Optimisation of Pad Thicknesses in Ironing Machines During Coupled Heat and Mass Transport

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1 Ryszrd Koryck *Hl Szrńsk ertmet o echcl Mechcs d omuter Scece Lodz Uversty o echology Zeromskego Lodz Pold E-ml: ryszrdkoryck@lodzl *ertmet o esg Shoes d lothg echology Uversty o echology d Humtes Rdom Rdom Pold Otmsto o Pd hckesses Irog Mches urg ouled Het d Mss rsort OI: 56/ Abstrct he m gol o the er s to determe the hyscl d mthemtcl models o couled het d mss trsort th ds durg rog s ell s otmze the ds thckesses Itroducg the ck s duso bers het d mss trsort eutos re ormulted d ccomed by set o boudry d tl codtos Otmzto o thckess s grdet oreted the ecessry objectve uctols re lyzed Numercl exmles o otmzto cocerg the ds thckess re reseted Key ords: rog mche couled het d mss trsort otmzto thckess Nomeclture A mtrx o het coducto coecets Wm-K- b vector o desg rmeters m c therml het ccty J kg-k- c v volumetrc het ccty o tle mterl J m - K - mtrx o ter vour duso coecets th bres m s - dv v tget dvergece o vector v o erl boudry - e ter vour ressure P objectve uctol - Lgrge uctol (the uxlry ucto - g g/b globl (mterl dervtve o g resect o desg rmeter b - g g/ b rtl (locl dervtve o g resect o desg rmeter b - H me curvture o the erl boudry m - H reltve humdty o r - H reltve humdty o bres - h surce lm coductce Wm-K- h mss trsort coecet o ter vour r m s- N umber o uctols durg the sestvty lyss - ut vector orml to erl boudry drected outrds to the dom Ω bouded by ths boudry - P umber o desg rmeters durg the sestvty lyss - roorto betee the sorto rtes - vector o het lux desty Wm- vector o mss lux desty kg m - s - het lux desty orml to the erl boudry Wm - mss lux desty orml to the erl boudry kg m - s - R R rst- d secod-stge sorto rtes kg m- s- s s djustble rmeters o the sorto rocess kg m- s- temerture K/ t rel tme the rmry d ddtol structures s t e tme to rech us-eulbrum durg the sorto rocess s v (xb trsormto velocty eld ssocted th desg rmeter b - v trsormto velocty orml to the erl boudry - ter vour cocetrto the r llg the terbre vod sce kg m - ter vour cocetrto th the bres kg m - W /r rctol ter cotet o bre surce - erl boudry o the structure - β roxmto coecet o sorto / desorto o the boudry o bres - γ boudry tegrd o the objectve uctol - eectve orosty o the tle mterl - η bsorto coecet - cross coecet descrbed s the het sorto o ter vour by bres J kg - Σ dscotuty le betee djcet rts o ecese smooth boudry - r desty o bres kg m- τ trsormed tme the djot structure s χ Lgrge multler - Ω dom o the structure m grdet oertor - Itroducto Irog mches re used to mrove the ulty o clothg comoets s ell s the rocess o het tretmet (e comresso eects orkg codtos d otmsto o the tme Ech ro gure Scheme o rog devce th moble uer d sttory loer lte: uer lte uer d turg rm roed clothg 5 loer d 6 loer lte 7 bse o loer lte 8 Koryck R Szrńsk H Otmsto o Pd hckesses Irog Mches urg ouled Het d Mss rsort IBRES & EXILES Ester Euroe 6 Vol (5: 8-5 OI: 56/666795

