Inverse Thermoelastic Problem of Semi-Infinite Circular Beam

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1 iol oul o L choloy i Eii M & Alid Scic LEMAS Volu V u Fbuy 8 SSN v holic Pobl o Si-ii Cicul B Shlu D Bi M. S. Wbh d N. W. Khobd 3 D o Mhic Godw Uiviy Gdchioli M.S di D o Mhic Svody Mhvidyly Sidwhi M.S di 3 D o Mhic RM Nu Uiviy Nu M.S di Abc- hi i cocd wih iv holic obl i which w d o di h u diibuio dilc ucio d hl o i-iii cicul b wh h boudy codiio ow. l o chiqu ud o obi h oluio o h obl. Ky Wod: Si-iii cicul b holic obl l o. NRODUCON 957 Nowci [] udid h o i hic cicul l du o u ild. Roychudhi [] dicud h qui-ic i hi cicul l du o i u lid lo h cicuc o cicl ov h u c Whd [3] udid h quiic hl i cicul l. Gh; Khl d Khobd [4] udid hl S i A hic Cicul Pl Wih l H Souc. Ghu; Mhl d Khobd [5] divd holic oluio o hi cicul l du o illy diibud h uly. H Pv d Khobd [6] dicud hl S O A hic Cicul Pl Du o H Gio. Khobd; Khl; Gh d Ph [7] udid i ho lic Pobl o Cicul Pl Wih H Gio. Khobd [8] ivid hl o hi cicul l wih il h ouc. Fuh Khobd [9] dicud holic lyi o hic cicul l. Lb d Khobd [] dvlod Alyicl hl S Alyi i hi cicul l du o diicl coio. Nod; Hi d iw [] ublihd boo o hl S cod diio. Vh d Khobd [] divd Aliv Soluio o i H Coducio i Cicul Pl wih Rdiio. hi h b d o olv wo iv obl o holiciy. h i dy- obl h b d o di h uow u dilc d ucio o h ou cuvd uc o hi cicul b occuyi h c D : wih hooou boudy codiio o h hid id iid o o h l uc o hi cicul l. h cod udy- obl h b d o di h uow u dilc d ucio o h ou cuvd uc o cicul b occuyi h c D : wih hooou boudy codiio o h hid id iid o o h l uc o cicul b.. SAEMEN OF HE PROBLEM- Coid cicul b occuyi h c D :. h diil quio ovi h dilc ucio U [] i U U. wih U = =. wh d h Poio io d h li coici o hl xio o h il o h b d i h u o h b iyi h diil quio ubjc o h boudy codiio.3 uow.4 h iio codiio i P 9

2 iol oul o L choloy i Eii M & Alid Scic LEMAS Volu V u Fbuy 8 SSN < < ow.7 wh d h diio co o h wo l uc. h ucio d iv by U.8 U.9 wh i h L co whil ch o h ucio o wihi h b i h l o. Equio. o.9 coiu h hicl oulio o h obl ud coidio.. SOLUON OF HE PROBLEM Alyi Foui coi o o h quio d ui.5.6 o obi d d wh d d wh do Foui coi o o d i Foui coi o. Equio 3. i Bl quio who oluio iv = A + B K 3.4 wh A B co d K odiid Bl ucio o i d cod id o od o civly. A K bu by hyicl coidio i ii. ho B u b o. Ui 3.3 i 3.4 o obi A B = Subiui h vlu o A d B i 3.4 o obi 3.5 Ui h codiio 3. o h oluio 3.5 o obi 3.6 Alyi v Foui coi o o h quio 3.5 d 3.6 o obi h xio o h u diibuio d uow u di wh co 3.7 co 3.8 co d Equio 3.7 d 3.8 h did oluio o h iv obl. V. DEERMNAON OF HERMOELASC DSPLACEMEN Subiui h vlu o o 3.7 i. o obi h holic dilc ucio U U co 4. V. DEERMNAON OF SRESS FUNCONS Ui 6.3. i 6..8 d 6..9 h ucio obid S co co V. SPECAL CASE P

3 iol oul o L choloy i Eii M & Alid Scic LEMAS Volu V u Fbuy 8 SSN Alyi Foui coi o o h quio 6. o obi co d / 4 6. Subiui h vlu o o 6. i h quio 3.7 d 3.8 o obi 6.3 / 4 co 6.4 S V. NUMERCAL RESUL = =.5 i 6.4 o obi / 4 co.5 V. SAEMEN OF HE PROBLEM- 7. Coid i-iii cicul b occuyi h c D :. h diil quio ovi h dilc ucio U [] i U U 8. wih U = = 8. wh d h Poio io d h li coici o hl xio o h il o h b d i h u o h b iyi h diil quio ubjc o h iiil codiio h boudy codiio uow 8.5 h iio codiio i < < ow 8.8 wh i h hl diuiviy o h il o h cicul b. h ucio d iv by U 8.9 U 8. wh i h L co whil ch o h ucio d o wihi h dic i h l o. Equio 8. o 8. coiu h hicl oulio o h obl ud coidio. X. SOLUON OF HE PROBLEM Alyi Foui coi o o h quio d ui o obi d d d d d d wh wh do Foui coi o o d i Foui coi o. Alyi Llc o o h quio d ui 9. o obi P

