1 Gii thiu1.1 C hc mi trng lin tc

Ni dung ca nhng tng c hc nhm nghin cu v cc chuyn ng v cc lc i vi cc cht rn, cht lng, cc loi kh v s bin dng hoc dng chy i vi cc vt liu ny. Trong mt nghin cu nh vy, chng ti a ra cc gi nh n gin ha, vi mc ch phn tch, vt liu c phn b lin tc, ngoi cc khong trng hoc cc khng gian trng rng (tc l, chng ta b qua cc cu trc phn t i vi cc vt liu ny). Mt vt liu lin tc gi nh nh vy c gi l mt mi trng lin tc. Thc cht , trong mt s lin tc bao gm cc i lng nh mt , chuyn v, vn tc, ng sut,v nh vy s bin i mt cch lin tc cho o hm ca n tn ti v lin tc. Gi nh mt mi trng lin tc cho php chng ta thu nh mt th tch bt k thnh 1 im, theo nhiu cch tng t khi chng ta ly gii hn trong mt o hm xc nh, v vy ti mt im chng ta c th xc nh cc i lng m chng ta cn. V d, mt ( khi lng chia cho th tch) ca mt vt liu ti mt im th c nh ngha l t s gia khi lng vi th tch . th tin ti , th nh so vi khong cch gia cc phn t

Trong thc t, chng ta cho gii hn 0. Mt nghin cu ton hc v c hc, mt mi trnglin tc l tng c gi l c hc mi trng lin tc.Mc ch chnh ca cun sch ny: (1) l nghin cu cc nguyn tc bo ton trong c hc mi trng lin tc v xy dng cc phng trnh m t chuyn ng v trng thi c hc ca vt liu v (2) l ch ra cc ng dng ca cc phng trnh nhm n gin cc i lng lin quan n dng chy ca cht lng, s dn nhit, v bin dng ca vt rn. L do cho vic xy dng cc phng trnh l t c mt s hiu bit v cc i lng ca mt h thng k thut. Hiu bit ny l hu ch trong vic thit k v sn xut cc sn phm tt hn. V d in hnh ca nhng vn k thut, tt c u c ch ra trong cun sch ny, c m t trong cc chng bn di.tht l da vo cc khi nim trc quan hoc nn ca ngi c t cc kha hc c bn trong c hc cht lng, truyn nhit v c hc ca vt liu (ng sut ko v ng sut nn) v cu trc nht, dn in, m un, v cc v d bn di. Nhng nh ngha chnh xc ca cc k hiu s ch ra trong cc chng di y.VN 1 (C HC VT RN)Chng ti mun thit k mt vng nhng b bi vi chiu di L (cho php cc vn ng vinc bi), c nh mt u v u kia t do (xem Hnh 1.1.1). Ban u Tm vn th thng v nm ngang, tit din ngang ng u. Qu trnh thit k bao gm vic la chn vt liu (vim un n hi E) v kch thc tit din ngang l b v h m tm vn c th nng ton b khi lng ca vn ng vin. Cc tiu chun v ng sut th khng vt qu cc gi tr ng sut cho php v lch ca u t do khng vt qu gi tri .mt thit k ca cc h thng u thng da trn phng trnh c hc vt liu. Cc thit k cui cng lin quan n vic s dng cc phng trnh phc tp hn, chng hn nh phng trnh n hi kch thc ba chiu (3D). Cc phng trnh ca l thuyt c s c th c s dng tm mi quan h gia lch ca u t do vi chiu di L,kch thc mt ct ngangkch thc b v h, m un n hi E, v trng lng W [xem Eq. (7.6.10)]:

( lch cho php) v ti W(trng lngti a c thca mt vn ng vin),ai c thchn vt liu ( m un n hi, E) v kch thc L, b, vh(m phi c gii hn trong kch thc tiu chun ch to bi nh sn xut). Ngoi cc tiu chun lch, ai cng phi kim tra nu ng sut gia tng ca tm vn vt qu ng sut cho php ca vt liu c la chn. Phn tch ca phng trnh thch hp nhm cung cp cho cc nh thit k vi gii php thay th la chn vt liu v kch thc ca tm vn sao cho ph hp.

