OPTIMUM THICKNESS OF THREE-LAYER SHRINK FITTED COMPOUND CYLINDER FOR UNIFORM STRESS DISTRIBUTION

Transcription

1 Intenatonal Jounal of Avances n ngneeng & Technology, May 0. IJAT ISSN: -96 OTIMM THICKNSS OF THR-LAYR SHRINK FITTD COMOND CYLINDR FOR NIFORM STRSS DISTRIBTION Ayub A. Maje an Sunl A. atl Dept. of Mech. ng, MIT College of ngneeng, une, INDIA Dept. of Mech. ng, Snhga Insttute of Technology & Scence, une, INDIA ABSTRACT Ths pape ntouces the optmum esgn fo mnmzaton of thckness of thee-laye shnk-ftte compoun cylne to get equal maxmum hoop stesses n all the cylnes. In the shnk-fttng poblems, conseng long hollow cylnes, the plane stan hypothess can be egae as moe natual. Geneally, hoop stess stbuton acoss the wall of thck cylne s non-lnea n natue fom nne to oute aus of the cylne. The stesses euce shaply towas the oute aus. Mateal s not utlze popely gvng unnecessay moe thckness. Hence two o moe cylnes can be compoune by shnkage pocess whee oute cylne s heate untl t wll sle feely ove nne cylne thus exetng the eque contact pessue on coolng. As a esult of shnkng, stess estbuton occus acoss the wall of the compoun cylne an euces the hoop stess an makes t moe o less unfom ove the thckness. In ths pape effot s mae to fn optmum mnmum thcknesses of thee cylnes so that mateal volume s euce an hoop stess s equal n all the cylnes. The analytcal esults of optmum esgn calculate wth compute pogammng ae valate n compason wth Fnte lement Analyss n ANSYS Wokbench. Both the esults agee wth each othe. Hence ths methoology can be apple fo eal-wol mechancal applcatons of mult-laye compoun cylnes. KYWORDS: Resual Stess, Contact (Shnkage essue, Mult-laye Cylne, Optmum Thckness I. INTRODCTION Multlaye compoun cylnes ae wely use n the fel of hgh pessue technology such as hyaulc pesses, fogng pesses, powe plants, gas stoages, chemcal an nuclea plants, mltay applcatons etc. To enhance loa beang capacty an lfe of multlaye pessue vessels, ffeent pocesses such as shnk ft an autofettage ae usually employe. Shnk ft nceases loa capacty. Many eseaches have focuse on methos to exten lfetmes of vessels. Majzoob et al. have popose the optmzaton of b-metal compoun cylnes an mnmze the weght of compoun cylne fo a specfc pessue []. The vaables wee shnkage aus an shnkage toleance. atl S. A. has ntouce optmum esgn of two laye compoun cylne an optmze ntemeate, oute amete an shnkage toleance to get mnmum volume of two laye compoun cylnes [- ]. Ham Jahe et al. have nvestgate the optmum esgn of a thee-layee vessel fo maxmum fatgue lfe expectancy une the combne effects of autofettage an shnk ft []. Maje Ayub A. an atl Sunl A. have foun mnmum volume of thee-laye open type compoun cylne conseng plane stess hypothess [5]. Yang Qu-Mng et al. have pesente a smple an vsual tool to calculate the esual stess an escbe the stbuton of esual stess fo both the elastcpefectly plastc moel an the stan-haenng moe [6]. To ncease the pessue capacty of thck-walle cylnes, two o moe cylnes (mult-laye ae shunk nto each othe wth ffeent ametc ffeences to fom compoun cylne. In thee-laye compoun cylne the usual pactce s to shnk the oute cylne on to the ntemeate cylne an then shnk the esultng compoun cylne on to the nne cylne as shown n fgue. 59 Vol., Issue, pp

