oorthootroopik metteeriyal

metteeriyal sciencilum soolid mechanicsilum, oorthootroopik metteeriyalukalkk oru prathyeka pooyintil metteeriyal propertykal undu, athu moonnu oorthoogoonal aaksukalilayi vyathyaasappedunnu, avide oro axisinum eratta bhramana samamiti undu. shakthiyile eee dishasoochana vyathyaasangal hankinsons samavaakyam upayogichu alakkaan kazhiyum.
avaa anisotropic vasthukkalude oru upavibhagamaanu, kaaranam vyathyastha dishakalil ninnu alakkumbol avayude gunangal maarunnu.
oru oorthootroopik vasthuvinte parichithamaaya udaaharanam maramaan. maratthil, gunangal vyathyasthamaaya oro pooyintilum paraspara lambamaya moonnu dishakal nirvachikkaan kazhiyum. mikka cellulose fibrilukalum aaa reethiyil vinyasikkappedunnathil ithu dhaanyathil (aksha dishayil) ettavum kaduppamullathum (shakthavumaan). ithu saadhaaranayaayi radial dishayil (valarchaa valayangalkkidayil) ettavum kadinavum chuttalav dishayil idatharam aanu. eee anisotropy parinaamathiloodeyaanu nalkiyathu, kaaranam ithu maratthe nivarnnu nilkkaan ettavum mikachathaakkunnu.
mungananayulla coordinate sisttam silindar-pollar aayathinal, itharathilulla orthotropiye pollar orthotropy ennum vilikkunnu. 
oru oorthootroopik metteeriyalinte mattoru udaaharanam kanatha rollerukalkkidayil lohathinte kattiyulla bhagangal amarthippidichu roopappedunna sheett lohamaanu. ithu athinte dhaanya ghadanaye parathukayum neettukayum cheiyunnu. thalphalamaayi, metteeriyal anisotropic aayi maarunnu-athinte gunangal athu uruttiya dishayilum rund vipareeta dishakalilum vyathyaasappettirikkunnu. gadanaaparamaaya steel beemukalilum aluminium vimaanangalude tholikalilum eee reethi upayogikkunnu.
oru vasthuvinullile pooyintukalkkidayil oorthootroopik gunangal vyathyaasappedunnundel, athinu orthotropiyum inhomogenityum undu. ithu soochippikkunnathu orthotropy ennathu oru vasthuvinullile oru binduvinte savisheshathayaanennu, vasthuvinte mothatthilulla gunathekkaal (vasthu ekathaanamallengil). oru pooyintinu chuttumulla oru cheria pradeshathinum anubandha samamithiyude thalangal nirvachikkappedunnu, mathramalla avaa muzhuvan vasthuvinteyum samamithiyude thalangalkk samaanamaayirikkanamennil.
oorthootroopik metteeriyalukal anisotropic metteeriyalukalude oru upavibhagamaanu; avayude gunangal avaa alakkunna dishaye aasrayichirikkunnu. oorthootroopik vasthukkalkk moonnu samatulita thalangal/akshangal undu. oru isotropic meteeriyalinu, neremarichu, ellah dishakalilum ore gunangalundu. rund samamithikalulla oru meteeriyalinu moonnaamathethu undaayirikkanamennu theliyikkaan kazhiyum. isotropic vasthukkalkk ananthamaaya samamithiyude thalangalundu.
transversley isotropic metteeriyalukal oru aksham samamithiyulla prathyeka oorthootroopik meteeriyalukalaanu (pradhaanatthinu lambamaya mattethenkilum jody achuthandukalum avaykkidayil oorthoogoonalum samamithiyude achuthandukalaanu). samamithiyude oru achuthandulla transversley isotropic metteeriyalinte oru saadhaarana udaaharanam samanthara glass allengil graafait naarukal shakthippeduthunna oru polymeraanu. atharam samyuktha vasthukkalude shakthiyum kaadinyavum saadhaaranayaayi izhakalkku samaantharamaayi oru dishayil vipareeta dishayilethinekkaal kooduthalaayirikkum, koodaathe kanam dishaykku saadhaaranayaayi vipareeta dishaykku samanamaaya gunangalundu. mattoru udaaharanam oru biological membron aayirikkum, athil membraninte thalatthile gunangal lambamaya dishayilullathil ninnu vyathyasthamayirikkum. oorthootroopik metteeriyal propertykal asthiyude ilaastik samamitiye kooduthal krithyamaaya praathinidhyam nalkunnuvennum asthiyude tissue-level metteeriyal propertykalude trimana dishayekkurichulla vivarangal nalkaanum kazhiyumennum theliyikkappettittund.