VN 2(C HC CHT LNG)

Chng ti mun o nht ca du bi trn c s dng trong my quay nhm ngn chn cc thit hi ca cc b phn ma st. nht,ging nh m un n hi ca vt rn, thuc tnh ca vt liu th hu ch trongvic tnh ton ng sut ct1.1 C hc mi trng lin tc

c pht trin gia mt lu cht v vt th rn. Mt ng mao dn c s dng xc nh nht ca mt l cht qua cng thc

Trong d l ng knh trong v L l chiu di ca ng mao dn, P l p sut ti hai u ng(dng du t u ny n u kia, c ch ra trong hnh1.1.2), v Q l t l th tch ca dng du m dng du ny c thi t ng.Phng trnh(1.1.3) th c pht hin.

VN 3(TRUYN NHIT)

Chng ti mun xc nh tn tht nhit qua cc bc tng ca mt l.Cc bc tng thng bao gm cc lp gch,vaxi mng, v khi than(xem Hnh 1.1.3).cc ti liu cung cp mc khngnhit khc nhau. nh lut dn nhit fourier (xem Phn 8.3.1) (1.1.4)Mt mi quan h gia dng nhit q(dng nhit trn din tch) v gradient nhit T. y k l h s dn nhit (1 /k l cc khng nhit) ca vt liu.Du - trong phng. (1.1.4) ch ra hng dng nhit

Hnh1.1.2. o nht camtuidfls dngngmao dn.

Khu vc c nhit cao s truyn nhit qua khu vc c nhit thp. ng dng cc phng trnh c hc mi trng lin tc, ta c th xc nh cc tn tht nhit khi nhit bn trong vbn ngoi ca ta nh . Nh thit k ta nh c th chn cc vt liu cng nh dy ca cc thnh phn khc nhau ca bc tng gim tht thot nhit( m bo bn kt cu cn ).Cc v d trc cung cp mt s du hiu cho thy s cn thit phi nghin cu phn ng c hc ca vt liu di nh hng ca cc ti trng bn ngoi. Cc phn ng c hc ca mt loi vt liu ph hp vi cc quy lut vt l v cc trng thi c bn ca vt liu.Cun sch ny nhm mc ch ca m t cc nguyn tc vt l v thu c cc phng trnh ca cc sut v bin dng ca vt liu lin tcv sau gii quyt mt s vn n gin t cc mc ch k thut khc nhau minh ha cho vic ng dng cc nguyn tc ny v nhng phng trnh c bn .1.2 NHN V PHA TRCMc tiu chnh ca cun sch ny gm hai phn: (1) s dng cc nguyn l vt l thu ccc phng trnh nhm chi phi cc chuyn ng v phn ng c nhit ca vt liu v (2) p dng nhng phng trnh ny cho vic gii quyt cc vn c th ca n hi tuyn tnh, truyn nhit v c hc mi cht. Cc phng trnh chi phi ny p dng cho vic nghin cu bin dng v ng sut ca mt vt liu lin tc khng l g c, nhng mt i din phn tch ca php lut ton cu v bo ton khi lng, xung lng v nng lng . Chng c p dng cho tt c cc vt liu m c coi nh l lin tc. Vic m x cc phng trnh cho cc vn c th v gii quyt chng to nn s cn thit cho cc phn tch k thut v thit k. Cc nghin cu v chuyn ng v bin dng ca mt mi trng lin tc (hoc mt "vt th" bao gm vt liu phn b 1 cch lin tc) c th c phn thnh bn loi c bn:(1) (phng trnh ng sut - chuyn v) Kinematics(2) Kinetics (bo tn ca momen)(3) Nhit ng lc hc (ng lut 1 v 2 ca nhit ng lc)(4) phng trnh c bn (quan h ng sut v bin dng)Kinematics l mt nghin cu v nhng thay i hnh hc hoc bin dng trong mt mi trng lin tc, ngoi vic xem xt cc lc gy ra bin dng. Kinetics l nghin cu v trng thi cn bng tnh hoc ng ca cc lc v m men tc ng ln mt mi trng lin tc.Bng 1.2.1. Bn ch chnh ca nghin cu, cc nguyn tc vt l v cc tin s dng, kt ququn phng trnh, v bin c lin quan

