Thermal Stresses of Semi-Infinite Annular Beam: Direct Problem
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1 iol ol o L choloy i Eii M & Alid Scic LEMAS Vol V Fy 8 SSN hl S o Si-ii Al B: Dic Pol Viv Fl M. S. Wh d N. W. hod 3 D o Mhic Godw Uiviy Gdchioli M.S di D o Mhic Svody Mhvidyly Sidwhi M.S di 3 D o Mhic RM N Uiviy N M.S di. Ac- hi i cocd wih dic holic ol i which w d o di h diiio dilc cio d hl o i-iii l wh h ody codiio ow. l o chiq d o oi h olio o h ol. y Wod: Si-iii l holic ol l o dic ol. NRODUCON 968 Oii [] h lihd oo o Body Vl Pol o H Codcio. Vh d hod [] did iv i holic ol o hi l dic. Vh d hod [3] dicd i holic lyi i hi l dic wih diio y odi codiio. Hiw d hod [4] did holic ol o hi l dic d o diio. L d hod [5] divd hl o hi l dic d o illy diid h ly. Wld d hod [6] dicd iv holic ol o hi l dic d o h io. Fh Wld d hod [7] divd hl dlcio o cld l dic d o h io. S d hod [8] divd olio o iv holic ol o h codcio wih il h io i l dic. hod [9] h dvlod holic lyi o hic l dic wih diio codiio. Fh hod [] divd hl dlcio o l dic d o h io. Nvl Wh d hod [] did h d hl o hic l dic d o h io. Ovi Ahd hod d hl [] ivid oi hl o hic l dic d o illy diid h ly. Si d hod [3] dvlod il o hod o iv ol o h codcio wih ow ody o i-iii hollow cylid d i. Pd d hod [4] did i holic ol o Si-ii cicl wih il h oc. hi h d o olv wo dic ol o holiciy. h i dy- ol h d o di h diiio dilc cio d hl o l. h i iid o o h l c o d i d o cvd c i i iid d civly. h cod i ol h d o di h diiio dilc cio d hl o l. h i iid o o h l c o d i d o cvd c i i iid d civly.. SAEMEN OF HE PROBLEM- Coid i-iii l occyi h c D :. h diil qio ovi h dilc cio U [] i U U. wih U = = d =. wh d h Poio io d h li coici o hl xio o h il o h civly d i h o h iyi h diil qio jc o h ody codiio P 78
2 iol ol o L choloy i Eii M & Alid Scic LEMAS Vol V Fy 8 SSN h cio d iv y U.8 U.9 wh i h L co whil ch o h cio d o wihi h i h l o. Eqio. o.9 coi h hicl olio o h ol d coidio.. SOLUON OF HE PROBLEM Alyi Foi i o o h qio d i.6.7 o oi d d wh d d wh do Foi i o o d i i o. h qio 3. i Bl qio who olio iv A B 3.5 wh A B co d odiid Bl cio o i d cod id o od o civly. Alyi h ody codiio 3.3 d 3.4 o h qio 3.5 o oi A A B 3.6 B 3.7 Solvi 3.6 d 3.7 o oi A B Sii h vl o A d B i 3.6 o oi 3.8 Alyi iv Foi i o o h qio 3.8 o oi h xio o h diiio wh i i i d d i d 3.9 V. DEERMNAON OF HERMOELASC DSPLACEMEN FUNCON Sii h vl o o 3.9 i. o oi h holic dilc cio U U i P 79
3 iol ol o L choloy i Eii M & Alid Scic LEMAS Vol V Fy 8 SSN i 4. V. DEERMNAON OF SRESS FUNCONS Ui h qio 4. i.8 d.9 h cio oid S i i i i V. SPECAL CASE Alyi Foi i o o h qio 6. o oi i d i d Sii h vl o d d 6.3 i h qio 3.9 o oi i o 6. i 6.4 V. NUMERCAL RESULS S =3.4 =.5. 5 d i h qio 6.4 o oi i V. SAEMEN OF HE PROBLEM- 7. Coid i-iii l occyi h c D :. h diil qio ovi h dilc cio U [] i U U 8. wih U = = d = 8. wh d h Poio io d h li coici o hl xio o h il o h P 8
