2.Finite elements in the analysis of pressure vessels and piping,.pdf

International Journal of Pressure Vessels and Piping 76 (1999) 461–485

Finite elements in the analysis of pressure vessels and piping,

an addendum (1996–1998)

J. Mackerle *

Link ¨ping Institute of Technology, Department of Mechanical Engineering, S-581 83 Link¨ping, Sweden

Received 5 February 1999; accepted 23 February 1999

Abstract

The article gives a bibliographical review of the 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 an addendum to the Finite elements in the

analysis of pressure vessels and piping-a bibliography (1976–1996) published in the Int. J. Press. Ves. Piping 1996;69:279–339. The added

bibliography at the end of the article contains approx. 630 references to papers and conference proceedings on the subject that were published

in 1996–1998. These are classiﬁed in the following categories: linear and non-linear, 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

Keywords: Finite element; Bibliography; Pressure vessels; Pipes; Linear and non-linear static and dynamic analysis; Fracture mechanics; Contact problem;

Thermal problem; Fluid–structure interaction; Welding

1. Introduction

This review on the subject is divided into following parts

and it concerns:

Pressure vessels and piping, with many more utilization

in reactor technology, chemical industry, marine and space

engineering, operating under extreme 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 mate-

rials are used in pressure vessels and their components more

frequently to replace in some cases the conventional steels.

During the last two decades considerable advances have

been made in the application of numerical techniques to

analyze pressure vessels and piping problems. Among the

numerical procedures, the ﬁnite element methods are the

most frequently used.

Pressure vessel and piping analyses may have some/all

phases as: elastic stress and deformation analysis where

both mechanical and thermal loads may be applied; heat

transfer analysis; dynamic analysis; plastic and creep analy-

sis; etc. There is in existence a large number of general

purpose and special purpose ﬁnite element programs avail-

able to cope with each phase of the analysis.

linear and non-linear, 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

special

ﬁnite

elements

for

pressure

vessels and pipes (ELE);

ﬁnite element software (SOF);

other topics (OTH).

The status of ﬁnite element literature published between

1976 and 1998, and divided into categories described above,

is illustrated in Fig. 1. Data presented in this ﬁgure include

published technical papers in the primary literature; this

means papers appearing in the various general and specia-

lized journals, conference proceedings as well as theses and

dissertations. If we take the number of published papers as a

measure for research activity in these various subjects, we

can see the priority trend in research in the past.

This article is organized into two parts. In the ﬁrst part,

* Corresponding author. Tel.:

46-13-28-1111; fax:

46-13-28-2717.

E-mail address: jarma@ikp.liu.se (J. Mackerle)

PII: S0308-0161(99)00012-5

462

J. Mackerle / International Journal of Pressure Vessels and Piping 76 (1999) 461–485

Fig. 1. Finite elements and various topics in pressure vessels and piping

each subject listed above is brieﬂy described by key words

where current trends in application of ﬁnite element techni-

ques are mentioned. The second part, the Appendix A, is a

listing of references on papers published in open literature

for the period 1996–1998, retrieved from the author’s data-

base MAKEBASE [1,2]. Readers interested in the ﬁnite

element literature in general are referred to [3] or to the

author’s Internet Finite Element Book Bibliography

(http://www.solid.ikp.liu.se/fe/index.html). This bibliogra-

phy is an addendum to the author’s earlier bibliography

[4] where approximately 1900 references have been listed.

ﬂanges; tube clamps; conical tubes; tube plugs; tube-in-

tube structures; perforated tubesheets; tee-ﬁttings; elbows;

nozzles; reinforced nozzle connections; pressure vessels;

vessels heads/end closures; pressurized domed closures;

conical and toriconical shells; cone-cylinder shells; spheri-

cal vessels; PWR vessels; nuclear pressure vessels; rectan-

gular pressure vessels; multi-shell pressure vessels;

intersecting cylinders; nozzle-cylinder intersections; high

pressure components; gas holders; storage tanks.

Materials under consideration : steel; stainless steel; ferri-

tic steel; aluminum; Incoloy; polymers; hyperelastic mate-

rials;

composites;

ﬁlament

wound

FRP;

layered

metal

matrix composites; ceramics.

2. Finite elements in the analysis of pressure vessels and

piping

2.2. Stability problems (STA)

Stability problems form the main subject of this section.

Other topics included are: stability and instability; buckling;

lateral buckling; local buckling; delamination buckling;

torsional buckling; local buckling and burst pressure;

creep buckling; dynamic buckling; strain localization;

limit load analyses; collapse; adaptive methods.

