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Review
Finite elements in the analysis of pressure vessels and piping,an addendum: a bibliography (19982001)
Jaroslav Mackerle*
Department of Mechanical Engineering, Linkoping Institute of Technology, S-581 83 Linkoping, Sweden
Received 28 September 2001; revised 8 October 2001; accepted 8 October 2001
Abstract
The paper gives a bibliographical review of nite 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 elementsin the analysis of pressure vessels and pipinga bibliography (19761996) published [Int J Press Vess Piping 69 (1996) 279] and Finite
elements in the analysis of pressure vessels and piping, an addendum (19961998) published [Int J Press Vess Piping 76 (1999) 461]. The
new bibliography at the end of the paper contains approximately 670 references to papers and conference proceedings on the subject that
were published in 19982001. These are classied in the following categories: linear and nonlinear, static and dynamic, stress and deection
analyses; stability problems; thermal problems; fracture mechanics problems; contact problems; uidstructure interaction problems;
manufacturing of pipes and tubes; welded pipes and pressure vessel components; development of special nite elements for pressure vessels
and pipes; nite element software; and other topics. q 2002 Elsevier Science Ltd. All rights reserved.
Keywords: Finite element; Bibliography; Pressure vessels; Pipes; Linear and nonlinear static and dynamic analysis; Fracture mechanics; Contact problems;
Thermal problems; Fluidstructure interaction; Welding
Contents
1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
2. Finite elements in the analysis of pressure vessels and piping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
2.1. Linear and nonlinear, static and dynamic, stress and deection analyses (STR) . . . . . . . . . . . . . . . . . . . . . . . 2
2.2. Stability problems (STA) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2.3. Thermal problems (THE) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2.4. Fracture mechanics problems (FRA) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2.5. Contact problems (CON) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2.6. Fluidstructure interaction problems (FLU) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2.7. Manufacturing of pipes and tubes (MAN) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2.8. Welded pipes and pressure vessel components (WEL) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.9. Development of special nite elements for pressure vessels and pipes (ELE) . . . . . . . . . . . . . . . . . . . . . . . . 4
2.10. Finite element software (SOF) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.11. Other topics (OTH) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
Appendix A. A bibliography (19982001) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
A.1. Linear and nonlinear, static and dynamic, stress and deection analyses (STR) . . . . . . . . . . . . . . . . . . . . . . . 4
A.2. Stability problems (STA) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
A.3. Thermal problems (THE) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
A.4. Fracture mechanics problems (FRA) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
A.5. Contact problems (CON) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
A.6. Fluidstructure interaction problems (FLU) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
A.7. Manufacturing of pipes and tubes (MAN) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
International Journal of Pressure Vessels and Piping 79 (2002) 126
0308-0161/02/$ - see front matter q 2002 Elsevier Science Ltd. All rights reserved.
PII: S0308-0161(01) 00128-4
www.elsevier.com/locate/ijpvp
* Tel.: 146-13-28-1111; fax: 146-13-28-2717.
E-mail address: [email protected] (J. Mackerle).
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A.8. Welded pipes and pressure vessel components (WEL) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
A.9. Development of special nite elements for pressure vessels and pipes (ELE) . . . . . . . . . . . . . . . . . . . . . . . . 24
A.10. Finite element software (SOF) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
A.11. Other topics (OTH) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
1. Introduction
Pressure vessels and piping are widely used in reactor
technology, the chemical industry, marine and space engi-
neering. 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 in pressure vessels and their components
more frequently 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 vessels and piping problems. Among the
numerical procedures, nite 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 nite element programs avail-
able to cope with each phase of the analysis.
This review on the subject is divided into the followingparts and it concerns:
linear and nonlinear, static and dynamic, stress and
deection analyses (STR);
stability problems (STA);
thermal problems (THE);
fracture mechanics problems (FRA);
contact problems (CON);
uidstructure interaction problems (FLU);
manufacturing of pipes and tubes (MAN);
welded pipes and pressure vessel components (WEL);
development of special nite elements for pressurevessels and pipes (ELE);
nite element software (SOF);
other topics (OTH).
The status of nite element literature published between
1976 and 2001, and divided into the categories described
earlier, is illustrated in Fig. 1. Data presented in this gure
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 in the past.