4 iol oul o L choloy i Eii M & Alid Scic LEMAS Volu V u Fbuy 8 SSN d d q d d wh q q Ui..4 i 9.3 o obi q q ci i ci d 9.4 o vlu h coou il 9.4 o obv h h id i il vlud ucio o o h o y u o h coou how i h iu. wh do Llc o o d i Llc o. Equio 9.5 i Bl quio who oluio iv = A q + B K q 9.9 wh A B co d K odiid Bl ucio o i d cod id o od o civly. A K q bu by hyicl coidio i ii. ho B u b o. Ui 9.8 i 9.9 o obi A q B = Subiui h vlu o A d B i 9.9 o obi q q 9. q q 9. Alyi iv-llc o o h quio 9. o obi * q L q 9. * * o vlu L [ ] wh * q 9.3 q h ol o h id h oi [ ] = 3 wh h oo o h cdl quio 9.5 Fo h hoy o Bl ucio i i ow h h oo o h quio 9.5 ll l d il. By i h diu o h cicl LMN o b / h will b o ol o h id o h cicuc o cicl d o h yoic xio o h odiid Bl ucio q q h il oud h cicul LMN d o. O y ho lc h li il o h ucio o h col coou. Hc o c lc i by h u o h idu o h ucio q / q i h l R < c. Now h idu o hi ucio h ol = i Li = Li Li P

5 iol oul o L choloy i Eii M & Alid Scic LEMAS Volu V u Fbuy 8 SSN P 3 = i i i W hv i i Hc h vlu o i 9.4 i obid 9.6 By lyi h covoluio ho h quio 9. iv d 9.7 Alo by ui h ul 9.6h quio 9.3 iv d 9.8 Alyi iv Foui coi o o h quio 9.7 d 9.8 o obi h xio o h u diibuio d uow u di co d 9.9 co d 9. wh oiiv i h oiiv oo o h quio. X. DEERMNAON OF HERMOELASC DSPLACEMEN Subiui h vlu o o 9.9 i 8. o obi h holic dilc ucio U co U d. X. DEERMNAON OF SRESS FUNCONS Ui. i 8.9 d 8. h ucio obid co 4 d. co 4 d. X. SPECAL CASE S. Alyi Foui coi o o h quio. o obi

6 iol oul o L choloy i Eii M & Alid Scic LEMAS Volu V u Fbuy 8 SSN / 4 co d. Subiui h vlu o o. i h quio 9.7 d 9.8 o obi S co / 4 co d.3 / 4 X. NUMERCAL RESUL d.4 = =.5 = c =.86 d h oo o h cdl quio [3] i.4 o obi co.5 / 4.86 d 3. XV. CONCLUSON boh h obl h u diibuio uow u di dilc ucio d hl hv b divd wih h hl o Foui coi o d Llc o chiqu. h ul h obid c b lid o h di o uul ucu o chi i ii licio. Ay icul c o cil i c b divd by ii uibl vlu o h d ucio i h xio. REFERENCES []. W. Nowci h o i hic cicul l du o u ild. Bull. Acd. Polo. Sci. S. ch []. K. Roychudhi A o o h qui-ic i hi cicul l du o i u lid lo h cicuc o cicl ov h u c Bull. Acd. Sci. S. ch [3]. P. C. Whd O h qui-ic hl i cicul l di. o Pu d Al. Mh [4]... Gh; L. H. Khl d N. W. Khobd hl i hic cicul l wih il h ouc oul o Siic d Mhic Vol. 3 u [5]. R. S. Ghu; Ahwii Mhl d N. W. Khobd holic oluio o hi cicul l du o illy diibud h uly.. o E. Ad oio choloy vol. 3 u [6]. H Pv d N. W. Khobd hl o hic cicul l du o h io Cdi oul o Scic d E. Mhic Rch Vol. 3 No [7]. N. W. Khobd; L. H. Khl;.. Gh d A. C. Ph i ho lic obl o cicul l wih h io.. o E. Ad oviv choloy vol. 3 u [8]. N. W. Khobd hl o hi cicul l wih il h ouc.. o E. Ad oio choloy vol. 3 u [9]. N. W. Khobd holic lyi o hic cicul l.. o E. Ad oviv choloy vol. 3 u []. N. K. Lb d N. W. Khobd Alyicl hl lyi i hi cicul l du o diicl coio. oul o L d i Mh Vol. No []. N Nod; R. B. Hi d Y. iw hl S cod diio ylo & Fci Nw Yo 3. []. V. Vh d N. W. Khobd Aliv oluio o i h coducio i cicul l wih diio. oul o Al. Mh. vol. No [3]. N. M. Oii: Boudy Vlu Pobl o H Coducio.iol x Boo Co. Sco Pylvi P 4

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