Applications to : pipes and tubes; tubular members; pipe-

lines; offshore pipelines; submarine pipelines; drill pipes;

pipe linings; braced elliptical tubes; elbows; bellows; high

pressure vessels; cylindrical vessels; axisymmetric shells;

cone-cylinder shells; spherical shells; cylinder-cylinder

intersection; imperfect ellipsoids and closed toroids.

Materials : steel; low-alloy steel; polymers; composites.

2.1. Linear and non-linear, 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 compo-

nents and piping, namely: 2D and 3D linear elastic static

and dynamic analyses; material and geometrical non-linear

static and dynamic analyses; shakedown analyses; stress–

strain investigations; stress concentration factor studies;

local stresses and deformations; studies of material and

mechanical properties; natural frequencies and mode

shapes; dynamic response analyses; seismic analyses; load

interaction studies; explosive detonation loading; solution

of creep problems; wave propagation in pipes; adiabatic

shear banding; external and internal pressure; tube twisting;

tube bending; compression response; determination of resi-

dual stresses; evaluation of structural integrity; reliability

studies; pressure design criteria; parametric studies, adap-

tive methods.

Applications to : thick–thin tubes; thick–thin pipes;

straight and curved geometry; pipelines; marine and

submarine pipelines; saddle-supported pipelines; oil ﬁeld

tubes;

2.3. Thermal problems (THE)

Heat transfer problems and thermomechanical ﬁnite

element analyses are the main subjects of this section. The

following topics are included: heat transfer analyses-forced

convection heat transfer, mixed convection heat transfer,

cyclic heat transfer, turbulent heat transfer, thermal radia-

tion; transient thermal loads; thermal shock; linear and non-

linear

thermomechanical

analyses;

thermoviscoplastic

boiler

tubes;

nuclear

piping;

pipe

linings;

pipe

analyses;

temperature

ﬁeld

studies;

creep

buckling

J. Mackerle / International Journal of Pressure Vessels and Piping 76 (1999) 461–485

463

elevated

temperatures;

thermal

contact

resistance;

tube

2.6. Fluid-structure interaction problems (FLU)

elongation process; frost-induced

deformations; residual

The main topics include: coupled ﬂuid-structure response

analyses; non-linear ﬂuid-structure interaction; vibration

analyses; computation of natural frequencies and mode

shapes; ﬂow-induced vibrations; seismic wave induced

ﬂuid-structure interaction problems; sloshing; wave propa-

gation; ﬂuid ﬂow analyses; liquid ﬁlling behavior; partial

ﬂuid-ﬁlled structures.

Applications to : pipes and tubes; pipelines; submarine

pipelines; tube bundles; pipe with ﬂanges; storage tanks;

submerged

thermal stresses.

Applications to : tubes and pipes; tubes with obstruction;

helical pipes; pipelines; shallow pipes in soils; boiler tubes;

tube bundles; tubesheets; tube ﬂanges; pressure vessels;

PWR vessels; cylindrical and spherical vessels; vessel

closures; energy storage exchangers; heat exchangers.

Materials : steel; stainless steel; alloys; Incoloy; compo-

sites; refractories.

2.4. Fracture mechanics problems (FRA)

structures;

cylindrical

shells;

ring

stiffened

circular cylinders; pressure vessels.

Materials : steels; metals; composites.

In this section the fracture mechanics and fatigue

problems are handled. The listing of references in Appendix

A includes: linear and non-linear static and dynamic frac-

ture mechanics problems; crack initiation; crack opening;

crack extension; crack size determination; crack kinking;

multiple cracks; surface and internal cracks; circumferential

surface ﬂaws; through-wall cracks; part-wall cracks; cracks

under bending and cyclic bending loads; cracks in joints;

cracks in welds; leak-before-break; dynamic crack propaga-

tion; vibration failure; failure prediction; low-cycle fatigue;

high-cycle fatigue; initial bending fatigue; fatigue life inves-

tigations; creep-fatigue crack growth; fracture toughness

testing; failure probability calculations; reliability analysis;

stress intensity factors; J -estimation; residual stresses; resi-

dual strength; strength degradation; damage; creep damage;

fretting-wear damage; micromechanical studies; parametric

studies.

Applications to : pipes and tubes; nuclear piping; pipe

connections; piping branch connections; pipe tees; tube-

sheets; pipelines; submarine pipelines; gas pipelines;

nozzles; elbows; pressure vessels; BWR pressure vessels;

reactor pressure vessels; vessel closures; pressurized fuse-

lages; heat exchangers.