This paper is organized into two parts. In the rst, each
subject listed above is briey described by keywords where
current trends in application of nite element techniques
are mentioned. The second part, Appendix A, is a listing
of references on papers published in the open literature for
the period 19982001, retrieved from the author's data-
base MAKEBASE [1,2]. Readers interested in the nite
element literature in general are referred to Ref. [3] or to
the author's Internet Finite Element Book Bibliography
(http://www.solid.ikp.liu.se/fe/index.html). The presented
bibliography is an addendum to the author's earlier bibli-
ographies [4,5] where approximately 1900 and 630 refer-
ences, respectively, have been listed.
2. Finite elements in the analysis of pressure vessels and
piping
2.1. Linear and nonlinear, static and dynamic, stress and
deection analyses (STR)
The main topics included deal with the static and dynamic
nite element analyses of pressure vessels, their compo-
nents and piping, namely: stress and deformation analysis;
2D and 3D linear elastic static and dynamic analysis;
material and geometrical nonlinear static and dynamic
analysis; shakedown analysis; stress concentration factor
studies; local stresses and deformations; free vibration
analysis; response to shock loading; cyclic loading; seismic
response analysis; random excitation; vibro-impact dyna-
mics; estimation of residual stresses; study of mechanical
properties; creep relaxation; whipping analysis; constraint
effects; prestressing effects; boundary conditions identica-
tion; stiffness properties identication; structural integrity.
Applications to: pipes; tubes; pipelines; pressure vessels;
J. Mackerle / International Journal of Pressure Vessels and Piping 79 (2002) 1 262
Fig. 1. Finite elements and various topics in pressure vessels and piping
(19762001).
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reactor pressure vessels; curved pipes; cantilevered pipes;
dented pipelines; multi-supported pipelines; saddle-
supported pipelines and pressure vessels; sling-supported
pressure vessels; pressure vessel heads; pressure vessel
components; anges; piping elbows; pipe bends; nozzles;
bellows; perforated tubesheets; framed-tube systems; verti-
cal pumps; conical reducers; burst discs; PWR cores;
boilers; corroded pipes; submarine pipelines; pipeline cross-
ings; inatable tubes; coaxial exible tubes; tubes with
coating; shell intersections.
Materials under consideration: steels; stainless steels;
aluminium; composites; polymers; lament wound compo-
sites; bre-reinforced composites; concrete-lled steel
tubes.
2.2. Stability problems (STA)
Stability problems are the main subject of this section.
Other topics included are: stability and instability; buckling;
postbuckling; local buckling; lateral buckling; torsionalbuckling; lateral thermal buckling; high-temperature buck-
ling; buckle propagation; collapse; plastic collapse.
Applications to: pipes; tubes; pipelines; pressure vessels;
ellipsoids and toroids; corroded pipes; braced tubes; elbows;
liners; bellows; conecylinder intersections; buckle arrestors.
Materials: steels; low-alloy steels.
2.3. Thermal problems (THE)
Heat transfer problems and thermomechanical nite
element analyses are the main subjects of this section. The
following topics are included: heat transfer analysis
natural convection, forced convection, mixed convection,radiation, turbulent problems; thermomechanical 2D and
3D analysis; thermoviscoplastic analysis; thermal deforma-
tion analysis; thermal shock; thermal ratchetting; transient
and residual thermal stresses.
Applications to: pipes; tubes; pressure vessels; reactor
pressure vessels; PWR vessels; tube bundles; tubesheets;
ns; pipe-cooling systems; liquid metal target container;
boiler drums.
Materials: steels; zircaloy; composites; glass reinforced
plastics.
2.4. Fracture mechanics problems (FRA)
In this section fracture mechanics and fatigue problems
are handled. The listing of references in Section A.4
includes: linear and nonlinear 2D and 3D static and dynamic
fracture mechanics problems; mechanical and thermal
loading; macromechanical and micromechanical studies;
cracks; multiple cracks; crack growth; crack opening;
crack path bifurcation; crack arrest; crack shape develop-
ment; circumferential cracks; longitudinal cracks; trans-
verse cracks; axial cracks; surface cracks; through-wall
cracks; part-through cracks; tight cracks; ductile fracture;
brittle fracture; residual strength; ultimate strength; fracture
toughness; fatigue studies; thermal fatigue; multi-axial
fatigue; damage; local damage; damage identication;
creep-damage analysis; creep failure; failure behaviour;
cleavage failure; damage tolerance; creep crack growth;
aws; aw detection; cladding effects; leak-before-break;
load bearing capacity; limit load analysis; wave scattering;
ring test; squash test; wide-plate test; failure probability;
stochastic analysis; autofrettage; parametric studies.