oru neela skailil anisotropic aaya oru metteeriyal mattoru (saadhaaranayaayi valia) neela skailil isotropic aayirikkaamenn oormmikkendathu pradhaanamaan. udaaharanathinu, mikka lohangalum valare cheria daanyangalulla polychrystaline lohangalaanu. oro daanyavum anisotropic aayirikkam, ennaal mothatthil meteeriyalil kramarahithamayi ooriyantad cheytha niravadhi daanyangal adangiyirikkunnuvenkil, athinte alakkunna mechanical gunangal vyakthigatha daanyangalude saadhyamaaya ellah ooriyanteshanukalileyum gunangalude sharaashariyaayirikkum.
bhauthikashaasthrathil orthotropy.
anisotropic bhauthika bandhangal.
bhauthika sidhaanthangalil bhauthika swabhaavathe prathinidheekarikkunnath gadanaaparamaaya bandhangalaan. oru valia tharam shaareerika perumaattangale randaam nira tensorinte roopamedukkunna leanier metteeriyal modalukal prathinidheekarikkam. metteeriyal tensor rund vektarukal thammilulla bandham nalkunnu, ithu ingane ezhuthaam
ivide formula _ 2 bhauthika alavukale prathinidheekarikkunna rund vektarukalaanu, formula _ 3 randaam nira metteeriyal tensoraanu. oru oorthoonoormal coordinate sisttavumaayi bandhappett gadakangalude adisthaanathil melpparanja samavaakyam prakadippikkukayaanenkil, namukk ezhuthaam.
melpparanja bandhatthil aavarthichulla soochikakalude sangraham anumaanikkappettittund. matricks roopathil namukkund
melpparanja templatinu anuyojyamaaya shaareerika prashnangalude udaaharanagal chuvadeyulla pattikayil pattikappedutthiyittundu.
metteeriyal samamithiyude avastha.
metteeriyal matricks formula _ 6 nuu aaa parivarthanatthinu vidheyamaakumbol athu maarunnillengil thannirikkunna oorthoogoonal parivarthanavumaayi (formula _ 7) bandhappett oru samamiti undu. 
atharam oru parivarthanatthinu keezhil bhauthika gunangalude vyathyaasathin namukk aavasyamaanu.
athinaal metteeriyal simetriyude vyavastha (oorthoogoonal parivartthanatthinte nirvachanam upayogichu)
oorthoogoonal parivartthanangale cartician kordinettukalil prathinideekarikkaan oru soothravaakyam _ 10 matricks formula _ 11 nalkunnu
athinaal, samamiti vyavastha matricks roopathil ingane ezhuthaam
oorthootroopik metteeriyal propertykal.
oru oorthootroopik meteeriyalinu moonnu oorthoogoonal simetri thalangalundu. moonnu samamiti thalangalilekkulla normalukalumaayi aaksukal poruthappedunna oru oorthoonoormal coordinate sisttam nammal thiranjedukkukayaanenkil, parivartthana maatriksukal ivayaanu
oru metteeriyalinte matricks formula _ 6 rund oorthoogoonal thalangalekkurichulla prathiphalanathinu keezhil maattamillaathathaanenkil, moonnaamathe oorthoogoonal thalathekkurichulla prathiphalanathinu keezhil athu maattamillaathathaanennu kaanikkan kazhiyum.
17 thalam enna soothravaakyathekkurichu prathiphalana soothravaakyam pariganikkuka. appol namukk
melpparanja bandham soochippikkunnathu formula _ 19. aduthathaayi formula _ 21 pleyininekkurichulla oru reflection formula _ 20 pariganikkuka. appol namukk
athu soochippikkunnathu formula _ 23. athinaal, oru oorthootroopik metteeriyalinte bhauthika gunangal matricks vivarikkunnu.
leanier ilaasthikathayil orthotropy.
anisotropic ilaasthikatha.
rekheeya ilaasthikathayil, sammarddavum sammarddavum thammilulla bandham parigananayilulla vasthuvinte tharatthe aasrayichirikkunnu. eee bandhathe hook niyamam ennu vilikkunnu. anisotropic metteeriyalukalkk hukkinte niyamam ingane ezhuthaam
ivide soothravaakyam _ 26 stress tensor aanu, soothravaakyam _ 27 strain tensor aanu, soothravaakyam _ 28 ilaastik stiphness tensor aanu. melpparanja padaprayogatthile tensorukal oru oorthoonoormal coordinate sisttavumaayi bandhapetta gadakangalude adisthaanathil vivarichittundenkil namukk ezhuthaam.
aavarthichulla soochikakalil sangraham anumaanikkappedunnu. stresses strain tensorukalum samamithiyayathinaal, leanier elaasthikathayile stress-strain bandham oru strain energy density functionil ninnu uruthirinjathinaal, inipparayunna samamithikal leanier ilaastik metteeriyalukalkk baadhakamaan.
