Yan-Lin Lu, Guo-Bin Zhou, Hong Jia, Jian-Fang Huang The MOE Key Laboratory of Mechanical Manufacture and Automation, China

Transcription

1 AEA-CN-55-03P RAPD DETERMNATON OF HSTORES OF SF DSTRBUTONS ALONG 3-D CRAC FRONTS OF RP SUBJECTED TO PTS BY UNERSAL WEGHT FUNCTON AND FNTE ARATON METHOD Yan-Ln Lu, Guo-Bn Zhou, Hong Ja, Jan-Fang Huang The MOE ey Laboraory of Mehanal Manufaure and Auomaon, Chna Emal addre of man auhor: Abra A varaonal negral expreon for he 3-D unveral wegh funon (UWF) mehod for Mode n an orop ela body propoed. The UWF mehod an be ued for effenly numerally deermnng he hore of SF drbuon along 3-D rak fron of a RP ubeed o boh mehanal and hermal loadng n preurzed hermal hok (PTS). The mulple vrual rak exenon (MCE) mehod, whh wa propoed by auhor o olve he 3-D hermal WF equaon, exended o a more general form, he fne varaon mehod (FM). A new proedure baed on he elf-oneny ondon of he FM wa alo nrodued for onvenenly and araely exrang he referene SF drbuon along 3-D rak fron. Example how very hgh effeny and good aray. eyword: fne varaon mehod; re neny faor; unveral wegh funon mehod; preurzed hermal hok.. nroduon The 3-D hermal wegh funon (TWF) mehod [-4] exended o a more general form, unveral wegh funon (UWF) mehod, whh an be ued for effenly numerally deermnng he hore of SF drbuon along 3-D rak fron of a RP ubeed o boh mehanal and hermal loadng n preurzed hermal hok (PTS). One he UWF for a pef rak and body geomery deermned, he SF for ha raked body ubeed o any loadng (hermal and mehanal load) an mply be allaed hrough negraon of he produ of he UWF and load. The repeaed deermnaon of he drbuon of re (or dplaemen) feld for ndvdual load and me nan are avoded n he UWF heme. The amoun of ompuaon an hu be grealy redued. A varaonal negral expreon of he ba equaon for he 3-D UWF mehod for Mode n an orop ela body propoed. The mulple vrual rak exenon (MCE) mehod, whh wa propoed by auhor o numerally olve he 3-D TWF equaon, exended o a more general form for olvng he ba equaon n he 3- D UWF heme, whh wll be renamed a fne varaon mehod (FM) from mahemaal meanng. A new proedure baed on he elf-oneny ondon of he FM wa alo nrodued for onvenenly and araely exrang he referene SF drbuonalong 3-D rak fron. From he vewpon of energy balane along

2 AEA-CN-55-03P rak fron, he SF drbuon exraed by h proedure ould be regarded a he mo aepable and arae numeral emaon orrepondng o he rren fne elemen drezaon of he body. 2. araonal negral expreon of he ba equaon of UWF mehod for Mode rak problem A varaonal negral expreon of he ba equaon for he 3-D UWF mehod for Mode n an orop ela body propoed. 2 * * * a( ) d = d u d + f d Γ H u E + * * Θ Θ α d n ( α ) d - 2ν Here he noaon (L) denoe he fr order varaon n he quany (L), vewed a a funon of rak poon and ome oher varable, when only he rak poon vared. 3. Fne varaon mehod The varaon (vrual rak exenon, CE) derbed by an nfnemal rak fron advane varaon a = a( ) along he whole rak fron Γ. Fne varaon mode are nrodued for olvng he UWF equaon. 0 0 a = ω ( ) a, a = g( ) a ( =,2, L, N) Here, g() he normalzed exenon funon for derbng he drbuon of he vrual rak fron advane, he eleed haraer varaon meaure for a he haraer rak lengh a. The funon ω () hould have loal propere. n he mean whle, fne lnearly ndependen peal eleed hape funon are nrodued for he drezaon of unknown SF. = Ψ N =, Ψ = Aω ( ) (3) Here, A are ome unknown oeffen and ω () are eleed hape funon for nerpolaon. The hape funon ω () an be equal o or dfferen from ω (). Fnally, a yem of lnear equaon obaned. N N 2 2 A ω ( ) [ ] ω ( ) g( ) d = H = { * a d u u * d + a f * a d +, ( =,2, L, N) (4) E * * [ α d ( α ) d ]} a 2ν Θ n a Θ - a Solvng h yem of equaon and from nerpolaon of unknown, he SF drbuon along rak fron an be deermned. 4. Self-oneny and deermnaon of SF drbuon for referene loadng 2