Applications to: pipes; tubes; pipelines; pressure vessels;
reactor pressure vessels; bellows; elbows; nozzles; pump
casing; threaded pressure vessels; pressure vessel closures;
ring joint groove; tube-gusset plate connections; adhesively
bonded connections; reinforced branch connections; ange
joints; welded pipes; pipe couplers; pipe piers; crushed tubes;
corroded pipes; shell intersections; concrete containments.
Materials: steels; stainless steels; low-alloy steels; alumi-
nium; zircaloy; zirconium; concrete; composites; bre-
reinforced composites; polymers; PVC; graphiteepoxy;
refractory; functionally graded materials.
2.5. Contact problems (CON)
2D and 3D nite element studies of static and dynamic
contact problems dealing with pipes and pressure vessels are
included in this section. Other subjects under consideration
are: mechanical behaviour of joints; structures under impact
loading; blast loading effects; stress concentration factors;
expansion and residual contact pressure.
Applications to: pipes; tubes; pressure vessels; reactor
pressure vessels; tube-to-tubesheet joints; reinforced nozzle
connections; gasket seal rings; cylindrical shell connections;
casing-tubing connections; threaded connections; bolted
joints; bonded connections; adhesive butt joints; pipe angeconnections; press t joining; piping branch junctions;
multi-connected systems.
Materials: steels; stainless steels; aluminium; composites.
2.6. Fluid structure interaction problems (FLU)
The main topics include: coupled uidstructure
response analyses; pipe/tube conveying uids; cross-ow-
induced vibrations; modal analysis and damping; active
modal control; dynamic analysis of uid-lled pipes;
uidstructure interaction under cavitation; large displace-
ment uidstructure interaction; Stokes ow problems;
internal unsteady ow; gassolid ow; instability analysis.
Applications to: pipes; tubes; pressure vessels; tube
bundles; submerged perforated tubes; cylindrical shells.
Materials: steels; composites; elastomers; uids; hot
liquid sodium; high temperature uids.
2.7. Manufacturing of pipes and tubes (MAN)
The nite element simulation of manufacturing processes
is the subject of this section. The main topics listed are:
material characteristics and formability; spring-back analysis;
drawing; bulge forming; hot extrusion process; isostatic
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pressing; hydro-bulge forming; roll bending; rolling;
extrudingbulging process; cold upsettingextruding; die-
less forming; hydroforming; backward tube spinning; local
induction heating; pressure ltrating process; hydraulic
bulge testing.
Applications to manufacturing of: pipes; tubes; pressure
vessels and closures; non-circular tubes; tube anges; pipe
bends; toroidal shells; elbows.
Materials: steels; stainless steels; metals; copper; tung-
sten; composites; silicon carbide; ferromagnetic materials.
2.8. Welded pipes and pressure vessel components (WEL)
The subjects in the simulation of welding processes
included here are: 2D and 3D thermomechanical analysis;
heat transfer analysis; shrinkage analysis; assessment of
creep behaviour; residual stresses; effect of welding condi-
tions on residual stresses; measurement of residual stresses;
burn-through prediction; effects of repair; friction welding;
seam welds; butt welds; multi-pass butt welds; multi-pass
girth welds; circular patch welds; spiral weld cladding;
bimetallic welds; wet repair welding.
Welding of: pipes; tubes; pressure vessels; reactor pressure
vessels; pipe-to-pipe; nozzles on spheres; pipeange.
Materials: steels; stainless steels; austenitic steels;
bimetallic materials.
2.9. Development of special nite elements for pressure
vessels and pipes (ELE)
In this section, references dealing with development as
well as applications of special nite elements used for
analyses of pressure vessels and piping systems are given.The element types included are: experiences with various
types of elements; 3D special shell element; axisymmetric
thin shell element; axisymmetric hybrid-stress displace-
ment element; enhanced pipe elbow element; interface
beam element.
2.10. Finite element software (SOF)
At present, thousands of nite element software packages
exist and new programs are under development. The exist-
ing software can vary from large, sophisticated, general
purpose, integrated systems to small, special purpose
programs for PCs. Most of these programs have beenmentioned and described in Ref. [4]. In Section A.10
some new references dealing with development/applica-
tions 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; soilstructure interaction; seismic studies; inspection
and maintenance; nondestructive testingeddy current,
neutron diffraction; health monitoring; design sensitivity
analysis; structural integrity assessment; pipeline bundles
on seabed; reliability analysis; optimization problems.