2 g mche hs to ltes rovded th ds o deret shes gure he loer lte s xed to the bse heres the uer oe s moble Irog mches c be dvded to the ollog: ( uversl geerl lcto ll tles re roed o ds o the sme she d ( seclsed rtculr lcto ech rt o clothg s roed o d o sutble she Both ltes secure deute seuece o rog d dsesble ressure he bse o the uer lte s usully mde o lumum heres the loer oe s o lumum d cst ro he stem resses re ddtolly eued th devces to dr the stem rom the oertos re to the surroudgs Pds re desged ccordg to the bse o the rog mche the oerto seuece the roduct le d the tye o rog (e ter-oertol or l rog Mterls re chrctersed by: deute elstcty euvlet r ermeblty uorm orosty sutble temerture resstce murty resstce mosture resstce er resstce mechcl durblty otml het d mosture trsort to the surroudgs mtblty d shblty oseuetly the d cossts o e deret tle lyers o deret reuremets he uversl ds re usully rectgulr hle seclsed ds hve she corresodg to the clothg elemet Hrd ds re led durg ter-oertol rog heres t s sot mterl durg the shg rocedure Alyss o vlble lterture shoed tht ublctos reltg to the theoretcl descrto o het d mss trsort th elemets o rog mches (e tle ds s ell s roed tles re so r uko he exstg ublctos descrbe some rctcl sects cocerg deret mterls chge o mterl chrcterstcs uder ressure d temerture etc he secc solutos o rog mches re oered by rtculr comes [ - ] Some terestg ormto cocerg the desg o rog mches tle ds led mterls etc c be oud ctlogues d sre rts lsts [ 5] here re some geerl orks here the uthors rovde ormto o recommeded rog techology the techologcl regme tme temerture humdty etc [6 7] he ds d roed mterl re subjected to het d ter vour trsort ouled het mosture d lud ter trser s dscussed by L Zhu [8] IBRES & EXILES Ester Euroe 6 Vol (5 L Zhu Yeug [9] hus the mosture s suled s ter vour durg rog d the recse descrto o couled het d ter vour trsort s lysed by L [] L Luo [] he uthors troduce the essetl ssumtos d the thrd euto ccordg to vd Nordo [] A Mthemtcl model s descrbed by secod-order deretl eutos th set o codtos he m gol o the ork s to determe the hyscl d mthemtcl models o couled het d mss trsort th ds durg rog s ell s otmse d thckesses Otmsto o the thckess s grdet oreted d eeds the rst-order sestvtes o the objectve uctol he drect d djot roches to sestvty lyss ere revously dscussed by ems Mróz [] & Koryck [ - 6] he grdet oreted otmsto o tles durg het d mss trsort s eso o revous ork cocerg tle egeerg otmsto [ - 6] he ovelty elemets re s ollos: ( comct modellg o het d mosture trsort rog ltes ( thckess otmsto o tle ds d ( lcto o mosture-deedet mterl rmeters he results obted ll be vered the er usg setg gurded hotlte hch smultes the couled emsso o het d mosture rom the sk Physcl d mthemtcl model o couled het d ter vour trsort Let us troduce hyscl model o the coued het d mss trser th rog mche eued th to ltes d to ds le ds re usully mde o to or three mterl lyers o deret chrcterstcs he comoets o otml rog rocess re s ollos: the rescrbed mosture lux desty dstrbuted rom the uer d loer ltes the drg o mosture the seced temerture d the relxto tme Pds re lled by ter vour becuse the mostursg tme s reltvely short d the mosture lux desty s reltvely sgct hus volume chges tles cused by mosture duso re eglgble resect o dry mterl L [] he m roblem lso s to otmse the mterl thckess o the tle d to secure the otml techologcl rmeters he most geerl cse s ormulto o the roblem Hoever the te elemet model s comlcted d the clcultos re tme-cosumg Let us troduce the geerl lcto o the rog mche d ltes o rectgulr she d sme dmesos o the cross-secto o smly the clcultos the stl roblem c be reduced to otol cross-secto o the d e le mterl thckess s lysed ouled het d ter vour trsort s chrcterstc or tle structures c L [] L Luo [] A rt o het s trsorted th mosture heres ter vour s trsorted th het t moleculr level Het s trsorted by coducto th the tle mterl s ell s by covecto d rdto rom the erl surces to the vod sces betee bres Mosture s trsorted by duso th bres d sces betee the tle mterl he le mterl o the d s homogeeous rresectve o the structure (e ove brc ktted brc ooves d should be homogesed he tle structure cossts o bres d ree sces betee them hch reures comlex to-stge homogesto rocedure bres re heterogeeous s result o the sg rocess d re homogesed resect o terl homogeety durg the terl homogesto he hole structure s homogesed s comosto o tle mterl d vod sces durg the erl homogesto he brous mterl s chrctersed by stteous therml eulbrum o cotct surces betee bres d ree sces he mterl chrcterstcs re orosty-deedet d c be determed ccordg to [7] he hyscl d mthemtcl stte o dymcl system subjected to couled het d mss trsort s descrbed by set o stte vrbles hch re or stce temerture mosture cocetrto etroy ressure terl eergy etc hese vrbles should be reresettve or the dymcl system d deed o roblem ormulto ouled het d ter vour trsort s determed by the het d mosture blces ccomed by the correlto o mosture duso th the bre hus the stte o the brous structure s descrbed by secod-order deretl correltos o the temerture d ter vour 9

3 g g l l g g r he eulbrum tme t e s deed exermetlly or some tles c L [] Hgh [7] he rog tme eul to 5 s s cosderbly shorter th the eulbrum tme t e 5 s Moreover the rctol ter cotet s reltvely lo becuse the lud ter s techologclly coveet hus the rst stge o sorto s determed by the roorto d ck s duso dry tle becuse the ter vour duses to the relxed mterl he geerl she o bres c be ssumed s cyldrcl By reso o stteous thermodymc eulbrum o cotct betee bres d vod sces th the mterl the ollog correlto c be troduced see Euto cocetrtos [ 6] hch re cosstetly the stte vrbles Mthemtclly sekg couled het d mss trsort s determed by the ollog: ( het d mss blces ( costtutve eutos o the mterl ( reltos betee the stte vrbles d (v hyscl d chemcl correltos deg ll hses o the mterl A tycl rog mche does ot co- gure Structure o rog ltes d ds structure o ltes ds d desg vrbles b erl boudry ortos o rog system g g ds thckesses (desg vrbles l l thckesses o tles subjected to rog uer lte llg d o uer lte rotectve brc o uer lte 5 roed tles 6 rotectve brc o loer lte 7 llg d o uer lte 8 loer lte ρ ( c d d d ( dv d t terl het d mss sources (e the source cctes re eul to zero or the tl het d mss luxes * * he het d mss trsort eutos the -th lyer hve the orm [] reseted the set o Eutos o solve the roblem let us troduce the exermetl reltosh L [] sho s Euto dv A d or W < 85 d t < te ( R R 5 or W t t 85 d < e or t > t R ( x d ( x R d[ rw ( H ] d( r d η b d r c Eutos d d ( dv d r e dr dv A ( ( ( ( Globl descrto o het d mss trsort eutos durg the rst sorto hse c be determed by Euto d the thrd euto ccordg to vd Nordo ( he sorto d desorto o ter vour o the bre surce c be roxmted by coecet β c rk [8] L [] rb coseuetly e deote or the -th lyer c Koryck [] - see the set o Eutos he trsort eutos re ccomed by the set o codtos sho gure he uer orto o the uer llg d cotcts the hetg d mosteg devces th the lte hch cretes the rescrbed vlue o temerture d mosture lux desty he model s chrctersed by the secod-kd codtos o het d ter vour trsort d the deute boudry ortos re d Sde boudres re