3 AEA-CN-55-03P We an onvenenly exra arae emaon of by onderaon of he elfoneny ondon of he FM. The ba equaon of UWF mehod (Eq. ) hold for any load ondon wh Mode. For he referene load elf, =. f a oare approxmae emaon of (or even a onan a all loaon) were ued n Eq., he arae emaon of referene SF drbuon hould be = 5. Numeral example Fg. how a fne elemen model of a nozzle orner rak problem for a RP. Fg.2 how he omparon of SF of he referene loadng (nner preure and orrepondng end load), J beng exraed from he ommeral MSC/MARC program by he J-negral mehod, COD beng exraed from he COD mehod [5,6] and FM beng exraed from he preen FM by onderaon of he elfoneny ondon. The dfferene for J, COD and FM are le han 5%. Fg.3 how he omparon of SF for a mehanal load (he rak fae loadng). The dfferene for 2J, 2COD and 2FM are le han 4%. Fg.4 how he varaon of ranen SF drbuon along he rak fron of a emellpal urfae rak n a plae ubeed o hermal hok. The dfferene beween FM and COD mehod a mo loaon are le han %. The maxmum dfferene are 2% - 2.5% orred only a 2φ/π= near he urfae pon C. Fg.5 how he varaon of ranen SF drbuon along rak fron of an axal em-ellpal urfae rak n a RP ubeed o PTS, allaed by he UWF heme. The reul are well onen wh hoe obaned by He and ozak (2000) hrough dre FEM. of very hgh effeny and of good aray. 6. Conluon By ung of he UWF heme and he numeral ehnque of FM, he hore of SF drbuon along 3-D rak fron of a RP ubeed o PTS an be deermned effenly and araely. praal o analyze h problem n deal. n he preen heme, he SF oluon of referene loadng an be drely deermned by ung of he elf-oneny ondon of he UWF heme (and program) elf, he prelmnary knowng abou whh no neeary. Example how very hgh effeny and good aray. Aknowledgemen Th work wa uppored by he Naonal Naural Sene Foundaon of Chna under Gran No Referene [] Lu, Y.-L., Lu, H., Ja, H., Yu, Z.-Q., (200). Fne elemen mplemenaon of hermal wegh funon mehod for allang ranen SF of a body ubeed o hermal hok, nernaonal Journal of Fraure, 08, [2] Lu, Y.-L., Zhang S.-J., Huang, X.-P. and Huang J., (2003). Deermnaon of hore of SF drbuon for axal em-ellpal urfae rak n hollow (5) 3

4 AEA-CN-55-03P ylnder ubeed o hermal hok, nernaonal Journal of Preure eel & Ppng, 80, [3] Lu, Y.-L., Huang, X.-P., Lu, C.-D. and Weng X.-H., (2004a). A novel ehnque for deermnaon of hore of SF drbuon along 3-D rak fron of a body ubeed o hermal hok, nernaonal Journal for Numeral Mehod n Engneerng, 60, [4] Lu, Y.-L., Huang, X.-P., Jang X.-F., and Zhang S.-J., (2004b). Rapd deermnaon of hore of SF drbuon along 3-D rak fron of a plae ubeed o hermal hok, Engneerng Fraure Mehan, 7, [5] Lu, Y.-L., (996). A praal proedure for evaluang SF along fron of emellpal urfae rak a weld oe n omplex re feld. nernaonal Journal of Fague, 8, [6] Lu, Y.-L., (997). Drbuon of SF for ymmeral par-ellpal and emellpal urfae rak n plae ubeed o rak fae hear loadng, nernaonal Journal of Fague, 9, [7] He, Y., and ozak, T., (2000). Fraure mehan analy and evaluaon for he RP of he Chnee Qnhan 300 MW NPP under PTS, Nulear Engneerng and Degn, 20, Fg.. FE meh of a nozzle orner rak problem of a RP FG.2. Comparon of SF for referene loadng. for a mehanal loadng. FG.3. Comparon of SF FG.4. Hore of hermal SF drbuon durng a hermal hok 4

5 AEA-CN-55-03P Fg.5. Hore of SF drbuon for an axal em-ellpal urfae rak n a RP ubeed o PTS 5