finite element method analysis of pipe …thermalscience.vinca.rs/pdfs/2011-1/tsci1101081b.pdffinite...

FINITE ELEMENT METHOD ANALYSIS OF PIPE MATERIAL TEMPERATURE CHANGES INFLUENCE ON LINE EXPANSION LOOPS

IN HYDRAULIC INSTALLATIONS ON MODERN TANKERS

by

Andrzej BANASZEK a*, Radovan PETROVI] b, and Bartlomiej ZYLINSKI c

a Fac ulty of Mar i time Tech nol ogy, West Pom er a nian Uni ver sity of Tech nol ogy, Szczecin, Po landb Fac ulty of Me chan i cal En gi neer ing Kraljevo, Uni ver sity of Kragujevac, Ser bia

c Strata Ma rine & Off shore AS, Oslo, Nor way

Orig i nal sci en tific pa perUDC: 673.6:620.16:66.011

DOI: 10.2298/TSCI1101081B

Fi nite el e ment method anal y sis of main lines of hy drau lic cen tral load ing sys tem in -stal la tion ex pan sion loops mounted on prod uct and chem i cal tank ers has been pre -sented in the pa per. The ax ial forces prob lem in in stal la tions mounted along theship’s open decks ex e cuted from hull de for ma tions on waves and ther mal stresses is given. Use of “U” type ex pan sion loops is de scribed. Re sults of forces in an chorpoints and stresses of Mises due to ex pan sion loop de for ma tions are shown. Cal cu -la tions were made by ABAQUS Ver.6.7 FEM com puter pro gram.

Key words: expansion loops, hydraulic installation, anchor points, Missesstresses, finite element method analysis, product and chemical tanker

In tro duc tion

Prod uct and chem i cal tank ers are ships in tended to the trans port of dan ger ous, pe tro -leum-based liq uid car goes and chem i cals (see fig. 1). There fore many types of pipes are in -stalled on decks of the prod uct and chem i cal tank ers as ships in tended to the sea car riage of liq -uid car goes. One of the most im por tant in stal la tions are hy drau lic in stal la tions of cen tralsup ply ing sys tems, in tended to the drive hy drau lic sub merged cargo pumps [1-5]. Work ing con -di tions un der which these hy drau lic in stal la tions are ex ploited at sea are ex tremely dif fi cult.This is the re sult of spec i fic ity of prev a lent cir cum stances on board of sea-go ing ves sels. One ofthe most im por tant prob lems is in flu ence of changes of the am bi ent tem per a ture, changes of thede gree of so lar ra di a tion, and tem per a tures of transfluent hy drau lic oil on stresses and ten sionsin pipes of hy drau lic in stal la tions.

It takes root that the change of the length of the line is pro por tional to the change of thetem per a ture of line ma te rial [6]:

l l TL= +0 1( )a D (1)

Banaszek, A., et al.: Finite Element Method Analysis of Pipe Material Temperature ...

THERMAL SCIENCE: Year 2011, Vol. 15, No. 1, pp. 81-90 81

* Corresponding author; e-mail: [email protected]

where l is the length of the line af ter the tem per a ture rise of pipe ma te rial, l0 – start length of theline, DT – tem per a ture rise of pipe ma te rial, and aL – co ef fi cient of lin ear ex pan sion of pipe ma -te rial.

In tab. 1 are pre sented val ues of the lin ear ex pan sion co ef fi cient for ma te ri als most of -ten used un der con struc tion of the hy drau lic drives in stal la tion on ships.

Equa tion (1) can be pre sented in folowing form, show ing the elon ga tion value of pipe -line af ter the tem per a ture rise of pipe ma te rial:

dx l l l TL= - =0 0a D (2)

In case of fixed two ends ofpipe line and lack of ex pan sionloops (com pen sa tors) in in stal-laton struc ture above elon ga tioncan leads, ac cord ing to Hook’s tofollowng ax ial type stresses inpipe line:

dxl

El TL= =

sa0

0 D (3)

s a= =Ex

lE TL

d

0

D (4)

where s is the ten sile stress inpipe line, dx – the elon ga tion of


82 THERMAL SCIENCE: Year 2011, Vol. 15, No. 1, pp. 81-90

Ta ble 1. Val ues of lin ear ex pan sion co ef fi cients forcho sen pipe ma te ri als