oe to the surroudgs Het s lost by covecto (thrd-kd codto rt d rdto (rt r d mosture by covecto (thrd-kd codto rt Het d ter vour re /trsorted rom the loer rt o the loer llg lte to the surroudgs hus the model s subjected to the rst-kd codtos or ortos d emerture dstrbuto s determed ccordg to gure he closed rog mche secures the ressure o tles rescrbed he model s descrbed by the ourthkd codtos o the commo surces betee mterls d he tl codtos determe the temerture d ter vour cocetrtos t the begg o rog he rtculr boudres s ell the tl codtos re reseted the reltoshs (5 IBRES & EXILES Ester Euroe 6 Vol (5

4 Uer boudry: Πt ( x cos 5 t x ( x 5 e t 5 s Sde boudres: [ ( x ] ( x h [ ( x ] ( x h x ( x σ r Loer boudry: t t s ( x x ( t t 5 s 5 Π ( x 8s t t 5 s Iterl boudres: ( ( x r ( x ( ( x ( x Itl codtos: ( Ω ( x x ( x x ( Ω Alcto o rst-order sestvty roch c (5 Otml thckesses o ds re determed usg the sestvty roch he mterl dervtve o the objectve uctol resect o desg rmeters s deed s the rst-order sestvty /b he objectve uctol s geerlly descrbed by vrbles t ( b γ( d (6 Itegrd γ s the cotuous d deretble ucto o the deute boudry rt tme he correltos re determed by mterl deretto o the rorte Eutos 5 Some comoets re o desg rmeter-deedet x b b b b x b ( Ω [] he l correltos re the reseted Euto 7 he rst-order sestvty correlto c be determed s reseted Euto 8 [] he ltertve djot roch troduces the set o djot roblems ssocted th ech objectve uctol e he deg N objectve uctols e must solve N djot roblems d d η ( β d r c r ( dv d dv A ( x v ( x v ( x h( v c ( x h ( v σ r ( x v v v x ( x v v v mx 5 ( ( ( ( ( ( t ( x( x ( x ( t t à x x x Г ( ( x x ( tx x x Г Ã 5 5 ( x v x ( Ω ( x v x ( Ω 5 5 t t s t ss gure Exmle o hses o rog cycle temerture o the loer surce o loer d t tme totl orkg tme closure o ltes mosture rom the uer lte mosture rom the loer lte 5 rtlly oe uer lte drg o mosture (7 ( ( he drect roch [ - 6] s coveet to otmse the shes descrbed by smll umber o desg vrbles or exmle d thckesses he roch s chrctersed by P roblems o ddtol het d mss trser ssocted th ech desg rmeter d rmry e (P roblems Stte vrbles re the temerture d the mosture cocetrtos he she mterl rmeters d trsort codtos re the sme rmry d ddtol structures but the dstrbuto o het d mosture elds s deret [ ] he drect d ddtol roblems re deed rel t [ ( ( ] γ v v γ v P d { γ γ ( v v } d [ γ h ( ] d γ ( γ Hγ v d ] γv υ[ Eutos 7 & 8 Σ P (8 IBRES & EXILES Ester Euroe 6 Vol (5

5 d η ( dv β d d r c ( dv A xτ x Ω xτ x ( ( ( x τ γ ( x x h * ( xτ γ ( x γ ( x xτ x Ω * ( ( ( xτ Ω ( xτ ( xτ x Ω ( xτ x ( Ω ( xτ γ ( x x r ( xτ x r ( xτ x t [ ( γ ( ] v v γ v d [( γ ( v v v ] d ( γ h v d [ ] ( γ Hγ v d γ d ] γv υ[ Eutos 9 & Σ c (9 ( l tme tt s redeed s the strtg tme τ ccordg to the rule τ t t he rst-order sestvty exresso hs the orm reseted Euto resect o [] Problem o otml desg he roblem o otml desg c be determed s mmsto o the objectve uctol ccomed by the costt temerture or het lux desty o the erl boudry (see Euto m t d m t d ( he eutos re rerrged usg the Lgrg uctol d ts sttorty codtos [] hch llos to ormulte deute otmlty codtos ycl o the djot structure s tme reversl betee the tme τ o the djot roch d the tme t o the rmry roch A bt o trouble mkes the ormto storge o tme becuse the the rmry roblem he smller the umber o uctols the greter the dvtge o the method Adjot roblems hve the sme geometry mterl rmeters