Applications to: crossbores; high-curvature well bores;
steam generator tubes; evacuation pipes; offshore pipelines;
pile-supported buried pipelines; metal beverage containers;
pressure vessels with embedded sensors.
Materials: steels; composites; braided composites; lament
wound composites.
Acknowledgements
The bibliography presented in Appendix A is by no means
complete, but it gives a comprehensive representation of
different nite element applications on the subject. The author
wishes to apologize for the unintentional exclusions of miss-
ing references and would appreciate receiving comments
and pointers to other relevant literature for a future update.
Appendix A. A bibliography (19982001)
This bibliography provides a list of literature references
on nite element analysis of pressure vessel structures/
components and pipes/tubes. The listings presented contain
papers published in scientic journals and conference
proceedings retrospectively to 1998. References have been
retrieved from the author's database, MAKEBASE. They
are grouped into the same sections described in the rst
part of this paper, and are sorted alphabetically according
to the rst author's name. In some cases, if a specic 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
deection analyses (STR)
1. STR Abdel-Hamid AN, Farahat WA. Evaluation of
stresses in piping systems subjected to unspecied
random excitation. 17th Int Modal Anal Conf. Kissim-
mee: IMAC, 1999. p. 4639.
2. STR Abdel-Haq M, et al. Constraint effects on energy
absorption in unidirectional PMC tubes. J Compos
Mater 1999;33(9):77493.3. STR Abhary K, et al. Exact analytical method for
stress analysis of pipelines. Int J Press Vess Piping
1999; 76(8):5615.
4. STR Afshari P, Widera GEO. Free vibration analysis
of composite plates. J Press Vess Technol, ASME
2000; 122(3):390 8.
5. STR Al-Hassani STS, Vartdal B. Investigation into the
effect of circumferential through-wall slits on a canti-
levered pipe subjected to a transverse end load. Proc
Inst Mech Engng, Part E 1998;212(3):16370.
6. STR Alexander CR. Analysis of dented pipelines
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considering constrained and unconstrained dent
congurations. 1999 ASME Energy Sources Technol-
ogy Conference, Houston. New York: ASME, 1999.
p. 113.
7. STR Alleyne DN, et al. The reection of guided waves
from circumferential notches in pipes. J Appl Mech,
ASME 1998;65(3):63541.
8. STR Averbuch D, et al. Implementation of elastoplas-
tic material laws in dynamic riser analysis with appli-
cations to reeled pipes. 9th International Offshore
Polar Engineering Conference, ISOPE, vol. 2. 1999.
p. 2727.
9. STR Babu S, Iyer PK. Inelastic analysis of components
using a modulus adjustment scheme. J Press Vess
Technol, ASME 1998;120(1):15.
10. STR Babu S, Iyer PK. A robust method for inelastic
analysis of components made of anisotropic material.
J Press Vess Technol, ASME 1999;121(2):1549.
11. STR Badr EA, et al. An analytical procedure for esti-
mating residual stresses in blocks containing cross-bores. Int J Press Vess Piping 2000;77(12):73749.
12. STR Baniotopoulos CC, Preftitsi F. Inuence of the
design parameters on the stress state of saddle-
supported pipelines: an articial neural network
approach. Int J Press Vess Piping 1999;76(7):4019.
13. STR Beltman WM, et al. The structural response of
cylindrical shells to internal shock loading. J Press
Vess Technol, ASME 1999;121(3):31522.
14. STR Betten J, Krieger J. Bestimmung des Aushartung-
seinusses bei FVK-Bauteilen mittels FEA. ZAMM
1999;79(S3):8556.
15. STR Binienda WK, Wang Y. Residual stress reductionin lament wound composite tubes. J Reinf Plast
Compos 1999;18(8):684701.
16. STR Blachut J, Jaiswal OR. On the choice of initial
geometric imperfections in externally pressurized
shells. J Press Vess Technol, ASME
1999;121(1):716.
17. STR Burdekin FM, Lidbury DPG. Views of TAGSI on
the current position with regard to benets of warm
prestressing. Int J Press Vess Piping 1999;76(13):885
90.