2 Intenatonal Jounal of Avances n ngneeng & Technology, May 0. IJAT ISSN: -96 Fgue. Thee Laye Compoun Cylne When the oute cylne contacts on coolng the nne cylne s bought nto a state of compesson. The oute cylne wll convesely be bought nto a state of tenson. If ths compoun cylne s now subjecte to ntenal pessue the esultant hoop stesses wll be the algebac sum of those esultng fom ntenal pessue an those esultng fom shnkage, thus a much smalle total fluctuaton of hoop stess s obtane. Desgne usually face the poblem of etemnng maxmum hoop stess o maxmum wokng stess to whch shunk-ft cylne s subjecte, the magntue of shnkage pessue o any combnaton. The esgn of shunk-ft cylnes s much smplfe f each cylne s consee as a sepaate cylne subjecte smultaneously to the shnkage pessue an the wokng pessue. Manufactung an assembly pocess of such cylnes of eal-wol applcatons ntouces some esual stesses. These esual stesses can be summe up wth hoop stess evelope ue to ntenal pessue to fn maxmum hoop stess n all the cylnes. The pape s oganze as follows: We have explane Lame s theoy as apple to compoun cylne n secton.optmum thckness methoology fo compoun cylne an analytcal esults n secton. Valaton usng FM an ANSYS esults n secton. Dscusson n secton 5 followe by Concluson n secton 6. II. LAM S THORY ALID TO COMOND CYLINDR a Cylne b Cylne c Cylne Fgue. Raal an hoop stess stbuton n thee sepaate cylnes 59 Vol., Issue, pp

3 Intenatonal Jounal of Avances n ngneeng & Technology, May 0. IJAT ISSN: -96 Fgue. Intefeence between cylne & Fgue. Intefeence between cylne & Nomenclatue Intenal pessue actng on the cylne o xtenal pessue on the cylne θ Hoop stess n the cylne Raal stess n the cylne z Longtunal (Axal stess n the cylne Inne aus of cylne Oute aus of cylne an Inne aus of cylne Oute aus of cylne an Inne aus of cylne Oute aus of cylne s Contact pessue between cylne an s Contact pessue between cylne an ε θo Hoop stan n the oute wall of cylne o Raal splacement at oute wall of cylne ε θ Hoop stan n the nne wall of cylne Raal splacement at nne wall of cylne δ Total ntefeence at the contact between cylne an ε θ o Hoop stan n the oute wall of cylne o Raal splacement at oute wall of cylne ε θ Hoop stan n the nne wall of cylne Raal splacement at nne wall of cylne δ Total ntefeence at the contact between cylne an ν osson s ato t / t t / Conse thee cylnes have same mateal. The metho of soluton fo compoun cylnes constucte fom smla mateals s to beak the poblem own nto fou sepaate effects: shnkage pessue s only on the cylne shnkage pessue s an s only on the cylne shnkage pessue s only on the cylne v ntenal pessue only on the complete cylne Thus fo each conton the hoop an aal stesses at any aus can be evaluate. 59 Vol., Issue, pp

4 Intenatonal Jounal of Avances n ngneeng & Technology, May 0. IJAT ISSN: -96. Raal an Hoop Stess n Cylne If = 0. e. no ntenal pessue, aal stess n cylne s gven by usng Lame s equaton = s ( s maxmum at oute aus of cylne. sng equaton ( = ( ( max at s Hoop stess n cylne s gven by usng Lame s equaton θ = s + Hoop stess at oute aus s + θ ( at = s Whle hoop stess at nne aus s s θ max ( at = (5 In the shnk-fttng poblems, conseng long hollow cylnes, the plane stan hypothess geneal, z 0 can be egae as moe natual. Hence as pe the elaton = ν + ( z θ the expesson fo the hoop stan s gven by + ν εθ = [ θ ν ν z ] = θ ν ν ( θ [( ν θ ν ] + =. sng equatons ( an (, assumng plane stan conton the hoop stan at the oute wall of cylne s + ν + ν + o εθ o = [( ν θ ν ] = ( ν s ( ν s = (6 Raal splacement o s s ( + ν ( + o = ν ν (7. Raal an Hoop Stess n Cylne Contact pessue s s actng as ntenal pessue an contact pessue s s actng as extenal pessue on cylne. sng Lame s equaton, aal stess n the cylne at nne aus s gven by = (8 ( at s Whle aal stess n the cylne at oute aus s gven by = (9 ( at s Hoop stess n the cylne at nne aus s gven by ( + ( s s θ max ( = at Whle hoop stess n the cylne at oute aus s gven by s ( s ( + θ ( at = ( sng equatons (8 an (0, assumng plane stan conton the hoop stan at the nne wall of cylne s ( ( (0 (n 59 Vol., Issue, pp