d trsort codtos s the rmry oe lthough some elds o stte vrbles re deret he stte vrbles re the temerture d e ter vour cocetrtos the djot structure Let us troduce the trsort eutos d boudry codtos o the orm logous to the rmry structure c [] see set o reltos (9 he vrtol roch to sestvty lyss ecessttes the uue hyscl lcto o the objectve uctol hereore cler hyscl detos o the otmsto roblems should be clssed he mortt techologcl crtero s correct mosture cotet th the ds durg rog Hece the mosture lux desty should be mmsed o the erl boudry orto o ds durg the techologcl rocess hch s descrbed s reseted by Euto Problem ormulto Irog ress Irog ltes d ds thckesses Physcl model Smlctos Physcl descrto Homogezto Mthemtcl model rsort eutos boudry d tl codtos Otmzto Sestvty lyss Prtculr orm o objectve uctol Numercl mlemetto Alyss: te Elemet Net Sythess: umercl otmzto o objectve uctol th costrts Results Otml thckess Stte vrbles th otml ds gure Algorthm o thckess otmzto o tle ds th rog ress t d m ( he correct drg o mosture reures the eulzsed dstrbuto o ter vour o the erl boudry he uctol s the globl mesure o ter vour cocetrto th bres o the erl surce o the ds Numerclly sekg the otmsto crtero rovdes the mml globl mesure hch mmzes the locl mxm o stte vrbles Loctos o the mxm c chge becuse the mxml vlues o cocetrtos re tme-deedet O the other hd the loctos re o lo mortce durg otmzto o costt d thckess (see Euto IBRES & EXILES Ester Euroe 6 Vol (5

6 A lgorthm o thckess otmsto o tle ds th rog mche s sho gure hckess otmsto o tle ds rog mche he m gol o the er reseted s to otmse d thckesses Let us ssume rog mche o geerl lcto rovded th rectgulr ds Otmsto c be reduced to otol cross-secto o the structure e the le roblem s lysed A udmetl rt o the techologcl rocess s closure o the rog mche d mosteg o tles by both the uer d loer ltes c gure Otml rmeters o the ds re determed durg ths rt o the rog rocedure Wter vour s trsorted rom the uer d loer ltes durg the tme seuece rescrbed he structure o rog ltes boudry ortos d desg vrbles re sho gure gure Let us troduce to-lyer ds mde o deret mterls he llgs re mde o dustrl elt K [9] hch s olyester brc o surce mss 6 - kg/m he mterl s exesve reltvely durble therml d ts mosture chrcterstcs re stble lthough dcult to dry Exterl rotecto s ove brc o hgh mechcl resstce d r ermeblty o surce mss 8 - kg/m esg vrbles re the thckesses g g he mterl rmeters deed o the rctol ter cotet o the bre surce e ter vour cocetrto bres d the mterl desty A orthotroc mtrx o the duso coecets o ter vour bres c be determed resect o [7] Let us ssume tht the tle mterl subjected to rog s cotto hus e c deote or the brous mterl o the -th lyer ( s rotectve oolle brc olyester elt cotto see Euto Both tles re homogesed usg the most ecet d smle rule o mxture [] he duso coecet o ter vour r s eul to 5e -5 he mterl orosty d sorto coecet o ter vour bres re troduced s costt the orm o Euto 5 Het coducto coecets the orthotroc mterl re deed s Euto 6 [7] IBRES & EXILES Ester Euroe 6 Vol (5 ool : olyester elt : cotto : ool : ool : ( ( ( 68W 59W ( ( W 859W he cross-trsort coecet d het ccty c re ssumed ccordg to Euto 7 [7] Het d mss trsort correltos or the rmry roblem re determed by Eutos Let us otmse the mterl thckess resect o the mml mosture lux desty o the loer boudry ortos the loer lte c Euto he cotuous costrt s the tme-deedet temerture he roblem s