18. STR Carter P. Stress analysis and design for cyclic
loading. J Press Vess Technol, ASME 2000;122(4);
42730.19. STR Chan WS, Demirhan KC. A simple closed-form
solution of bending stiffness for laminated composite
tubes. J Reinf Plast Compos 2000;19(4):27891.
20. STR Chawla DS, et al. Assessment of operability and
structural integrity of a vertical pump for extreme
loads. Int J Press Vess Piping 1998;75(4):297306.
21. STR Cohn MJ, Yee RK. Creep relaxation behavior of
high energy piping. ASME/JSME Joint Pressure
Vessel Piping Conference PVP 380, New York:
ASME, 1998. p. 13550.
22. STR Cunha J, Piranda J. Identication of stiffness pro-
perties of composite tubes from dynamic tests. Exp
Mech 2000;40(2):2118.
23. STR Da Dilveira JLL, et al. Shakedown and limit
analysis in a pressure vessel. Fourth World Cong
Comput Mech, Buenos Aires, 1998. p. 198.
24. STR Datta TK. Seismic response of buried pipelines:
a state-of-the-art review. Nucl Engng Des 1999;
192(2/3):27184.
25. STR Desikan V, Sethuraman R. Analysis of material
nonlinear problems using pseudo-elastic nite element
method. J Press Vess Technol, ASME
2000;122(4):45761.
26. STR El-Abbasi N, et al. Three-dimensional nite
element analysis of saddle supported pressure vessels.
Int J Mech Sci 2001;43(5):122942.
27. STR Filippov SB, et al. Free vibrations of square elas-
tic tubes with a free end. Mech Res Commun 2000;
27(4):45764.
28. STR Franco JRQ, Barros FB. Advances in nite
element modelling of plastic behaviour of pressurevessels. 4th World Cong Comput Mech, Buenos Aires.
1998. p. 185.
29. STR Frikha S, et al. Boundary condition identication
using condensation and inversionapplication to
operating piping network. J Sound Vib
2000;233(3):495514.
30. STR Fyrileiv O, et al. Free span assessment of the
Zeepipe IIA pipeline. 17th Int Conf Offshore Mech
Arctic Engng. Lisbon: OMAE, 1998. p. 18.
31. STR Goncalves JPM, De Castro PMST. Application of
the line spring model to some complex geometries,
and comparison with three-dimensional results. Int JPress Vess Piping 1999;76(8):55160.
32. STR Hajjar JF, et al. Distributed plasticity model for
concrete-lled steel tube beam-columns with inter-
layer slip. Engng Struct 1998;20(8):66376.
33. STR Halldorsson B. On modeling of earthquake wave
motion and its effects on multi-support pipelines. Acta
Polytech Scand, Civ Engng Build Cons 1999;(115):1
29.
34. STR Hamilton R, et al. A simple upper-bound method
for calculating approximate shakedown loads. J Press
Vess Technol, ASME 1998;120(2):195 9.
35. STR Hari Y, Williams DK. Analysis of transition radii in
conical reducers. ASME/JSME Joint Press Vess PipingConf PVP 360. New York: ASME, 1998. p. 33542.
36. STR Hauch S, Bai Y. Bending moment capacity of
groove corroded pipes. 10th Int Offshore Polar Engng
Conf, Seattle. 2000. p. 25362.
37. STR Hersh CL, Herakovich CT. Local effects in
stiffened composite tubes under generalized plane defor-
mation. J Compos Mater 1999;33(5):42042.
38. STR Hsieh CS, et al. Investigation of anges subjected
to operating conditions of pressure, temperature and
bending moments. ASME/JSME Joint Press VessPiping
Conf PVP 368. New York: ASME, 1998. p. 24557.
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39. STR HsuPW.Stresses in a uniformly paralelepiped solid
with a pressurized cylindrical cavity. 42nd Str, Str Dyn
Mater Conf, Seattle. 2001. p. 294750.
40. STR Hu G, et al. Mechanical behaviour of lament-
wound glass-bre/epoxy-resin tubes. III. Macro-
mechanical model of the macroscopic behaviour of
tubular structures. Compos Sci Technol 1998;58(1):
1929.
41. STR Hyer MW, Riddick JC. Internal pressure loading of
segmented-stiffness composite cylinders. Compos Struct
1999;45(4):31120.