5 Intenatonal Jounal of Avances n ngneeng & Technology, May 0. IJAT ISSN: -96 ε + + = = ( ν + ν s θ [( ν θ ν ] ( ν s ( ν s = Raal splacement ( + ν + s = s ( ν + ν ( ν Refeng fgue an usng equatons (7 an (, total ntefeence cylne an s δ = o = ( ν ( ν ( ( δ at the contact between ν ν s s s ( ν ( ν ν ( ν + + = s + s sng equatons (9 an (, hoop stan n the oute wall of cylne s gven by + ν + ν s ( s ( + o εθ o = [( ν θ ν ] = ( ν ( ν s = (5 Hence aal splacement o ( ν s + o s ( ν ( ν ( = + ν (6. Raal an Hoop Stess n Cylne Contact pessue s s actng as ntenal pessue on cylne an extenal pessue o s zeo. Raal stess n the cylne at nne aus s gven by = (7 ( at s Hoop stess n the cylne at nne aus s gven by ( + s θ max( at = Whle hoop stess n the cylne at oute aus s gven by ( = s θ ( at sng equatons (7 an (8, hoop stan at nne wall of cylne s gven by ε + ν + ν s θ = [( ν θ ν ] ( ν ν ( s = (8 (9 ( + = (0 Raal splacement s ( + ν ( + = ν + ν ( Refeng fgue an usng equatons (6 an (, total ntefeence δ at the contact between cylne an δ = o ( ( s ν + s ν + = ( ν s ( ν ( ν + + ν + ν 595 Vol., Issue, pp

6 Intenatonal Jounal of Avances n ngneeng & Technology, May 0. IJAT ISSN: -96 ( ν + + s = s + ( Hoop stess at any aus n compoun cylne ue to ntenal pessue only s gven by θ = + (. ncple of Supeposton Afte fnng hoop stesses at all the a, the pncple of supeposton s apple,.e. the vaous stesses ae then combne algebacally to pouce the esultant hoop stesses n the compoun cylne subjecte to both shnkage pessues an ntenal pessue... Resultant hoop stess n Cylne a Hoop stess ue to b Resual stess ue to s (c Resultant stess θ Fgue 5. Supeposton of hoop stess ue to & esual stess ue to s n cylne sng equatons ( an (5, maxmum hoop stess at the nne sufaces of cylne at + θ = s (.. Resultant hoop stess n Cylne a Hoop stess ue to b Resual stess ue to s & s (c Resultant stess θ Fgue 6. Supeposton of hoop stess ue to & esual stess ue to s & s n cylne sng equatons ( an (0, maxmum hoop stess at the nne sufaces of cylne at 596 Vol., Issue, pp

7 Intenatonal Jounal of Avances n ngneeng & Technology, May 0. IJAT ISSN: ( + s s θ = + (5.. Resultant hoop stess n Cylne a Hoop stess ue to b Resual stess ue to s (c Resultant stess θ Fgue 7. Supeposton of hoop stess ue to & esual stess ue to s n cylne sng equatons (8 an (, maxmum hoop stess at the nne sufaces of cylne at + + θ = + s.. Resultant hoop stess n Compoun Cylne (6 a Hoop stess ue to b Resual stess ue to s & s (c Resultant Hoop stess Fgue 8. Supeposton of hoop stess ue to & esual stesses ue to s & s n all cylnes III. MTHODOLOGY OF OTIMM THICKNSS FOR COMOND CYLINDR To obtan optmum values of the contact (shnkage pessues s an s whch wll pouce equal hoop (tensle stesses n all the thee cylnes, maxmum hoop stesses gven by the equatons (, (5 an (6 have been equate. quatng equatons ( an (5. e. = an eaangng, θ s + = + s θ Let the atos t = =, t = =, t = = (8 (7 597 Vol., Issue, pp