solved by mes o drect d djot roches to sestvty lyss he rmry roblem s deed usg Eutos & Eutos 5 d the ( ( ( W 8W ( ( W W ( ( ( 88 56W W ( ( 88 9W 5W olyester elt : cotto : A ( ( ( 8 9 7W W W ( ( 6 9 7W 9W W olyester elt : cotto : ool : ( d m ( ( ( 88 ( ( ( ( 6W ( 6W ( 65 ex( 7W 5 ( olyester elt : cotto : t t ( ( 85 η ( ( ( ( 75 η ( 5 ( 9ex( 9 5 W Eutos 5 6 & η 75 drect roch by Eutos 7 me chges rom the tl t to l t k 5 s d the dscrete crese s ssumed s Δt s ovecto s chrctersed by h 8 W/(m K d the surroudg codtos by 6 kg/m Itroducg the ler erl boudry e the me curvture H the otmsto roblem d l orm o the sestvty exresso re descrbed s ollos comre th Euto 8 Eutos & Euto sho Euto 8 (see ge he djot roch s deed by Eutos 9 d sestvty exresso by c 7 66 W ( c 6 9 c ( 66 8W 69 ( W ( ( (5 (6 (7

7 t d m t ( d x t P t [ h ( v ] d ] v υ[ Σ (8 [ v ] dω η Ω bρ t t υ Σ t t ( [ ( x d ] b t [ ( v v v ] d v d ] v [ t t d Π cost 5 - ( ( b m 5 ( v d v υ dσ - Σ (9 ( ( Eutos 8 9 & Euto hvg the orm o Euto 9 Ech ste o the tertve rocedure cossts o sythess d lyss stge he thckess t the lyss stge s roxmted durg the clcultos o het d mosture trsort by the sme te elemets o the seredty mly ccordg to Zekecz [] Let us troduce the le rectgulr -odl elemets o the odes the corers All ds re roxmted by 6 elemets o 6 odes Stte elds or the rmry set o the ddtol d djot roblems re clculted by soluto o the bsc te elemet euto he drec- tol mmum t the sythess stge s clculted by mes o the secod-order Neto rocedure d ltertvely y the rst-order method o steeest descet he tl d otml thckesses o the ds re lsted ble the thckesses o roed cotto lyers re costt l l m he mml objectve uctol s obted stes d reduced to 57% relto to the tl vlue Ech otml lyer mde o olyester elt s thcker th the tl (98% d 57% heres the otml rotectve oole brcs re ther th the tl (7% d % he sum o the otml s 5% greter th tht o the tl thckesses he other techologcl crtero s the eulsed dstrbuto o mosture o the uer surce o the uer d he otmsto uctol s globl mesure o locl mosture cocetrto bres o the surce he cotuous costrt s the tmedeedet het lux desty he roblem s solved usg the drect roch c Eutos Euto see Euto he rmry roblem s deed usg Eutos & Eutos 5 d the drect roch by Eutos 7 he sestvty exresso o the drect roch c be smled by Euto 8 to the orm reseted Euto ble Itl d otml thckesses o ds durg mmzto o mosture lux desty esg vrble -m g g l l g g Itl vlue Otml vlue ble Itl d otml thckesses o ds durg eulzed dstrbuto o mosture esg vrble - m g g l l g g Itl vlue Otml vlue he cross-secto o the structure s roxmted t the lyss stge usg the sme te elemet et or the rmry d the set o ddtol roblems he drectol mmum t the sythess stge s clculted usg the Neto rocedure d ltertvely the method o steeest descet he tl d otml vlues re lsted ble he mml objectve uctol s obted IBRES & EXILES Ester Euroe 6 Vol (5

8 stes d reduced o % relto to the tl vlue It ollos tht the otml olyester lyers re g thcker d the oole oe ther hoever the otml thckesses re comrble to the tl vlues he mxmum derece dmesos s 5% oclusos he otmsto o d thckesses rog mche subjected to couled het d mss trsort s multdsclry egeerg roblem It s ecessry to troduce the hyscs o het d mss trser descrto by mes o secod-order deretl eutos th boudry d tl codtos s ell s determe otml soluto I order to descrbe the mthemtcl model e hve to lyse the het d mss blces ormulte trsort