Amaqokobhe ziinkxaso zomphezulu, ezomhlaba ophakathi ongengosicaba kodwa ugobile ngokucacileyo. Ukuziphatha kwazo okungaguquguqukiyo kude kakhulu nokwipleyiti. Xa zinobume obufanelekileyo, zixinezeleka kancinci kakhulu, ukuqina kwazo kuphezulu ngokufanelekileyo, yaye ukubala kwazo, kwiimeko ezininzi, kulula ngakumbi.
Uxinzelelo lweqokobhe ngalinye lunokwahlulwa lube ngamacandelo amabini: uxinzelelo lwe-membrane nokugoba. Uxinzelelo lwe-membrane, ngendlela efanayo noxinzelelo kwiplate elayishwe kwindawo yayo, lungachazwa ngamandla okusika kwinqanaba elithambekileyo – ezi zizezi, umzekelo, kwicandelo x=const. amandla aqhelekileyo _Nx=_σx*t kunye namandla okusika _Nxy=_τxy*t, apho t bubukhulu beqokobhe. Uxinzelelo olubangelwa kukugoba lufana nolo lweeplate yaye lunokumelwa ziimoment zokugoba Mx, iimoment zetorsion Mxy kunye namandla okusika Qx.
Iimpawu ezibalulekileyo zamaqokobhe zisekelwe kwinto yokuba, ngokomgaqo, uxinzelelo olubangelwa kukugoba alunabo ubukhulu okanye ukubaluleka koxinzelelo lwe-membrane, ngoko ke amaxesha amaninzi lunokushiywa ngokupheleleyo. Kule meko, zonke iintlobo zoxinzelelo zisasazwa ngokulinganayo kubukhulu beqokobhe yaye zisebenza ngokuthambeka kumphezulu ophakathi. Iibalo ezisekelwe kwezi ngcinga zingena ngaphakathi kwethiyori ye-membrane yeqokobhe.
Ithiyori ye-membrane yamaqokobhe ajikelezayo alingene, phantsi komthwalo ojikelezayo alingene
Iifom eziqhelekileyo
Kwimigca yolungelelwaniso kusetyenziswa ii-meridian kunye nezangqa ezifanayo kumphezulu ophakathi weqokobhe, ngoko ke uququzelelo ngu: i-azimuth ϑ (“ubude bejografi”) kunye nokuthambeka φ kwetangenti kwi-meridian ngokuthelekiswa nomphezulu onqamlezileyo kwi-axis yolungelelwaniso (umz. 1a). Ngokwenjenje imikhosi yokunqumla yile: amandla aqhelekileyo Nφ kwicala le-meridian kunye namandla aqhelekileyo Nϑ kwisangqa (umz. 1b). Amandla okucheba Nφϑ awaveli ekuxinaniseni okuhambelana nokujikeleza. Umthwalo kwiyunithi yomphezulu uchazwa ngolu hlobo lulandelayo (umz. 1b): Y ichukumisa i-meridian, ilungile kwicala apho φ ikhula khona, Z iqhelekile kwiqokobhe, ilungile ngakwi-axis yolungelelwaniso.
Umz. 1
Fig. 2
Masingathi iradiyasi yokugoba kwemeridiyane ngu_r1_. Isebenza njengomsebenzi we-engile φ ngoko ngothethwano _r1=r1(φ) kumiselwa imo yemeridiyane. Oku kunokuthathwa njengomgaqo wemmeridiyane kwaye kuthi, umzekelo.
kwisangqa r1=a=const.