8 Intenatonal Jounal of Avances n ngneeng & Technology, May 0. IJAT ISSN: -96 Whee,,, ae ametes coesponng to a,,,. Hence tt. = =, tt = =, tt t =. = Let + t t + k = (9 + = + t t + + t t t + t t + k = = (0 t t t t t t t k = ( = t Hence equaton (7 becomes [ k / ] [ / ] = k + k k ( s s quatng equatons (5 an (6. e. = an eaangng, θ θ + ( + ( + + s = + s + ( ( ( Let + t + k = = ( t k ( + ( + t + t t + ( ( 5 = = t t t t t t (5 k + t + t 6 = + = + t t Hence equaton ( becomes [ / ] [ / ] = k k + k k (7 s 5 s 6 quatons ( an (6 have been solve to get s an s n tems of as follows, ( k5 / k6 ( k / k ( k / k6 ( k / k ( k5 / k ( k / k ( k / k ( k / k s = s = 6 uttng the values of t, t an t, the equatons ( an ( can be wtten as ( ν + + t t t δ = s + s t t t ( ν t t + + s δ = s + t t t. Analytcal Metho Fo the gven volume of flu to be stoe, the ntenal amete of cylne ( s known. Hee t s assume as 00 mm. Mateal fo all the thee cylnes s assume as same. e. steel. Yel stength of the steel mateal s = 50 Ma. Maxmum hoop stess s majo stess whch s esponsble fo y falue of cylne. Maxmum pncpal stesses n all the cylnes (hee t s maxmum hoop stess shoul not excee the yel stess of the mateal to avo the falue of the compoun cylne. Optmum mateal volume (assumng unt length can be calculate usng followng steps. (6 (8 (9 (0 ( 598 Vol., Issue, pp

9 Intenatonal Jounal of Avances n ngneeng & Technology, May 0. IJAT ISSN: -96. Assume ntenal amete of cylne ( say 00 mm.. Select the atos t = =, t = =, t = =. Fo the gven ntenal pessue, one can fn contact (shnkage pessues s an s n tems of atos t, t an t.. Fn the volume of the compoun cylne usng Fx = π.( / 5. Mnmze the volume subjecte to the constants, θ <= y θ <= y θ <= y v δ > 0 v δ > 0 6. Optmze paametes t, t, t ae use fo the esgn. In compute pogammng, the values of t, t an t ae selecte fom. to. wth the ncement of 0.0, 0.05 an efne up to Thus wth lot of combnatons of t, t & t mateal volume s foun. A numbe of combnatons of t, t an t satsfy the conton of equal maxmum hoop stesses n all thee cylnes whch s less than yel stess of the mateal. Out of these combnatons some mpotant combnatons ae pesente n ths pape fo compason. Howeve thee s one unque combnaton whee volume s mnmum. In pogammng, equatons (8 an (9 ae use to fn contact (shnkage pessues s an s fo gven ntenal pessue esp. Also equatons (0 an ( ae use to fn ntefeences δ, δ esp. These ntefeences ae late use n secton fo moelng n Fnte lement Metho. Assgn values to, y, an. Algothm of Compute ogam Fo ( t.0 to. wth ncement of 0.0 Fo ( t.0 to. wth ncement of 0.0 Fo ( t.0 to. wth ncement of 0.0 { Calculate k, k, k, k, k5an k 6 n tems of t, t, t. Calculate s an s n tems of k, k, k, k, k5an k 6. Calculate δ an δ n tems of s, s an k, k, k, k, k 5, k 6. Calculate maxmum hoop stesses θ, θ, θ Check the contons θ <= y, θ y Calculate the volume n tems of an t, <= <= an θ y Fx = π.( / Compae new calculate volume wth pevous one. }// n of loops fo t, t an t nt the paameteze values an Mnmum Volume".. Analytcal Results Results fom compute pogammng ae lste n table an. t, t Table. Dametes an atos of ametes an Volume fo compoun cylne (assumng = 00 mm Combnaton t Fx Table. Maxmum hoop stess, contact pessue an ntefeence fo compoun cylne Combnaton θ θ θ s s δ δ Vol., Issue, pp

10 Intenatonal Jounal of Avances n ngneeng & Technology, May 0. IJAT ISSN: The mnmum volume of thee-laye compoun cylne s mm coesponng to values n combnaton whee atos t =.85, t =.05, t =.5. Hence optmum thckness of cylne s 8.5 mm, cylne s 9. mm an cylne s 5.5 mm. IV. VALIDATION SING FM AND ANSYS RSLTS sng optmze paametes t, t, t fom the combnaton set numbe of the table an takng = 00 mm emanng ametes,, ae calculate as follows. = t x = 8.5mm, = t x = 67.7mm, = t x =.mm. The optmze values of δ, δ ae aus base. These values ae ouble to take ametc effect n the thee mensonal Fnte lement Moel. sng these values, nne amete of cylne ( an nne amete of cylne ( fo shnk ft ae calculate as shown n table. Table. Data fo moelng n ANSYS (fo combnaton set numbe t t t δ δ whee, = nne & oute ametes of cylne espectvely., = nne & oute ametes of cylne espectvely fo shnk ft., = nne & oute ametes of cylne espectvely fo shnk ft. sng the values of δ, δ shnk ft s apple between cylnes & an between cylnes & espectvely n ANSYS Wokbench. Contact between cylnes & as well as between cylnes & s apple usng contact tool n ANSYS Wokbench. Smlaly, ata fo moelng s pepae fo combnaton set numbes as well as an moelng s one n ANSYS Wokbench. Fgue 9. Thee Laye Compoun Cylne Fgue 0. Fnte lement Mesh 600 Vol., Issue, pp