ng dng cc nguyn tc bo ton xung lng. Nghin cu ny dn n phng trnh chuyn ng cng nh s i xng ca ng sut ko i vi s thiu ca cp vt th. Nguyn tc nhit ng lc hc c lin quan vi vic bo tn nng lng v quan h gia nhit, c hc, v tnh cht nhit ng ca mi trng lin tc. Phng trnh c bn m t trng thi c nhit ca vt liu lin tc, v chng lin quan ti s bin i ph thuc c gii thiu trong vic m t kinetic .Bng 1.2.1 cung cp mt bng tm tt ngn gn v cc mi quan h gia cc nguyn tc vt lv phng trnh chi phi, v cc thc th vt l lin quan n cc phng trnh.

1.3 Tm tt

Trong chng ny, khi nim v mi trng lin tc c tho lun, mc tiu chnh ca vic nghin cu ny, c th l, s dng cc nguyn l vt l thu c cc phng trnh chi phi mi trng lin tc v trnh by ng dng ca phng trnh ny trong vic gii quyt cc nhim v c th nh tnh n hi tuyn tnh, truyn nhit,v c hc lu cht, c trnh by. Nghin cu cc nguyn tc vt l c phn chia thnh bn ch , nh c nu trong Bng 1.2.1. tng ng vi Bn ch t chng 3 n chng 6. M hnh ton hc ca phng trnh phn chiat mi trng lin tc nht thit i hi vic s dng cc vect v tensor, Mc tiu l n gin ho m hnh phn tch cc quy lut t nhin.V vy, iu th rt hu t cho vic nghin cu cc tnh cht ca vect v tensor. Chng 2 c dnh ring cho mc ch ny. Cun sch ny hin nay ch yu l gii thiu v c hc mi trng lin tc, nhng cun sch khc c th cung cp cc cch x l i tng mt cch tin tin. c gi quan tm c th tham kho kin cc chc danh c lit k trong danh sch ti liu tham kho cui cun sch.VN

1.1. nh lut th hai Newton F = ma, (1)trong F l lc tc ng ln vt th,m l khi lng vt th, v mt s tng tca l gia tc ca vt th khi chu lc tc ng. S dng phng trnh(1) xc nh phng trnh chi phi ca mt vt th ri t do. Ch xem xt cc lc do trng lc v sc cn khng kh, c gi nh l t l tuyn tnh vi vn tc ca vt th ri t do.

1.2 Xt s truyn nhit n nh thng qua mt thanh tr c tit din ngang khng ng nht. Bit c nhit T0 (0C) u cui bn tri ca thanh ny , c trn b mt v u cui bn phi, t trong mi trng (nh lu cht hoc khng kh mt) nhit T . gi s nhit ng u mi phn ca thanh, T = T (x). S dng cc nguyn tc bo ton nng lng (trong yu cu t l thay i (tng) ca nng lng bn trong bng tng nhit tng do truyn nhit, i lu v sinh nhit bn trong) (xem Hnh P1.2) thu c cc phng trnh chi phi.

1.3 Gi thuyt Euler-Bernoulli lin quan n bin dng un ca trc dm gi nh rng cc ng thng vung gc vi trc dm trc bin dng gm (1) thng, (2) vung gc vi ng tip tuyn vi trc dm v (3) khng ko dn trong sut qu trnh bin dng. Nhng gi nh ny dn n chuyn v sau:

Trong (u1, u2, u3) l chuyn v ti 1 im (x,y,z) dc theo trc x,y,z) v u l chuyn v ng ca dm ti im (x,0,0). Gi s rng dm chu lc phn phi q(x). xc nh phng trnh chi phi bng cch tng hp cc lc v momen trn mt phn t ca dm(xem Hnh P1.3). Lu rng cc quy c du cho momen v lc ct c da vo nh ngha.

v khng c chp nhn vi nhng quy c k hiu c s dng trong ti liu c hc ca vt liu.

1.4 Mt b cha hnh tr vi ng knh D cha mt lng cht lng vi chiu cao ca ct cht lng lh (x, t). Cht lng c cung cp cho b vi tc dng chy qi (m3/ngy) v lm cn vi tc ca q0 (m3/ ngy). S dng cc nguyn tc bo ton khi lng c c phng trnh chi phi sau.