for parabola r1=a/cos3__φ
yesangqa r1=a2b2(a2sin2__φ+b2cos2__φ)-3/2
Ukuze kubalwe amandla aqhelekileyo N__φ kwicala le-meridian kufuneka kumiselwe imeko yokulingana kwenxalenye yeqokobhe elele ngaphezu kwesangqa esihambelanayo φ (fig. 2). Iresultanti R yemithwalo Y ne Z ehlasela le nxalenye ime nkqo, ngenxa yokulinganisa. Ubukhulu bayo bufunyanwa ngokudibanisa phezu komphezulu weqokobhe ukusuka φ’=0 ukuya ku φ’=φ. Ummandla wento yeqokobhe ngu dF=r1d__φ’*rd__ϑ, ngoko icandelo elime nkqo lomthwalo (Ysin__φ’+Zcos__φ’)dF. Kwonke umsesane weqokobhe ophakathi kwezangqa φ’ no φ’+dφ’ iresultanti yomthwalo wangaphandle ithi:
dR=2__πr (Ysin__φ’+Zcos__φ’) r1d__φ’,
apho ngokudibanisa ngokwe φ’ kwinxalenye yeqokobhe elele ngaphezulu kwesangqa esihambelanayo φ’=φ kufunyanwa:
Isiq. 1
Lo mthwalo uthwalwa ngamandla aqhelekileyo kwicala lemeridian, asebenza ejikeleze umjikelezo obonakalisiweyo; icandelo elithe nkqo lesiphumo saloo mandla ngu 2__πr * N__φ sin__φ, ngoko ke ngokulinganisa ukusuka apha kufunyanwa amandla aqhelekileyo afunekayo
Isib. 2
Ukuba iqokobhe kwindawo ephezulu lisikwe ecaleni kwesangqa φ=φ0 (umzekelo, ukuvuleka kokukhanya kwi-dome), umda ongezantsi we-integral, ngokuqondakalayo, ngu φ0, hayi u-zero. Ukuba kumda weqokobhe owenziwe ngale ndlela kusebenzela nomthwalo R0, nawo kufuneka wongezwe kwiresiltenti R (umz. 3).
Umz. 3
Ukuze kumiselwe amandla aqhelekileyo N__ϑ kufuneka kubekwe imeko yokulingana yecandelo leqokobhe elithe nkqo kwinqwelo yotangential (umz. 4). Iresulti yomthwalo wangaphandle kweli cala yi Z r1 d__φ r d__ϑ. Amandla N__φ*r d__ϑ alele kwinqwelo ye-meridional enza phakathi kwawo i-engile encinane d__φ, ngoko ke iresulti yawo kwicala le-normali kwi-qokobhe yi N__φ r d__ϑ*dφ. Ngokufanayo, namandla Nϑ r1 dφ alele kwinqwelo yesangqa esithe tye aze phakathi kwawo enze i-engile dϑ aneresulti Nϑ r1 dφ*dϑ ekwangoku elele kwinqwelo yesangqa esithe tye, yaye ke ngoko nenormali kwi-qokobhe enza i-engile 0,5_π-φ_, ukuze kwimeko yokulingana kungene kuphela isakhi sawo Nϑ r1 dφ dϑ*sinφ. Ngoko ke imeko yokulingana ithi
okanye, xa yahlulwe ngo r r1 dϑ dφ:
Nye.3
Apha ngo r2=r/sinφ kuchazwe elinye iradiyasi enkulu yokugoba yeqokobhe.
Fig. 4
Idome ejikelezayo
Xa imilo yemeridiyani inikwe ngokuhlalutywa ngesibalo r1=r1(φ) yaye xa iintlawulo Y(φ) ne Z(φ) zinikwe ngeentetho ezihlalutywayo, amandla okusika kwigobolondo anokuhlala emiselwa ngokudibanisa ngendlela evaliweyo okanye ngokwamanani, kusetyenziswa umthetho ka_Simpson_. Kwi-dome ejikelezayo enobubanzi a, koku kulandelayo kunikwa amandla okusika kwezinye iimeko zokulayisha:
Umzekelo wokugqibela, othi ku φ=0 unike amandla okusika angapheliyo, usebenza kuphela kumgama othile ukusuka kwindawo yokusebenza kwamandla. Kwindawo esondeleyo apho amandla asebenza khona, kwanaxa asasazwa phezu komhlaba wesangqa esinobubanzi obuphelileyo kodwa obuncinci, umthwalo ubukhulu becala uthuthwa ngokugoba.
Iindlela zeqokobhe ezivulekileyo kwicala elingasentla zinokufunyanwa kwezi zangaphambili, ukuba kumthwalo wokwenene kongezwa umthwalo oyintsomi P kwincam, ubukhulu bawo bumiselwa ngolu hlobo xa amandla aqhelekileyo ewonke kwicala lemeridiyani asebenza kumda ongaphezulu weqokobhe φ=φ0 alingana Nφ=0, okanye alingana nexabiso elithile elimiselwe yimikhosi yangaphandle eli qokobhe liyayamkela apha.