11 Intenatonal Jounal of Avances n ngneeng & Technology, May 0. IJAT ISSN: -96 Fgue. Shnk ft between cylne & Fgue. Shnk ft between cylne & Results by ANSYS Wokbench fo set numbe ae shown n the fgues to 7. COMBINATION ST ( t =.70, t =.90, t =.60 Fgue. Maxmum ncpal Stess n cylne Fgue. Maxmum ncpal Stess n cylne Fgue 5. Maxmum ncpal Stess n cylne 60 Vol., Issue, pp

12 Intenatonal Jounal of Avances n ngneeng & Technology, May 0. IJAT ISSN: -96 Fgue 6. Contact pessue between cylne & Fgue 7. Contact pessue between cylne & s = 9.50 Ma (Avg ( wthout s = 0.0 Ma (Avg ( wthout Results by ANSYS Wokbench fo set numbe ae shown n the fgues 8 to. COMBINATION ST ( t =.85, t =.05, t =.5 Fgue 8. Maxmum ncpal Stess n cylne Fgue 9. Maxmum ncpal Stess n cylne Fgue 0. Maxmum ncpal Stess n cylne 60 Vol., Issue, pp

13 Intenatonal Jounal of Avances n ngneeng & Technology, May 0. IJAT ISSN: -96 Fgue. Contact pessue between cylne & Fgue. Contact pessue between cylne & s =.58 Ma (Avg (wthout s = 9.00 Ma (Avg ( wthout Results by ANSYS Wokbench fo set numbe ae shown n the fgues to 7. COMBINATION ST ( t =.70, t =.8, t =.8 Fgue. Maxmum ncpal Stess n cylne Fgue. Maxmum ncpal Stess n cylne Fgue 5. Maxmum ncpal Stess n cylne 60 Vol., Issue, pp

14 Intenatonal Jounal of Avances n ngneeng & Technology, May 0. IJAT ISSN: -96 Fgue 6. Contact pessue between cylne & Fgue 7. Contact pessue between cylne & s =.6 Ma (Avg ( wthout s = 9.0 Ma (Avg ( wthout V. DISCSSION Analytcal esults an FM (ANSYS esults ae summaze n Table an 5. VI. Table. Compason of hoop stesses by Analytcal an ANSYS esults Maxmum hoop Maxmum hoop stess Maxmum hoop Combnatons Results stess n cylne n cylne θ ( stess n cylne θ ( Ma Ma θ (Ma Analytcal ANSYS Analytcal ANSYS Analytcal ANSYS Table 5. Compason of contact pessues by Analytcal an ANSYS esults Combnatons Results Contact pessue between cylne & Contact pessue between cylne & ( Ma ( Ma CONCLSION s Analytcal ANSYS Analytcal ANSYS Analytcal ANSYS Fom the tables an 5 t s clea that the ffeence n analytcal an ANSYS Softwae esults s wthn acceptable lmts. Ths ffeence s ue to numecal technques of Fnte lement Metho n ANSYS. Snce analytcal esults ae valate by FM calculatons, the esgn methoology popose n ths pape can be successfully apple nto the eal-wol mechancal applcatons fo mnmzng the mateal volume of mult-layee compoun cylnes to assue best utlzaton of mateal. atl S. A. [-] has foun mnmum volume of two laye compoun cylnes as mm (fo ntenal amete = 00 mm an steel mateal wth yel stength = 50 Ma. Maje Ayub A. an atl Sunl A. [5] have foun mnmum volume of thee-laye open type compoun cylne as mm conseng plane stess hypothess. In compason wth ths, plane stan hypothess gave mnmum volume as mm (as pe combnaton set whch s qute sgnfcant to save the mateal. Accongly optmum thckness of cylne s 8.5 mm, optmum thckness of cylne s 60 Vol., Issue, pp