Materials : steel; stainless steel; low-alloy steel; Zircaloy;

polymers; composites; ceramics.

2.7. Manufacturing of pipes and tubes (MAN)

The ﬁnite element simulation of manufacturing processes

is the subject of this section. The main topics listed: draw-

ing; drawing without plug; extrusion process; radial extru-

sion; hydrostatic extrusion; cold forging; injection forging;

hydroforming; electromagnetic forming; compacting

process; preforming; superplastic bulging; sinking process;

backward spinning; stagger spinning; blowing operations;

hydraulic expansion; elongation process.

Applications to manufacturing of : pipes and tubes; tubu-

lar components; tubes with ﬁttings; pressure vessel compo-

nents.

Materials : steel; bimetallic materials; copper; copper-

clad aluminum; titanium alloys; polymers; composites.

2.8. Welded pipes and pressure vessel components (WEL)

The subjects in simulation of welding processes included

here are: 2D and 3D thermomechanical analyses; heat trans-

fer analyses; analysis of shrinkage; fracture mechanics

studies of welding; weld fatigue; residual stresses; circum-

ferential welding; butt welds; multi-pass butt welds; girth

welds; friction welding; GTA welding; electro-fusion weld-

ing; spiral weld cladding; underwater welding; weld repairs;

parametric studies.

Welding of : pipes and tubes; pipelines; pipe-ﬂange joints;

pipes penetrating pressure vessels; pressure vessels; nuclear

reactor pressure vessels.

Materials : steel; stainless steel; austenitic stainless steel;

ferritic steel; aluminium; polymers.

2.5. Contact problems (CON)

2D and 3D ﬁnite element studies of static and dynamic

contact problems dealing with pipes and pressure vessels are

included in this section. Other subjects under consideration

are: contact–impact problems; hypervelocity impact; fric-

tional contact problems; dynamic friction modelling; adhe-

sive bonding; penetration problems; stress concentration

factors; expansion and residual contact pressure; residual

stresses; parametric studies.

Applications to : tubes and pipes; deep ocean pipes;

submarine pipelines; gas pipelines; supported pipelines;

tube to tubesheet joints; piping branch junctions; pipe ﬂange

connections;

2.9. Development of special ﬁnite elements for pressure

vessels and pipes (ELE)

In this section, references dealing with development as

well as applications of special ﬁnite elements used for the

analyses of pressure vessels and piping systems are given.

The element types included are: general axisymmetric thin

shell element; special element for shell intersections; special

junction shell element; hybrid stress elements; double scale

ﬁnite element; consistent dynamic pipe element; geometric-

casing-tubing

connections;

threaded

end

connections;

self-scaling

connections;

expansion

joints;

pressure vessels; heat exchangers.

Materials :

steel;

alloys;

concrete

ﬁlling;

polymers;

composites.

464

J. Mackerle / International Journal of Pressure Vessels and Piping 76 (1999) 461–485

non-linear pipe element; curved pipe element; line-spring

element.

A.1. Linear and nonlinear, static and dynamic, stress and

deﬂection analyses (STR)

2.10. Finite element software

1. STR Abah L, Limam A. Upon the effects of cutouts on

the behaviour of axially crushed tubes. In: ASME/

JSME Joint Press Vess Piping Conf PVP 361. New

York: ASME, 1998:187–194.

2. STR Alleyne DN, Cawley P. Effect of discontinuities

on the long-range propagation of lamb waves in pipes.

Proc Inst Mech Engng E 1996;210(3):217–226.

3. STR Alleyne DN et al. The reﬂection of guided waves

from circumferential notches in pipes. J Appl Mech

1998;65(3):635–641.

4. STR Arsene S, Bai J. New approach to measuring

transverse properties of structural tubing by a ring

test. J Test Eval 1996;24(6):386–391.

5. STR Arsene S, Bai J. New approach to measuring

transverse properties of structural tubing by a ring

test-experimental

At present, thousands of ﬁnite element software (SOF)

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 [4]. In the respective

section of the Appendix some new references dealing with

development/applications of FE software are listed. They

are concerned with: code developments for pressure vessels

and piping, code evaluations, users experiences, etc.

2.11. Other topics (OTH)

In this section subjects not treated earlier are included.

They deal with: static and dynamic geomechanical analyses

of pressure vessels and pipes in 2D and 3D; buried struc-

tures; soil-pipe interaction problems; seismic response

analyses; effects of trenching; uplift behaviors; simulation

of corrosion processes; cathodic protection; non-destructive

evaluation and inspection-eddy current testing, magnetic

ﬂux leakage detection, structural health monitoring, vibra-

tion control, etc.