eutos ccomed by the set o codtos s ell s troduce hyscl descrto o mosture duso bres ccordg to ck s L he objectve uctols led hel to determe techologcl mrovemets e mml mosture lux desty durg rog d the eulsed dstrbuto o mosture It ollos tht thckess otmzto hels to solve the umber o rctcl roblems cocerg the rog I cocluso the roblem seems to be romsg tool or geertg the otml thckess o ds durg the rog rocess Numercl otmsto s cheer d more uversl th comlex lyss o shed rototyes d rovdes rctcl beets he otmzto uctols led mmze the mosture lux desty s ell s the globl mesure o mosture cocetrto heres costrts re the temerture rescrbed or het lux desty he ltertve tegrds c descrbe some heome o the het trser heres the costrts c determe the mosture cocetrtos rescrbed or mosture lux desty Geerlly sekg the otml solutos c be lmted to ermssble creses dmesos mml mterl thckesses mml rmeters o het d mss trsort etc he otmsto rocedure c be lso eded to the desg rocess o ltes drg chels o otml dmesos the trsort o med th het d mosture chels etc he cosecutve ovelty elemets re the ely troduced hyscl roblems s ell s otmsto techues mlemeted to develo the lyss he er reseted s theoretcl otmsto o d thckesses by mes o comuter lyss he other roch s rctcl lyss here the ecessry rmeters re temerture ressg tme s ell s the mml tme o the oerto cycle together th the mml eergy ecessry to relse the roduct A sgct ctor s lso the reetto tme O the other hd omogrms c be led to determe the oertol rmeters reured he theoretcl results o otml d thckesses obted should be comred th corresodg tests hch s beyod the scoe o the er reseted he tl results llo to coclude tht rctcl vercto should be dscussed the cosecutve er Reereces htt://somtexcoml/ odktegor7ky_ okrycoehtm vetde/e/rog-d-ressggrmets/ressg-mches/ htt://bellusscoml/dexh/ct/ c5_prsyhtml htt://semcocoml/e/ ctlogs-m-sre-rts-lsts 5 htt://lstrmcom/?lge 6 Węźlk W Elmrych-Bocheńsk J Zelńsk J lothg: structure roertes d roducto ( Polsh IE Lodz 9 7 Błczk B Kotrosk A Mkosk R lothg mches d devces ( Polsh echcl Uversty o Rdom Rdom 8 L Y Zhu Q Smulteous het d mosture trser th mosture sorto codesto d cllry lud duso orous tles Res J 7 6: L Y Zhu Q Yeug KW Iluece o thckess d orosty o couled het d lud mosture trser orous tles Res J 7 5: 5-6 L Y he scece o clothg comort le Progress 5( L Y Luo Z A mroved mthemtcl smulto o the couled duso o mosture d het ool brc Res J : vd HG Nordo P se studes o couled het d mosture duso ool beds Res J 969 9: 66-7 ems K Mróz Z Sestvty lyss d otml desg o erl boudres d terces or het coducto systems J herml Stresses 998 -: 6-88 Koryck R Sestvty oreted she otmzto o tle comostes durg couled het d mss trsort It J Het Mss rser 5: Koryck R She Otmzto d She Idetcto or rset uso Problems le Structures bres & les Ester Euroe 7 5 6: -9 6 Koryck R Method o thckess otmzto o tle structures durg couled het d mss trsort bres & les Ester Euroe 9 7 (7: 8 7 Hgh AK ctors eectg tervor trsort through bers heoret Al Mech : rk J Mthemtcs o duso Oxord Uversty Press htt://eergo-mrl/verso_uk/ dustrl_eltshtm Golsk erd K Kkuch N Mcro d mcro scle modelg o therml resdul stresses metl mtrx comoste surce lyers by the homogezto methods omuttol Mechcs 997 9: 88- Zekecz O Methode der te Elemete VEB chbuchverlg Lezg 975 Receved 95 Reveed 75 bres & les Ester Euroe reches ll corers o the orld! IBRES & EXILES Ester Euroe 6 Vol (5 5