42. STR Jacquelin E, et al. Modelling the behaviour of a
PWR core by a homogenization technique. Comp
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43. STR Jones DP, Holliday JE. Elasticplastic analysis of
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44. STR Jones DP, et al. Application of equivalent elastic
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45. STR Kabir MZ. Computer analysis of lament over-
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51. STR Koerner JP, Hiller W. Elasticplastic nite element
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52. STR Koh BK, Park GJ. Analysis and optimization of
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53. STR Konno K, et al. Study on mechanical property of
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54. STR Kosasayama H, et al. New stress analysisprocedure
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55. STR KristiansenNO,et al.Structural modelling of multi-
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56. STR Kumar R, Saleem MA. Bend angle effect on B2 and
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57. STR Kussmaul K, Mayinger W. Numerical and experi-
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58. STR Lengsfeld M, et al. Spring rates for low type tank
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61. STR Liang CC, et al. Curvature effect on stress concen-
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63. STR Lin CY, Chan WS. Stiffness evaluation of elliptical
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64. STR Liu J, Hirano T. Design and analysis of FRP pres-
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65. STR Lo YL, et al. Pressure vessel wall thinning
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66. STR Loktionov VD, et al. Numerical investigation of
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71. STR Matzen VC, Yu L. Elbow stress indices using
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72. STR McGrath TJ. Replacing E prime with the con-
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73. STR Miki C, et al. Study on seismic resistance of steel
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76. STR Mohan R, et al. A study of effects of pipe geome-try on FAD curves for austenitic stainless steel and
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77. STR Mourad HM, Younan MYA. The effect of model-
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84. STR Muller C, Bohmann A. Numerical simulation of
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85. STR Nadarajah C, Foo LT. Finite element study of
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89. STR Porter MA, Martens DH. Stress evaluation of a
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91. STR Price NM, et al. Vibrations of cylindrical pipes
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93. STR Ramos R, et al. Comparative analysis between
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95. STR Reid SR, Yang JL. Non-linear dynamic analysis
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101. STR Sarma GB, et al. Modeling studies to predict
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102. STR Sattari-Far I, Dahlberg L. Sensitivity study of the
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103. STR Schneider SP. Flexural capacity of pressurized
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104. STR Schneider SP. Axially loaded concrete-lled steel
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105. STR Seay PA, Plaut RH. Three-dimensional behavior
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106. STR Seibi AC, Al-Shabibi AM. Pipe bending and
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108. STR Shalaby MA, Younan MYA. Nonlinear analysis
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111. STR Sherry AH, et al. Application of local approach to
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113. STR Shoji Y, Nagata S. On the modeling of pressurevessel shell portion affecting local deformation at
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115. STR Sinha JK, et al. Parameter identication techni-
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116. STR Skopinsky VN.Stress analysisof shell intersections
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118. STR Skopinsky VN. Stress concentration in cone
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119. STR Takahashi H, et al. Multiple-slip work-hardening
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120. STR Taljat B, et al. Mechanical design of steel tubing
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121. STR Taware A, Brown RH. Dynamic linear nite
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123. STR Tripa VM, et al. On the transfer-matrix method
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124. STR Truong KT. Improved FCCU refractory-lined
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125. STR Tsukimori K. Theoretical modeling of creepbehavior of bellows and some applications. J Press
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126. STR Ukadgaonker VG, Kale PA. Finite element stress
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127. STR Varga L. Design of pressure vessels taking plastic
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128. STR Vitali L, et al. Hotpipe project: capacity of pipes
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130. STR Wada H, Oguchi N. Interaction between double
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132. STR Xu JJ, et al. Local pressure stresses on lateral
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136. STR Yokoyama T. Finite element computation of
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137. STR Yoshizaki K, et al. Large deformation behavior of
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6. STA Bastard AH. New buckle arrestor for reeled pipe-
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7. STA Blachut J, Jaiswal OR. Buckling of imperfect
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9. STA El-Sawy K, Moore ID. Stability of loosely tted
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15. STA Koundy V, et al. Effects of torsional buckling
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20. STA Miles DJ, Calladine CR. Lateral thermal buckling
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21. STA Mou Y, et al. Plastic instability in pressure vessels
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22. STA Netto TA, Kyriakides S. Dynamic performance of
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6. THE Diaz V, et al. Simplied thermo-visco-plastic
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12. THE Igari T, et al. Mechanism-based evaluation of
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