Iqokobhe lekhone
Umz. 5
Kwimeko yeshelli yeconical, ithambeka le-meridian φ alinakusetyenziswa njengekhowudi, kuba linexabiso elifanayo kuzo zonke iindawo. Endaweni yalo kufakwa umgama s ukusuka kwincopho yedome, olinganiswa ecaleni komgca wokuzala (fig. 5). Amandla aqhelekileyo kwicala le-meridian ngokuhambelana noku achazwa ngo Ns. Iifom ezifunekayo zinokufunyanwa kwezo zikhankanyiweyo phantsi kwe 1 xa kusenziwa umda wokutshintsha. Kwii-equation (2) kufunyanwa ngale ndlela
kwaye ukusuka kwiyantlukwano (3)
Nϑ = -r2 Z = -Z s ctga.
Kwiimeko ezibalulekileyo zomthwalo kusebenza ezi fomula zilandelayo:
Inkqubo yemizobo yobume obungaqhelekanga bemeridian
Fig. 6
Xa ijika le-meridiani linganikwanga ngentetho yohlalutyo, kodwa, masithi, ngokomzobo, ukumisela iradiyasi yokugoba kunzima kakhulu kwaye akunembi ngokwaneleyo. Kule meko kungcono ukusebenzisa indlela yomzobo (umz. 6).
Iqokobhe lahlulahlulwe ngeenqwelwana ezininzi φ=const., kubalwa ubunzima Δ_R bemimandla emisesane elele phakathi kweenqwelwana yaye kungcono kwangoko bazahlule ngo-2_π_. La mandla ΔR/2π afakwa kwiplani yamandla (sl. 6b). Ukuba ke emva koko, umzekelo, ngendawo yokwahlula 7 kutsalwe umgca othe ngqo ulingana netangenti kwimeridiyane kwindawo yemeridiyane 7, umgca othe tye odlula kwindawo ephezulu yeplani yamandla uya kuwunqamla kuyo ubude R1/2π sinφ7 apho, ngokusekelwe kwintsebenziswano (2), ngokuwahlula ngo r ofanelekileyo kufumaneka amandla aqhelekileyo afanelekileyo kwicala lemeridiyane.
Ukumisela amandla kwiiringi kusetyenziswa imeko yokulingana kwamandla athe tye kwinto enye yegobolondo. Ukuba zisebenza kuphela iintlawulo ezithe nkqo, le meko ithi (sl. 4):
Xa apha dφ itshintshwa ngumahluko ogqityiweyo Δφ, ohambelana nolwahlulo olwamkelweyo lweqokobhe, kwaye xa endaweni ye r1 dφ kufakwa ubude Δs bento ye-meridian, ukusuka apha kufunyanwa
Kwibakethi ekwicala lasekunene kukho i-cut-off kumgca othe tye othe tye kwiplani yamandla. Ngenxa yoko, lonke icala lasekunene limela amacandelo phakathi kwamanqaku okwahlula kulo mgca. Ukuze sikwazi ukuwafunda ngokuchaneka okwaneleyo, iplani yamandla kufuneka izotywe ngononophelo yaye ngomlinganiselo owaneleyo.
Iringi ezitsaliweyo nezicinezelweyo
Iqokobhe ngalinye elinesimmetri yokujikeleza lilinganiselwe sisangqa esinye okanye amabini athe tyaba (umz. 7). Kule miphetho linokwamkela kuphela loo mithwalo kunye neempendulo zezixhaso ezinesalathiso setangenti kwi-meridian. Ukuba amandla angaphandle anesalathiso esinye esahlukileyo, njengomthwalo P osuka kwinxalenye ephezulu yesakhiwo okanye impendulo S yezantsi yetanki eboniswe kumz. 97, la mandla kufuneka, njengoko kubonisiwe emfanekisweni, ahlulwe abe zizinto ezilandelayo kwicala lesangqa esithe tyaba kunye netangenti kwi-meridian. Icandelo P/sinφ0 okanye S/sinφu lilingana namandla aqhelekileyo kwicala le-meridian Nφ asebenza apho, ngelixa ukwamkela amandla athe tyaba Pctgφ0 okanye Sctgφu kufuna umsesane owamkela ukutsalwa, okanye ukucinezelwa, apho lo mthwalo werediyali ubangela amandla aqhelekileyo + P r0 ctgφ0, okanye -S ru ctgφu. Imisesane enjalo, ngaphandle kwemiphetho yeqokobhe, kufuneka ibekwe nakuzo zonke iindawo apho igophe le-meridian linokugotywa. Zisoloko zibangela ukuphazamiseka kwemeko yoxinzelelo ye-membrane.
