.
Materials:steels;stainless steels;austenitic steels; polymers.
2.9.Development of specialfinite elements
for pressure vessels and pipes(ELE)
In this section,references dealing with development as well as applications of specialfinite elements used for analyses of pressure vessels and piping systems are given. The element types included are:modelling experiences with various types of elements;pipe and tube elements;contact elements;elbow elements;shell elements;toroidal shells; shell elements for collapse load analysis;elements for generalized in-plane pipe loading;3D elements for saddle support pressure vessels;special element for the study of
J.Mackerle/International Journal of Pressure Vessels and Piping82(2005)571–592573
drag chains;special tube element for thermomechanical analysis;exact Timoshenko pipe element.
2.10.Finite element software(SOF)
At present,thousands offinite element software packages exist and new programs are under development.The existing software can vary from large,sophisticated,general purpose, integrated systems to small,special purpose programs for PCs.Most of these programs have been mentioned and described in[1,8].In the respective section of the Appendix some new references dealing with development/applications of FE software are listed.They are concerned with:code for prestressed concrete containment vessels;code for thermal-hydraulics pressurized thermal shock analysis; new pressure vessel code for ASME;software for lifetime assessment;software for offshore pipelines;finite element parallel processing;distributed computation.
2.11.Other topics(OTH)
In this last section subjects not treated earlier are included.They deal with:static and dynamic geomechani-cal analyses of pressure vessels and pipes in2D and3D; buried structures;soil–structure i
nteraction;side and deep excavations;laying operations;deflection analysis;surface impact;pipelines subject to settlement;buried pipes under vehicle loads;cyclone effects;pipes in sediment pocket; seismic analysis;noise transmission;deployment dynamics of inflatable tubes.
Applications to:pipes;tubes;submarine pipelines; pipelines with elbows;pumping well pipes;perforated drainage pipes;perforated stiffening tubes;sandwich pipes; pipe-in-pipe;pipe culverts;water piping systems;tunnel face reinforced with pipes;microtunneling applications; nuclear fuel channels;check valves;servovalves;catenary risers;anchorage;relaxed hanger spans.
Materials:steels;stainless steels;concrete;polymers; composites;thermoplastics;geotextile;inflated fabrics. Acknowledgements
The bibliography presented in the Appendix is by no means complete but it gives a comprehensive representation of differentfinite element applications on the subject.The author wishes to apologize for the unintentional exclusions of missing references and would appreciate receiving comments and pointers to other relevant literature for a future update.
Appendix A.A bibliography(2001–2004)
This bibliography provides a list of literature references onfinite element analysis of pressure vessel structures/components and pipes/tubes.The listings presented contain papers published in scientific journals and conference proceedings retrospectively to2001.References have been retrieved from the author’s database,MAKEBASE.Also COMPENDEX has been checked.References are grouped into the same sections described in thefirst part of this paper,and are sorted alphabetically according to thefirst author’s name.In some cases,if a specific paper is relevant to several subject categories,the same reference is listed under the respective section headings.
A.1.Linear and nonlinear,static and dynamic,
stress and deflection analyses
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3.Asada S,et al.Verification of alternative criteria for shakedown
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ASME Press Vess Piping Conf,PVP2002;439:23–30.
4.Ayob AB,et al.The interaction of pressure,in-plane moment and
torque loadings on piping elbows.Int J Press Vess Piping2003;
80(12):861–9.
5.Beltman WM,Shepherd JE.Linear elastic response of tubes to
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6.Bjorset A,et al.Titanium pipes subjected to bending moment and
external pressure.Int Conf Offshore Mech Arctic Engng,Rio de Janeiro.New York:ASME2001;33–41.
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external pressure.Comput Struct2003;81(30):2691–704.
8.Bjorset A,et al.Probabilistic analysis of bending moment capacity of
titanium pipes.Struct Safety2004;26(3):241–69.
9.Blyukher B,et al.Computer simulation of pipeline deformations on
the basis of data from an intelligent caliper inspection tool.ASME Press Vess Piping Conf,PVP2003;458:309–12.
10.Boot JC,et al.Predicting the creep lives of thin-walled cylindrical
polymeric pipe linings subject to external pressure.Int J Solids Struct 2003;40(26):7299–314.
11.Borvik T,et al.Empty foam-filled aluminium tubes subjected to
axial and oblique quasistatic loading.Int J Crashworth2003;8(5): 481–94.
12.Caillaud S,et al.Aeroacoustical coupling and its structural effects on
a PWR steam line Part2-Vibroacoustical analysis of pipe shell
deformations.ASME Int Mech Engng Cong Expo,AMD2002;253: 843–50.
13.Chapuliot S,et al.Mechanical behavior of a branch pipe subjected to
out-of-plane bending load.J Press Vess Tech,ASME2002;124(1): 7–13.
14.Chattopadhyay J.The effect of internal pressure on in-plane collapse
moment of elbows.Nuclear Engng Des2002;212(1/3):133–44. 15.De Sousa JRM,et al.Local mechanical behaviour offlexible pipes
subjected to installation loads.Int Conf Offshore Mech Arctic Engng, Rio de Janeiro.New York:ASME2001;219–27.
16.Demma A,et al.Mode conversion of longitudinal and torsional
guided modes due to pipe bends.AIP Conf,No.557A2001;172–9.