Name of ma te rialThe co ef fi cient of lin ear

ex pan sion aL, [K–1]

Car bon steel St37.0 16.0×10–6

Stain less steel AISI 304 16.0×10–6

Stain less steel AISI 316 17.3×10–6

Cop per 16.6×10–6

Iron 11.0×10–6

Inwar 1.0×10–6

Source: The Vademecum of hydraulics,Vol. 3, Mannesmann Rexroth [7]

Figure 1. Product tanker B573-I/1 class m/t “Engen Rainbow”, built by Shipyard SzczecinskaS. A., Poland, for the ship-owner Unicorn Tankers from Republic of South Africa

pipe line de ter mined by tem per a ture rise of pipe ma te rial, and E – Young’s modulus of pipe ma -te rial.

Nor mal length of main lines of hy drau lic cen tral load ing sys tems, mounted on board of mod ern prod uct and chem i cal tank ers can reach 150 m. Sys tem can be ex ploited from tem per a -ture (in win ter) 253 K, and temprerature of hy drau lic oil can reach 343 K [8].

There fore, this sit u a tion can cre ated, ac cord ing to eq. (4), dan ger ous high, ax ial stressin hy drau lic pipes. One of the ways to avoid de scribed prob lems is the as sem bly of line ex pan -sion com pen sa tions of the “U” type. The lack of above men tioned com pen sa tions in case of ap -pear ing of ax ial ten sions can lead to burst ing and lack of hy drau lic lines tight ness. Ac ci dentswith de scribed prob lems were no ticed on board of many ships, es pe cially tank ers, to ex am ple on prod uct tank ers B560 type m/t “Boris” and “Anatoli” (Li be ria), dur ing sea tri als. Com pen sa torsof “U” type in hy drau lics are most of ten used. It is re sult of ex pe ri ences at sea, dur ing ex ploi ta -tions on ships, be cause they are the most safe. Other type com pen sa tors, with flex i ble el e ments(i. e. hoses), mem bra nous, follicular, very of ten dam aged in hard sea at mo sphere or are notenought strength on high pres sure oil in side (300 bar). There fore com pen sa tors “U” ex e cuteddi rectly from own pipe ma te rial are so pop u lar in ex e cu tion of high pres sure hy drau lics in ship -build ing. Ex pan sion loops, with other shape, as to ex am ple “V” type, are not ex ploited in prac -tice. It is re sult of prob lems with hy drau lic pipe bend ing. In hy drau lics are strictly al lowed only“cold” type bend ing pro ce dure. In case of pipe bend ing with de gree big ger than 90 de gree, atrel a tive big pipe thick ness refering to pipe di am e ter (to ex am ple size of pipe Æ130 ́ 13), cre ateprob lems with re duc tion of ma te rial thick ness, break ing or fold ing in pape, in bend ing area.There fore “V” type ex pan sion loops, or equiv a lent, are not used in prac tice on ships.

The above events are un prof it able for the ship owner be cause they can cause dam agesof hy drau lic drive sys tems and en vi ron men tal pol lu tion by leak ing of hy drau lic oil. This can re -sult in heavy fi nan cial pen al ties pay ments, es pe cially when the event takes place di rectly in theport. De scribed prob lem is im por tant not only from prac tice, but from scientistic side too. In sci -en tist lit er a ture is lack of pub li ca tions re fer ring to cal cu la tions of ex pan sion loops in high pres -sure hy drau lic sys tems, es pe cially mounted on ships. Some pa pers de scribed fi nite el e mentmethod (FEM) ana lyse of pipes mounted in low pres sure in stal la tions, es pe cially in heat sys -tems (Koorey [9], Fedorov, [10], Jo., et al. [11], etc.). Mahmood, et al. [12] are shown study ofper for mance lim i ta tion in mi cro heat pipes with diammeter to only 3 mm. Next au thors con cen -trated on anal y sis of ther mal efects in sim ple straight pipes (i. e. Rajeev et al. [13], Madenci, etal. [14], Deng Zhi-Wei, [1-6, 9]). Im por tant anal y sis of fas ten ing of pipes was pre sented byVakharia, et al. [15]. Lack of same pub li ca tions in area of high pres sure oil hy drau lic sys tems,re quired own ana lyse of prob lems, es pe cially re fer ring to forces in an chor points and stressescre ated dur ing ac tiv ity of ex pan sion loops as re sult of pipe line squeez ing de for ma tions.