Applications to : pipes and tubes; buried pipes; pipelines;

pressure vessels.

Materials :

investigation.

Test

Eval

1998;26(1):26–30.

6. STR Avalle M, Goglio L. Static lateral compression of

aluminum

tubes:

strain

gauge

measurements

and

discussion

theoretical

models.

Strain

Anal

Engng Des 1997;32(5):335–343.

7. STR Axenenko O, Tsvelikh A. Hybrid ﬁnite element

approach to the solution of creep problems. Comp

Mater Sci 1996;6(3):268–280.

8. STR Ayob AB et al. Load interaction in pressurized

structures using the ﬁnite element method. Int J Press

Vess Piping 1997;73(1):3–9.

9. STR Babu S, Iyer PK. Inelastic analysis of compo-

nents using a modulus adjustment scheme. J Press

Vess Tech 1998;120(1):1–5.

10. STR Baniotopoulos CC. Saddle-supported pipelines:

inﬂuence of unilateral support and thickness on the

stress state. Int J Press Vess Piping 1996;67(1):55–64.

11. STR Batra RC, Rattazzi D. Adiabatic shear banding in

steel;

reinforced

concrete;

composites;

geotechnical materials.

Acknowledgements

The bibliography presented in the Appendix is by no

means complete but it gives a comprehensive representation

of different ﬁnite elements applications on the subjects. 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.

thick-walled

steel

tube.

Comp

Mech

1997;20(5):412–426.

12. STR Batra RC et al. A comparison of 1-D and 3-D

simulations of the twisting of a thermoviscoplastic

tube. Int J Plasticity 1996;12(1):29–33.

13. STR Becht C, Chen Y. External pressure evaluation

for existing pressure vessels. In: ASME Press Vess

Piping

Appendix A. A bibliography (1996–1998)

This bibliography provides a list of references on ﬁnite

element analysis of pressure vessel structures/components

and pipes/tubes. Presented listings contain papers published

in scientiﬁc journals and conference proceedings retrospec-

tively to 1996. References have been retrieved from the

author’s database, MAKEBASE. They are grouped into

same sections described in the ﬁrst part of this article, and

sorted alphabetically according to the ﬁrst author’s name. In

some cases, if a speciﬁc paper is relevant for several subject

categories, the same reference is listed under respective

section headings.

Conf

PVP

359.

New

York:

ASME,

1997:213–216.

14. STR Beghini M et al. Creep behaviour of a nuclear

pressure vessel under severe accident conditions. In:

ASME Press Vess Piping Conf PVP 331. New York:

ASME, 1996:137–143.

15. STR Behrend J et al. Stress investigations of oil ﬁeld

tubes in long-term use applying the ﬁnite element

method. EKEP 1997;113(10):421–424.

16. STR Bezdikian G et al. PWR vessel management:

French

approach

for

integrity

assessment

and

J. Mackerle / International Journal of Pressure Vessels and Piping 76 (1999) 461–485

465

maintenance strategy. In: ASME/JSME Joint Press

Vess

ﬁnned tubes. In: ASME Press Vess Piping Conf PVP

354. New York: ASME, 1997:11–15.

33. STR Franco JRQ, Barros FB. Advances in ﬁnite

element modelling of plastic behaviour of pressure

vessels.

Piping

Conf

PVP

365.

New

York:

ASME,

1998:3–10.

17. STR Blachut J. Maximization of shakedown loads for

internally pressurized steel domed closures. In: Fifth

International Conference on Computer Aided Optim

Des Structure. Rome: CMP, 1997:33–41.

18. STR Boot JC et al. Structural performance of thin-

walled polyethylene pipe linings for the renovation

of water mains. Tunnell Underground Space Tech

1996;11(S1):37–51.

19. STR Boussaa D et al. Finite pure bending of curved

pipes. Computers and Structures 1996;60(6):1003–

1012.

20. STR Chen HF et al. Study on the stress concentration

at the round corners of ﬂat heads to internal pressure. J

Press Vess Tech 1996;118(4):429–433.

21. STR Chen HF et al. A numerical method for reference

stress in the evaluation of structure integrity. Int J

Press Vess Piping 1997;71(1):47–53.

22. STR Chung JS, Cheng BR. Nonlinear coupled

responses to impact loads on free-span pipeline:

torsional coupling, load steps and boundary condi-

tions. Int J Offshore Polar Engng 1996;6(1):53–61.