melpparanja samamiti kaaranam, leanier ilaastik metteeriyalukalude stress-strain bandham matricks roopathil prakadippikkaan kazhiyum
voyigt notteshanile oru badal praathinidhyam
allengil 
melpparanja bandhatthile stiphness matricks formula _ 34 pooyint samamiti thripthippeduthunnu.
metteeriyal samamithiyude avastha.
stiphness matricks formula _ 34, anubandha oorthoogoonal parivarthanatthinu vidheyamaakumbol maarunnillengil oru nischitha samamiti vyavasthaye thripthippeduthunnu. oorthoogoonal parivartthanam oru pooyint, axis allengil playin ennivayumaayi bandhapetta samamitiye prathinidheekarikkam. leanier elaasthikathayile oorthoogoonal parivartthanangalil bramanangalum prathiphalanangalum ulppedunnu, pakshe maarunna parivartthanangale roopappeduthunnilla, koodaathe oorthoonoormal kordinettukalil, oru soothravaakyam _ 10 matricks formula _ 37 upayogichu prathinidheekarikkam
voyigt notteshanil, stress tensorinte parivartthana matricks oru formula _ 39 matricks formula _ 40 aayi prakadippikkaam
notteshan thiranjedukkunnathinaal strain tensorinte parivarthanatthinu alpam vyathyasthamaaya roopamundu. eee parivartthana matricks
aaa formula _ 43 kaanikkam.
oru oorthoogoonal parivartthana soothravaakyathinu keezhil oru thudarchayude ilaastik gunangal maattamillaathathaanu _ 37
oorthootroopik elaasthikathayile kaadinyavum paalikkal maatriksukalum.
oru oorthootroopik ilaastik meteeriyalinu moonnu oorthoogoonal simetri playinukalundu. moonnu samamiti thalangalilekkulla normalukalumaayi aaksukal poruthappedunna oru oorthoonoormal coordinate sisttam nammal thiranjedukkukayaanenkil, parivartthana maatriksukal ivayaanu
oru leanier ilaastik metteeriyalinte matricks formula _ 34 rund oorthoogoonal thalangalekkurichulla prathiphalanathinu keezhil maattamillaathathaanenkil athu moonnaamathe oorthoogoonal thalathekkurichulla prathiphalanathinu keezhil maattamillaathathaanennu namukk kaanikkan kazhiyum.
17 thalam enna soothravaakyathekkurichu prathiphalana soothravaakyam _ 48 pariganikkukayaanenkil, namukk undu.
appol aavasyakatha soothravaakyam _ 45 soochippikkunnathu
melpparanja aavasyakatha niravettaan kazhiyunnath
namukk aduthathaayi formula _ 21 pleyininekkurichulla reflection formula _ 54 pariganikkaam. aaa saahacharyathil
veendum invarians avastha upayogichu, namukk adhika aavasyakatha labikkum
moonnaamathe samamiti thalathekkurichulla prathiphalanam nammal ithinakam pariganicha thalangalekkurichulla prathifalanangalil ninnu swathanthramallaathathinaal kooduthal vivarangal nedaan kazhiyilla. athinaal, oru oorthootroopik leanier ilaastik metteeriyalinte kaadinyam matricks ingane ezhuthaam
eee maatriksinte vipareethabhagam saadhaaranayaayi ingane ezhuthappedunnu
soothravaakyam _ 60 ennathu axis formula _ 61-lulla yamginte modulus aanu, soothravaakyam _ 62 ennathu dishayile formula _ 63-leeii shear modulus aanu, athinte normal dishayilulla formula _ 61 aanu, koodaathe formula _ 65 ennathu disha formula _ 61-ll oru ekstenshan prayogikkumbol disha formula _ 63-leeii sankochavumaayi poruthappedunna poyson anupaathamaan.
oorthootroopik ilaastik vasthukkalude moduli athirukal.
oorthootroopik leanier ilaastik metteeriyalukalude strain-stress bandham voyigt notteshanil ingane ezhuthaam
ivide compliance matricks formula _ 69 nalkunnu
compliance matricks samamithiyaan, strain energy density positteev aakunnathin positteev krithyamaayirikkanam. ithu silvesttarinte maanadandatthil ninnu soochippikkunnathu maatriksinte ellah pradhana minorukalum positteev aanennaan, i.iii., 
ivide formula _ 72 ennathu formula _ 69-nte formula _ 73 pradhana upavibhagamaanu.
appol, 
eee vyavasthakalude koottam soochippikkunnathu
allengil
ennirunnaalum, poysaninte anupatha soothravaakyam _ 78-nte moolyangalil samanamaaya thaazhnna athirukalonnum sthaapikkaan kazhiyilla.