As re sult of these in ves ti ga tions, the FEM anal y sis of ex pan sion loops “U” type,mounted on hy drau lic in stal la tions of cen tral load ing sys tems on mod ern prod uct and chem i caltank ers, has been pre sented in the pa per. Re sults of above men tioned cal cu la tions were used inShip yard Szczecinska S. A. in prac tice.

Idea of line ex pan sion loops “U” type

As al ready men tioned in the in tro duc tion, in or der to avoid burst ing of pipe in stal la -tions mounted along the ship’s open deck it is nec es sary to in stall suit able quan tity of line ex -pan sion com pen sa tors. In gen eral, com pen sa tors of follicular or pipe-slid ing types are used in



low-pres sure ship’s in stal la tions. Be cause of the lim ited range of pres sures they can not be usedin hy drau lic sys tems. There fore the com pen sa tors used in main lines of hy drau lic cen tral load -ing sys tems or other hy drau lic in stal la tions mounted along ship’s open decks are pipe ex pan sion loops “U” type. The idea of above men tioned com pen sa tors is pre sented in fig. 2.

The com pen sa tors are prop erly bent pipe inthe shape of the “U” al pha bet-let ter. Ifpostaxial forces ap pear in the in stal la tion, thiskind of com pen sa tor is prop erly de formed. Itsshape makes easy this type of de for ma tion andlim its the height of ten sions in the re main ingpart of pip ing in stal la tion. For the high pres -sure main line with size of 130 ´ 13 mm fromthe hy drau lic cen tral load ing sys tem, stan darddi men sions of the ex pan sion loops are given intab. 2.

Pre sented (in tab. 2) line ex pan sion loops, made of car bon steel St52.4 (see tab. 3) were in stalled on board of prod uct tanker B578-I/1 m/t “He lix” built by Szczecinska S. A. Ship yardfor the Shell ship-owner from Aus tra lia. Main pres sure line P Æ 130 ́ 13 mm was a main sup ply hy drau lic line for the team of cargo pumps equipped into hy drau lic drive [1, 2, 4]. The over alllength of the ship was 183 m and above men tioned hy drau lic line was in stalled along the wholeopen deck, from the su per struc ture to the bow.

For the as sess ment of cor rect ness of hy drau lic in stal la tion de sign and ex e cu tion onboard are used fol low ing criteria:(a) Line strength criterion – whether the tightness of the installation is kept at the test pressure,



Figure 2. Geometry of line expansion loops“U” type [8, 16]

Ta ble 2. Di men sions of stan dard ex pan sion loop “U” type for high pres surehy drau lic pipe P Æ 130 ´ 13 mm

Nom i naldi am e ter

Pipe sizedz ´ g[mm]

Ma te rialMax.work ing

presure[MPa]

Bend ing ra dius,Rg

[mm]

Di men sion,e

[mm]

Di men sion,f

[mm]

110 Æ 130.0 ´ 13.0 St52.4 32.0 325 1500 1400

Source: [8, 16]

Ta ble 3. Me chan i cal prop er ties of car bon steel St52.4/DIN 1630

Steelsym bol

Ma te rialNr/DINstan dard

Stretch en dur ance (min.) [MPa]

Rm

Yield strength(min.) [MPa]

Rp0.2

Elon ga tion atbreak ing (min.) [%]

A5

En dur ance co ef fi cientK [MPa] acc, instr. AD

W4 at temperature20 °C

Car bon steel St52.4

1.05811630

490 350 21 355

Source: Vademecum of hydraulics, Vol. 3, Mannesmann Rexroth [7]

(b) Correctness of pipe holders criterion – whether lines under external mechanical loads (fromhull vibrations, knocks of the wind, etc.) and internal mechanical loads (from turbulence oftransfluent medium – hydraulic oil) pipes do not fall in excessive mechanical vibrations,especially the resonance type, and

(c) Criterion of the resistance of lines on longitudinal extensions – whether sufficient quantity of expansion loops are installed and whether they are correctly situated so that in the case ofline extensions appearing in the installation:– forces generated in anchor points of the installation will not exceed limited values (given

by the maker), and– stresses in the pipe installation and expansion loops will not exceed limited values.