23. STR Cramer BH et al. Reliability evaluation of

evacuation pipes on the troll GBS. In: 17th Interna-

tional Conference on Offshore Mechanical and Arctic

Engineering. Lisbon: OMAE, 1998:1–7.

24. STR Da Dilveira JLL et al. Shakedown and limit

analysis in a pressure vessel. In: Fourth World Cong

Comp Mech. Buenos Aires, 1998:198.

25. STR DePadova TA, Sims JR. Fitness for continued

service:

In:

Fourth

World

Cong

Comp

Mechan,

Buenos Aires, 1998:185.

34. STR Fujita T et al. Seismic proving test on reactor

shutdown cooling systems: pressure pulsation of

instrumentation piping induced by seismic motion.

In: ASME Press Vess Piping Conf PVP 345. New

York: ASME, 1997:207–211.

35. STR Fukuoka T, Takaki T. Three-dimensional ﬁnite

element analysis of pipe ﬂange-effects of ﬂange inter-

face geometry. In: ASME/JSME Joint Press Vess Piping

Conf PVP 367. New York: ASME, 1998:125–131.

36. STR Fyrileiv O et al. Free span assessment of the

zeepipe IIA pipeline. In: 17th Int Conf Offshore

Mech Arctic Engng. Lisbon: OMAE, 1998;1–8.

37. STR Giglio M. Spherical vessel subjected to explosive

detonation

Int

Press

Vess

Piping

1997;74(2):83–88.

38. STR Guan B et al. Application of artiﬁcial neural

network to inverse problems of estimating inner etch

of elastoplastic pipe under pressure. Acta Mech Solida

Sinica 1996;9(1):88–93.

39. STR Guedes E, De Noronha RF. Circular opening

reinforcement to ASME Code Section VIII analytical

procedure versus ﬁnite element analysis. In: ASME

Press

Vess

Piping

Conf

PVP

353.

New

York:

ASME, 1997:325–332.

40. STR Guo YZ, Zeng ZJ. Six-plate analytical method

for rectangular pressure vessels of ﬁnite length. Int J

Press Vess Piping 1997;74(1):1–6.

41. STR Hari Y, Williams DK. Analysis of transition radii

in conical reducers. In: ASME/JSME Joint Press Vess

Piping Conf PVP 360. New York: ASME, 1998:335–

342.

42. STR Harsokoesoemo D, Santoso G. Numerically

calculated stress concentration factors for two

normally intersecting cylinders due to internal pres-

sure. In: Eighth Int Conf Press Vess Tech, Montreal.

New York: ASME, 1996:61–68.

43. STR Harsokoesoemo D, Santoso G. Stress distribution

in the region around two normally intersecting pipes

due to in-plane bending moments using ﬁnite element

method. In: ASME Asia Cong Exhib, Singapore. New

York: ASME, 1997:AA-58.

44. STR Hassan T et al. Improved ratcheting analysis of

piping

local

thin

areas.

In:

Eighth

International

Conference

Press

Vess

Tech,

Montreal.

New

York: ASME, 1996:175–181.

26. STR Dekker CJ, Bos HJ. Nozzles-on external loads

and

internal

pressure.

Int

Press

Vess

Piping

1997;72(1):1–18.

27. STR Dekker CJ, Cuperus J. Local load stresses in

cylindrical shells at plate clips. Int J Press Vess Piping

1996;67(3):263–271.

28. STR Desquines J et al. In-plane limit moment for an

elbow. Lower-bound analytical solution and ﬁnite

element processing by elastic compensation method.

Int J Press Vess Piping 1997;71(1):29–34.

29. STR Dragoni E. The radial compaction of a hypere-

lastic tube as a benchmark in compressible ﬁnite elas-

ticity. Int J Non-Linear Mech 1996;31(4):483–493.

30. STR Elawadly KM et al. Compression response of

ﬁber reinforced composite tubes. Adv Compos Mater

1996;5(4):269–281.

31. STR Erzingatzian A et al. Mechanical behaviour of

ﬁlament wound FRP pipes on saddle supports. In:

Eighth Int Conf Press Vess Technol, Montreal. New

York: ASME, 1996:307–314.

32. STR Flanders HE et al. Bending moment capacity of

components.

Int

Press

Vess

Piping

1998;75(8):643–652.

45. STR Hollinger GL, Hechmer JL. Summary of example

problems from PVRC project on three dimensional

stress criteria. In: ASME Press Vess Piping Conf

PVP 338. New York: ASME, 1996:209–218.

46. STR Holzer SM, Yosibash Z. The p-version of the

ﬁnite element method in incremental elasto-plastic

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