17.Dixon RD,et al.Stress concentration factors of cross-bores in thick
walled cylinders and square blocks.ASME Press Vess Piping Conf, PVP2002;436:31–6.
18.Duffey TA,Romero C.Vibration modes of spherical shells and
containment vessels.ASME Press Vess Piping Conf,PVP2002;440: 177–84.
J.Mackerle/International Journal of Pressure Vessels and Piping82(2005)571–592 574
19.Estrada H.Axisymmetric analysis of a laminated cylindrical shell
with variable thickness.Int SAMPE Tech Conf,Long Beach 2004;2589–98.
20.Ezekoye LI.An examination of the effect of valve design on stifffiess.
ASME Press Vess Piping Conf,PVP2001;426:153–7.
21.Famiyesin OOR,et al.Post-finite-element prediction strategies for
engineering structures.J Struct Engng,ASCE2001;127(11):1366–9.
22.Famiyesin OOR,et al.Semi-empirical equations for pipeline design
by thefinite element method.Comput Struct2002;80(16):1369–82.
23.Florizone DJ.Design of ellipsoidal heads using elastic–plasticfinite
element analysis.ASME Press Vess Piping Conf,PVP2002;440: 163–70.
24.Franco JRQ,et al.Adaptive FE method for the shakedown and limit
analysis of pressure vessels.Eur J Mech,A/Solids2003;22(4): 525–33.
25.Fujita K,et al.Seismic response analysis of piping systems with
nonlinear supports using differential algebraic equations.ASME Press Vess Piping Conf,PVP2001;428:57–65.
26.Fujiwaka T,et al.Simulation of excessive deformation of piping due
to seismic and weight loads.ASME Press Vess Piping Conf,PVP 2002;439:345–52.
27.Fukuda N,et al.Changes in tensile properties due to cold bending of
line pipes.Int Conf Offshore Mech Arctic Engng,Oslo.New York: ASME2002;189–96.
28.Fukuda N,et al.Effect of changes in tensile properties due to cold
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4th Int Conf Offshore Mech Arctic Engng,Oslo.New York:ASME 2002;363–70.
29.Guillot MW,Helms JE.Comparison of different methodologies for
stress analysis of reinforcing pads.ASME Press Vess Piping Conf, PVP2003;459:75–9.
30.Gupta NK,et al.A study of lateral collapse of square and rectangular
metallic tubes.Thin-Wall Struct2001;39(9):745–72.
31.Haapaniemi H,et al.Numerical simulation of piping vibrations using
an updated FE model.Proc SPIE2002;4753:193–9.
32.Hardy SJ,et al.Upper lower bound limit and shakedown loads for
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33.Hardy SJ,et al.Elastic and elastic–plasticfinite element analysis of
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34.Hart JD,et al.Development of acceptance criteria for mild ripples
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35.Hsieh MF,et al.Limit loads for knuckle-encroaching nozzles in
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36.Hsu PW.Stresses in a uniformly paralelepiped solid with a
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37.Hub NS,et al.Effect of nozzle geometry on leak-before-break
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38.Kumar IS.Application of code case N-597for local thinning
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39.Joshi B,et al.Finite element modeling of a PE pipe heap leachate
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40.Kalnins A.Guidelines for sizing of vessels by limit analysis.Weld
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42.Kalnins A.Shakedown ratchetting directives of ASME B and PV
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439:47–55.43.Karadeniz H.A method for including ovalization effects of tubular
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44.Kim YJ,et al.Estimation of non-linear deflection for cylinder under
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45.Kochekseraii SB.Finite element modelling of plastic collapse of
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46.Kochekseraii SB,Robinson M.Flexural behavior of a polyvinyl
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48.Kulikov YA,et al.Numerical–experimental investigation of the
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49.Kumar R,Saleem MA.Bend angle effect on B2and C2stress indices
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50.Kumar R,Saleem MA.B2and C2stress indices for large angle bends.
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51.Kumar R,Saleem MA.B2and C2stress indices for large-angle bends.
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52.Laszlo JL,et al.Non-linear vibrations of the tube bend region of
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53.Leila K,et al.Application of the simplified analysis to real structures.
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54.Leishear RA.Dynamic pipe stresses during water hammer:II—a
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55.Leishear RA,et al.Dynamic pipe stresses during water hammer:I—a
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56.Lengsfeld M,et al.Analysis of loads for nozzles in API650tanks.
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57.Lengsfeld M,et al.Stiffness coefficients for nozzles in API650tanks.
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58.STR,Lin CY.Analysis of laminated composite tubular structure.PhD
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59.Lin CY,Chan WS.Stiffness evaluation of elliptical laminated
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60.Lubis A,Boyle JT.The pressure reduction effect in smooth piping
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64.Mangalaramanan P.Accelerated limit loads using repeated elastic
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65.Mantena PR,Mann R.Impact dynamic response of high-density
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66.Marie S,Nedelec M.Elastic stresses in elbows submitted to in-
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69.Megahed MM,et al.Shakedown loads for structures with severe
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72.Miller GA,et al.An elastic-perfectly plastic limit load analysis of a
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73.Mirza S,et al.Fiber-reinforced composite cylindrical vessel with
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74.Moffat DG,et al.An assessment of ASME III and CEN TC54
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77.Muscat M,Hamilton R.Elastic shakedown in pressure vessel
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78.Muscat M,Mackenzie D.Elastic shakedown analysis of
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82.O’Brien BJ,et al.Three dimensionalfinite displacements and
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