Pipe in stal la tion strength and cor rect ness of pipe hold ers are checked by in spec tors ofin ter na tional classi fi ca tory so ci et ies in the ship yard ac cord ing to So ci et ies Rules.

The great est dif fi culty is de sign of line ex pan sion loops sys tem in or der to ful fill thelast cri te rion. Gen er ally speak ing, there are not enough pro ce dures and reg u la tions in the de signpro cess, es pe cially the ones re lated to ship ping-hy drau lic in stal la tions.

Nu mer i cal anal y sis, re sults, and dis cus sion

The pip ing in stal la tion mounted on board of ship’s deck must be fas tened to the deckcon struc tion (see re quire ments [17]). As a rule, places, called an chor points of the pip ing in stal -la tion, are sit u ated next to the ex pan sion com pen sa tors. Namely, in case of ax ial forces in the in -stal la tion, an chor points lock ing the ax ial pipes move and ac ti vate the tak ing over of de for ma -tions and stresses in in stal la tion by the ex pan sion loop. At lon ger in stal la tion, an chor pointspre vent con cen trat ing all postaxial forces on one com pen sa tor only, spread ing them in pro por -tion to all re main ing com pen sa tors mounted along all in stal la tions. The struc ture of the an chorpoints are com par a tively straight. It con sists of the plate brack ets welded di rectly to the pipe line and the elas tic el e ments (rub ber) fas tened to the foun da tion con struc tion – see fig. 3.

With tak ing over pe riod of the ax ial re ac tion forces by an an chor point, the de gree ofthe de for ma tion of the ex pan sion loop grows up as well as the pres sure on the elas tic el e mentmounted in the an chor point. An aim of the anal y sis is de ter mi na tion of the ex pan sion loop elas -tic ity char ac ter is tics i. e. de pend en cies be tween the value of re ac tion forces gen er ated on one



Figure 3. Constructions of anchor points of hydraulic lines [8](a) construction of the horizontal type anchor points; (b) construction of the vertical type anchor points

end of the com pen sa tor (in the an chor point) and the value of the free ax ial de for ma tion on theother end. A row of the mag ni tudes has the in flu ence on the value of the above men tioned func -tion:– mechanical properties of material whence the expansion loop is executed,– size of the pipe diameter and its thickness,– expansion loop dimensions, and– values of hydraulic oil pressure inside the line.

In FEM anal y sis model, the right end of loop was fas tened by pin type el e ment [18].Si mul ta neously left end of loop was free (see model in fig. 5). As signed loop de for ma tion dx[mm] are given on the left end. The anal y sis of de for ma tions and gen er ated forces in the pin fas -

ten ing of the com pen sa tor was ex e cuted innu meric way by means of FEM sys tem. Cal -cu la tions were ex e cuted with the uti li za tionof the com puter sys tem ABAQUS Ver. 6.7[18] by means of FEM 3-D el e ment S4Rtype. This is the el e ment of the space type,with 9 nodes and 45 de grees of the free dom(see fig. 4). This el e ment is well suit able tomod el ing of shell struc tures, pipes, and in -stal la tions in cluded. Cal cu la tion re sults ofthe an chor forces gen er ated in the right endof the loop are given in tab. 4. For de ter mi -na tion of the oil pres sure in flu ence on thevalue of the an chor point forces, cal cu la -tions were ex e cuted at tak ing into ac countand with out tak ing into ac count in side pres -sures of hy drau lic oil. An a lyzed ex pan sionloop re mains as the re sil ient el e ment withthe lin ear char ac ter is tic (see fig. 6). This is a big ad van tage of this type of ex pan sioncom pen sa tors. It may ex plain why an a lyzed