15 Intenatonal Jounal of Avances n ngneeng & Technology, May 0. IJAT ISSN: -96 s 9. mm an optmum thckness of cylne s 5.5 mm. Hence t can be conclue that plane stan hypothess gves bette esults to fn optmum thcknesses of long hollow compoun cylnes. ACKNOWLDGMNT The autho s gateful to the Management, xecutve Decto, ncpal, Hea-Depatment of Mechancal ngneeng of MIT College of ngneeng, une, Ina fo tme to tme encouagement an suppot n cayng out ths eseach wok. RFRNCS [] Majzoob G.H. & Ghom A., (006 Optmzaton of compoun pessue cylnes, Jounal of Achevements n Mateals an Manufactung ngneeng, Vol. 5, Issue - Mach-Apl. [] atl Sunl A., (005 Optmum Desgn of compoun cylne use fo stong pessuze flu, ASM Intenatonal Mechancal ngneeng Congess an xposton (oceeng of IMC05, Nov 5-,005,Olano, Floa SA. [] atl Sunl A., (0 Fnte lement Analyss of optmze compoun cylne, Jounal of Mechancal ngneeng Reseach, Vol. (, Issue Mach. [] Jahe Ham, Fash Behooz & Kam Mova, (006 Optmum Autofettage & Shnk-Ft Combnaton n Mult-Laye Cylnes, Jounal of essue Vessel Technology, Tansactons of the ASM, pp , Vol. 8, MAY 006. [5] Maje Ayub A., atl Sunl A.,(0 Mnmzaton of mateal volume of thee laye compoun cylne havng same mateals subjecte to ntenal pessue, Intenatonal Jounal of ngneeng, Scence an Technology, Vol., No. 8, 0, pp [6] Yang Qu-Mng, Lee Young-Shn, Lee un-yup, Km Jae-Hoon, Cha K-p an Hong Suk-Kyun, (009 A esual stess analyss pogam usng a Matlab GI on an autofettage compoun cylne, Jounal of Mechancal Scence an Technology, Vol., pp [7] Lee un-yup, Lee Young-Shn, Yang Qu-Mng, Km Jae-Hoon, Cha K-p an Hong Suk-Kyun, (009 Autofettage pocess analyss of a compoun cylne base on the elastc-pefectly plastc an stan haenng stess-stan cuve, Jounal of Mechancal Scence an Technology, (009, pp. 5~60. [8] ak Jae-Hyun, Lee Young-Shn, Km Jae-Hoon, Cha K-p & Hong Suk-Kyun, (008 Machnng effect of the autofettage compoun cylne une vayng ovestan levels, Jounal of Mateals ocessng Technology, pp [9] Toback W. (007 Numecal stength an fatgue analyss n applcaton to hyaulc cylnes, Jounal of Achevements n Mateals an Manufactung ngneeng, Vol. 5 Issue, Decembe 007. [0] Hojjat M.H. & Hassan A., (007 Theoetcal an fnte-element moelng of autofettage pocess n stan-haenng thck-walle cylnes, Intenatonal Jounal of essue Vessels an png, 8 ( [] Gbson Mchael C. (008 Detemnaton of Resual Stess Dstbutons n Autofettage Thck- Walle Cylnes, h. D. Thess, Canfel nvesty, Defense College of Management an Technology nte Kngom, Apl 008. Bogaphy Ayub A. Maje s a Assstant ofesso n the Depatment of Mechancal ngneeng at M I T College of ngneeng, une, Ina. He has 7 yeas of teachng expeence an yea of nustal expeence. He has to hs cet 0 papes n Intenatonal an Natonal Confeences. Hs eseach nteests nclue esgn optmzaton, fnte element analyss, compute ae esgn an manufactung. He s a Lfe Membe of IST (Ina. Sunl A. atl s a ofesso n the Depatment of Mechancal ngneeng at Snhga Insttute of Technology an Scence, une, Ina. He has 0 yeas of nustal expeence an 7 yeas of teachng expeence. He has to hs cet papes n Intenatonal Confeences an papes n Intenatonal Jounals. Hs eseach nteests nclue compute ae esgn an manufactung, Robotcs, computatonal flu ynamcs, esgn optmzaton. 605 Vol., Issue, pp