4 iol ol o L choloy i Eii M & Alid Scic LEMAS Vol V Fy 8 SSN civly d i h o h iyi h diil qio jc o h iiil codiio h ody codiio h cio d iv y U 8.9 U 8. wh i h L co whil ch o h cio d o wihi h i h l o. Eqio 8. o 8. coi h hicl olio o h ol d coidio. X. SOLUON OF HE PROBLEM Alyi Foi i o o h qio d i o oi d d d d d d wh wh do Foi i o o d i i o. Alyi Llc o o h qio d i h codiio 9. o oi d d q d d wh q wh do Llc o o d i Llc o. Eqio 9.6 i Bl qio who olio iv A q B q 9.9 wh A B co d odiid Bl cio o i d cod id o od o civly. Ui 9.7 d 9.8 i 9.9 o oi A A q B q 9. q B q 9. Solvi 9. d 9. o oi A B q q q q q q q q q q q q q q q q q q q q Sii h vl o A d B i 9.9 o oi q q q q q q q q q q q q q q q q 9. P 8
5 iol ol o L choloy i Eii M & Alid Scic LEMAS Vol V Fy 8 SSN P 8 Alyi iv Llc o o h qio 9. o oi L L 9.3 wh q q q q q q q q 9.4 q q q q q q q q 9.5 o clcl h iv Llc o o 9.4: Alyi iv Llc o o h qio 9.4 o oi d q q q q q q q q i i c i c 9.6 wh c i h h l o h ilii o h i d h id i il vld cio o. h ol o h id h oi wh h oiiv oo o h cdl qio 9.7 h o o q q q q ll l d il. h ol o h id 9.6 = 3 Ui h coo o i iv low h id 9.6 i ql o i i h o h id h ol o h id. o id h id h oi o qi h l: q q q q q q q q q d d q q q q q 9.8 wh q d q q q q h qio 9.8 dc o h o 9.9 Alo q q q q 9. Ui 9.8 d 9. i 9.6 o oi Alyi h d ov o o oi Alyi covolio ho o h qio 9.3 o oi S
6 iol ol o L choloy i Eii M & Alid Scic LEMAS Vol V Fy 8 SSN P 83 d d 9. Alyi iv Foi i o o h qio 9. o oi i d i d 9. wh oiiv i d h oiiv oo o h cdl qio 9.3 d i d d i X. DEERMNAON OF HERMOELASC DSPLACEMEN Sii h vl o o 9. i 8. o oi h holic dilc cio U i U d i d. X. DEERMNAON OF SRESS FUNCONS Ui. i 8.9 d 8. h cio oid i d i d.
7 iol ol o L choloy i Eii M & Alid Scic LEMAS Vol V Fy 8 SSN P 84 i d i d. X. SPECAL CASE S. Alyi Foi i o o h qio. o oi d. d d.3 wh i oiiv i. Sii h vl o d o. d.3 i h qio 9. o oi i d i d.4 X. NUMERCAL RESUL S =.5 =.5 d = c d h oo o h cdl qio [3] i.4 o oi i d
8 iol ol o L choloy i Eii M & Alid Scic LEMAS Vol V Fy 8 SSN XV. CONCLUSON oh h ol h diiio dilc cio d hl o l hv divd. h Foi i o d Llc o chiq d o oi h icl l. h l h oid c lid o h di o l c o chi i ii licio. Ay icl c o cil i c divd y ii il vl o h d cio i h xio. REFERENCES []. N. M. Oii. Body Vl Pol o H Codcio iol xoo Coy Sco Pylvi 968 [].. W. hod; V. Vh d N.W. hod A iv i holic ol o hi l dic Al. Mh. E-No [3]. V. Vh d N. W. hod i holic lyi i hi l dic wih diio y odi codiio iol ol o P d Alid Mhic vol. 4 No [4]. Pyl Hiw d N.W. hod holic ol o hi l dic d o diio. ol o P d Al. Mh Vol. 7 No [5]. N.. L d N.W. hod hl o hi l dic d o illy diid h ly. ol o L d i Mh Vol. No..8- [6]. R.. Wld d N. W. hod v holic ol o hi l dic d o h io Cdi ol o Scic d E. Mhic Rch Vol. 3 No [7]. R.. Wld d N.W. hod hl dlcio o cld l dic d o h io. ol o L d i Mh Vol. No.. -3 [8]. C. S. S d N.W. hod Solio o iv holic ol o h codcio wih il h io i l dic. ol o Mhic Rch Vol. 5 No [9]. N.W. hod holic lyi o hic l dic wih diio codiio.. o E. Ad oio choloy vol []. N.W. hod hl dlcio o l dic d o h io.. o E. Ad oio choloy vol []. A. Nvl; M. S. Wh d N. W. hod H d hl o hic l dic d o h io. E Vol []. Ovi A. Ahd; N. W. hod d L. H. hl Oi hl o hic l dic d o illy diid h ly E Vol [3]. S. S. Si d N. W. hod l o hod o iv ol o h codcio wih ow ody o i-iii hollow cylid d i LEMAS Vol [4]. R. N. Pd d N. W. hod i holic ol o i-ii cicl wih il h oc LEMAS Vol P 85
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