Figure 4. Model of FEM element 3-D ShellS4 type used in the FEM analysisSource: User’s Manual ABAQUS Ver. 6.7 [18, 19]

Ta ble 4. Re sults of FEM cal cu la tions of an chor forces FA in ex pan sion loop at com pres sion dx

Di men sions of ex pan sion loop “U” type

dx3-D FEM el e ment S4R type

Pres sure in side 0 MPa 3-D FEM el e ment S4R type

Pres sure in side 32 MPa

PipeÆ 130 ´ 13 mmL = 2550 mmRg = 325 mm

[mm] [N] [N]

5 5096 6794

10 10180 11900

15 15252 17000

20 20312 22100

25 25360 27200

30 30395 32300

com pen sa tors are so of ten used in the ship build -ing area and in other in dus try branches. Nu mer -i cal cal cu la tions are ver i fied by ex per i men talmea sure ments ex e cuted in the work shopFramo/Nor way [15]. If oil pres sure is taken intoac count or if it is skipped, there are not large er -rors, not cross ing the level of 10%.

In ad di tion to cal cu la tions of the an chorforces cal cu la tions of stresses in the ex pan sionloops were also car ried out. In tab. 5 re sults ofcal cu la tions of max i mum Huber-Mises stressessHM are pre sented. Cal cu la tions were per -formed in the loop un der con struc tive de for ma -tions, with and with out tak ing into ac count thehy drau lic oil pres sure. Re ceived de pend en ciesare pre sented in fig. 8. An a lyzed de pend ence ofmax i mum value Huber-Mises stresses in theloop from size of de for ma tion dx has also a lin -ear char ac ter and is strongly re lated to val ues ofin side oil pres sure. There fore if oil pres sure isnot taken into ac count in Huber-Mises anal y sis,there are large er rors un like the an chor forcecal cu la tions. Max i mum val ues of Huber-Misesstresses in an a lyzed loops were sit u ated inplaces of bends (see fig. 7).

Re sults and dis cus sion

In this pa per we used “U” type ex pan sionloops be cause this type con nec tions (fixed with -



Figure 5. Digitalization of analyzed expansionloop by means of FEM-3-D element ShellS4 type

Figure 6. Dependence of the anchor forces values FA from the dx deformation in expansion loopÆ 130 ´ 13 mm

Ta ble 5. Re sults of max i mum value of Huber-Mises stress sHM cal cu la tions of the ex pan sionloop Æ 130 ´ 13 mm size at dx squeez ing de for ma tion

Di men sions of ex pan sion loop “U” type

dx3-D FEM el e ment S4R type

Pres sure in side 0 [MPa] 3-D FEM el e ment S4R type

Pres sure in side 32 [MPa]

Pipe130 ´ 13 mmL = 2550 mmRg = 325 mm

[mm] [MPa] [MPa]

5 39.7 179.0

10 79.5 213.7

15 119.3 246.5

20 159.1 284.7

25 198.8 321.4

30 238,6 358.5

out flex i ble foses or euivalent) are the mostsafe, other com pen sa tions very of ten bro ken inex ploi ta tion time on board of tank ers or are notsuf fi cient on oil high pres sure in side (300 bar).

The “V” type ex pan sion loops are NOT used in our area be cause is big prob lem with bend ing.Please re mem ber that maximum an gle in case of bend ing pipes is 90 de gree. It is im -

por tant in big pipes as my main lines with size di am e ter 130 mm + thick ness 13 mm. In prep a ra -tion of cold bend ing (with out heat ing – this is trickly re quired for hy drau lics) of pipes, in case ofbend ing with an gle > 90 de gree is prob lem with break ing of ma te rial pipes and re duc tion of ma -te rial thick ness in pipe in bend ing area in out side of pipe. There fore “V” type ex pan sion loopsare not used in prac tice on ships.

Sci en tific im por tance of this work is high be cause wrong prep a ra tion of hy drau lic in -stal la tions on board of tank ers can lead to break ing of hy drau lic pipes and a big pol lu tion of seaand wa ter in har bours, also prob lems with trans ship ment op er a tions on tank ers.

Strictly ther mal stress are not to im por tant be cause stresses from mech a nisms of me -chan i cal work of com pen sa tions and stresses from high oil pres sure in side are a lot big ger. Tem -per a ture rise causes on pipes ma te rial elon ga tions and prob lems con nect with this phe nom ena.

Con clu sions

Long main pipe lines of the hy drau lic cen tral load ing sys tems mounted on mod ernprod uct and chem i cal tank ers are sen si tive to ther mal stresses and ther mal elon ga tions. It can of -ten cause break ing of pipes and dam age of very ex pen sive hy drau lic sys tem. In or der to avoidex ces sive stresses in these in stal la tions it is nec es sary to mount suit able ex pan sion com pen sa -tors. Ex pan sion loops of “U” type are very of ten used in hy drau lic sys tems. The quan tity of com -pen sa tors nec es sary to in stall on board the ship is re lated to the row of fac tors, as among otherthings, max i mum changes of the pipe ma te rial tem per a ture as re sult of am bi ent and transfluenthy drau lic oil tem per a ture (the size of de for ma tions the hull on the wave in cluded). So far prac ti -cal ap prox i ma tion meth ods for cal cu la tions and pro ce dures have of ten made large er rors and in -flat ing of the quan tity of nec es sary com pen sa tors in the ar range ment. FEM nu mer i cal cal cu la -tions with the uti li za tion of shell fi nite el e ments pro vide more ex act de ter mi na tion of forceval ues gen er ated in an chor points of the in stal la tion and max i mum stresses in the mo ment of de -



Fig ure 8. Con cen tra tions of Huber-Mises stressessHM in the ex pan sion loop un der squeez ing de for ma tions (color im age see on our web site)

Figure 7. Dependence of the maximumHuber-Mises stresses values sHM from the dx squeezing deformation in expansion loop Æ 130 ´ 13 mm

for ma tions. It al lows safer and more eco nom i cal de sign of the hy drau lic in stal la tion mounted ondecks of mod ern prod uct and chem i cal tank ers. In Huber-Mises stress anal y sis in hy drau licpipes, should be taken into ac count in cal cu la tion model, the oil pres sure in side pipes. Lack ofthis, can leads to large er rors dur ing max i mum stress cal cu la tions.

Ref er ences

[1] Banaszek, A., Cen tral Hy drau lic Load ing Sys tems Used on Board Prod uct and Chem i cal Tank ers (in Pol -ish), Hydraulika i Pneumatyka, (2003), 4, pp. 13-17

[2] Banaszek, A., Big Power Cen tral Hy drau lic Load ing Sys tems on Board Prod uct and Chem i cal Tank ers,Pro ceed ings, 19th In ter na tional Con fer ence Hy drau lics and Pneu mat ics, Prague, Czech Re pub lic, 2006,pp. 52-59

[3] Banaszek, A., Petrovic, R., Cal cu la tions of the Un load ing Op er a tion in Liq uid Cargo Ser vice with HighDen sity on Mod ern Prod uct and Chem i cal Tank ers Equipped with Hy drau lic Sub merged Cargo Pumps,Strojniski Vestnik, 56 (2010), 3, pp. 186-194

[4] Banaszek, A., The Con cept of Cen tral Hy drau lic Load ing Sys tem on Board Prod uct and Chem i cal Tank -ers, Pro ceed ings, 1st In ter na tional Con fer ence Ship Ma chines and Equip ment Op er a tion, Swinoujscie--Ystad – Co pen ha gen 2003, Sci en tific Books of Mar i time Acad emy Nr. 68, Szczecin, Po land, 2003,pp.19-28

[5] Banaszek, A., The Con cept of Ca pac ity Con trol of Sub merged Cargo Pumps in Liq uid Car goes Trans portat Sea, Pol ish Acad emy of Sci ences, Branch in Gdansk, Ma rine Tech nol ogy Trans ac tions, 16 (2005), pp.25-32

[6] Deng, Z.-W., Anal y sis on the Op er a tional Con di tions and Ma te rial Re quire ments of the Pres sure Pipe,Pipe line Tech nique and Equip ment, 4 (2009), 6, pp.173-184

[7] ***, Mannesmann Rexroth GmbH, Vademecum of Hy drau lics, 3, De sign and Struc ture of Hy drau lic Sys -tems, Mannesmann Rexroth Verlag (Pol ish edi tion), RPL 00281/10.88, Lohra, Main, Ger many 1992 (inPol ish)

[8] ***, Stocznia Szczecinska SA, Tech no log i cal Doc u men ta tion B578-I /542-1 (Fac tory In side Ma te ri als)(in Pol ish), Szczecin, Po land, 1997

[9] Koorey, K., De ter mi na tion of Op ti mal Pipe Sup port Span for Geo ther mal Pipe lines, Pro ceed ings, WorldGeo ther mal Con gress, Kyushu-Tohoku, Ja pan, 2000, pp. 1361-1364

[10] Fedorov, M., Ther mal Modes Sim u la tion of Heat Exchangers Net works Hav ing Turbo-Ma chines, Pro -ceed ings, 4th In ter na tional Con fer ence on Ma rine Tech nol ogy, Wes sex In sti tute of Tech nol ogy, UK, WITpress, Southampton-Boston, 2001, pp. 309-314



No men cla ture

A5 – elongation at breaking (min.), [%]dx – horizontal squeezing deformation of

– expansion loop [mm]dz – outside pipe diameter, [mm] E – Young’s modulus of pipe material, [MPa]e, f – characteristic dimensions of expansion

– loop, [mm]FA – force in anchor point, [N]g – pipe wall thickness, [mm]K – endurance coefficient at temp. 20 °C acc,

– instr. AD W4, [MPa]L – total length of expansion loop, [mm]l – length of the line after the temperature

– rise of pipe material, [m]l0 – start length of the line, [m]n1 – normal axis of FEM element

Rg – bending radius, [mm]Rp0.2 – yield strength (min.), [MPa]Rm – stretch endurance (min.), [MPa]DT – temperature rise of pipe material, [K]u1, u2, u3 – possible axial movements in node of

– Shell type FEM elementur4, ur5 – possible rotations in node of shell type

– FEM element

Greek let ters

aL – coefficient of linear expansion of pipe– material, [K–1]

h, x, z – local axes in FEM element of shell types – temsile stress in pipeline, [MPa]sHM – maximum Huber-Mises stress, [MPa]

[11] Jo, J. C., Choi, J. H., Choi, S. K., Nu mer i cal Anal y sis of Unstady Con ju gate Heat Trans fer and Ther malStress for a Curved Pip ing Sys tem Sub jected to Ther mal Strat i fi ca tion, Jour nal of Pres sure Ves sel Tech -nol ogy, 125 (2003) 4, pp. 467-475

[12] Mahmood, L., Akhanda, Md. A. R., Ex per i men tal Study on the Per for mance Lim i ta tion of Mi cro HeatPipes of Non Cir cu lar Cross-Sec tions, Ther mal Sci ence, 12 (2008), 3, pp. 91-102

[13] Rajeev, T., et al., A Nu mer i cal Study for In ward So lid i fi ca tion of a Liq uid Con tained in Cy lin dri cal andSpher i cal Ves sel, Ther mal Sci ence, 14 (2010), 2, pp. 365-372

[14] Madenci, E., Guven, I., The Fi nite El e ment Method and Ap pli ca tions in En gi neer ing Us ing ANSYS,Springer Sci ence+Busi ness Me dia LLC, New York, USA, 2006

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[16] ***, Framo Ser vices AS Op er a tion of FRAMO Cargo Pumps, Ser vice Bul le tin No. 10, Bergen, Nor way,1993

[17] ***, Stauff – Clamps, Cat a logue , Wal ter Stauffenberg Gmbh, Werdhol, Ger many, 2000[18] ***, Hobbit, Karlsson, Soersen, Inc. ABAQUS ver.6.7 User’s Man ual, Pawtucket, USA, 2006[19] Zylisnki, B., Fi nite El e ment Lo cal Anal y sis of Wave Slam ming on Off shore Struc ture, Pol ish Mar i time

Re search,18 (2009), 1, pp. 8-12

Paper submitted: June 1, 2010Paper revised: September 16, 2010Paper accepted: September 29, 2010



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