Umz. 7
Iingcinezelo ezibangelwa kukugoba kumaqokobhe ajikeleze ngentsingiselo enye
Iifom zesayensi ye-membrane azinani laneleyo leekonstanti zokudibanisa ukuze zonke iimeko zomda ezihambelana ngokwenene nomsebenzi obekiweyo zifezekiswe. Ngokukodwa kwizigqubuthelo ezinesimetriki yokujikeleza, akunakwenzeka ngokukhetha ngokufanelekileyo iikonstanti zokudibanisa ukufikelela ekubeni ukwanda εϑ = Nϑ/Et kwicala lesangqa ecaleni komda wesigqubuthelo lilingane nokwandiswa okufanelekileyo kwelinye ilungu lesakhiwo elidityaniswe ngokuqinileyo nalo apho. Oku kuyasebenza nakwiigqubuthelo apho ecaleni kwesangqa esithe tye esinye ukugoba kwemeridiyane, ubukhulu besigqubuthelo okanye umthwalo kwiyunithi yommandla kutshintsha ngesiquphe. Kwanaxa isigqubuthelo singaqiniswa ngesangqa ecaleni komda othile, kodwa kule ndawo sinomthwalo onemikhosi enecomponent kwicala le-normal kwisigqubuthelo (umz. umthwalo P ku fig. 7 xa kucingelwa ukuba isangqa sisusiwe), asinakuwamkela loo mithwalo kuphela ngeemikhosi zemembrane. Kwiimeko ezinjalo amandla okucheba kunye neethemomenti zokugoba (fig. 8) zidlala indima ebalulekileyo kulwabiwo lwemikhosi kwisigqubuthelo, nto leyo ekubalweni kwe-static kufuneka ithathelwe ingqalelo.
Umz. 8
Ukubala ngokuchanileyo iqokobhe ekugobeni, ngaphandle kwimeko ekhethekileyo elula kakhulu yeqokobhe le-cylinder, ngumsebenzi onzima kakhulu. Kumaqokobhe aneendonga ezibhityileyo kunokwakhiwa ithiyori elula neyisebenziseka kakhulu esekelwe kwinyani eyaziwa kwithiyori engqongqo, yokuba iindawo zoxinzelelo ngenxa yokugoba zilinganiselwa kummandla omxinwa kufuphi nomda kwaye ziyehla ngokukhawuleza njengoko umgama ukusuka emdeni usanda. Oku kwenza kube nokwenzeka ukushiya ngaphandle inani elikhulu lamalungu kwisibalo se-differential esichanekileyo, yaye eso sibalo sifumana imo elula.
Ukuba ngaphakathi kwendawo engqinelana nomda κ kuphela ebalulekileyo kufakwe ixabiso eliphakathi, kwaye oku phantse kusoloko kunokwenzeka, isisombululo sobalo lelithi
Izinto 4 ne 5
apho a1, b1, a2, b2 zizigxina zokudityaniswa. Kuba isisombululo sinomdla kuphela kufutshane nomda φ=φ0, kuyafaneleka ukuba umgama we-angle ω=φ0-φ okanye ω=φ-φ0 ukusuka kulo mda ungeniswe njengekhowudi, ngoko ke ngokuguqula isisombululo esingentla kufumaneka intetho yesibini ekhankanyiweyo. Apha kuvela kuphela izigxina ezimbini zokudityaniswa A, B okanye C, ψ, kuba inxalenye yesibini yesisombululo equlathe into eκω, yaye ke ngoko enganciphi ngokwanda kwe ω, inokukhutshelwa ngaphandle kokuqwalaselwa.
Ngokusekelwe kwinxaki 5 kufumaneka la maxabiso alandelayo eenyanzeliso ezinqamlezayo kunye nokujika κ kwetangente ye-meridian:
Uxinzelelo oluphuma ekugobeni kwiitanki zesimo sesilinda esijikelezayo
Masithi isikhongozeli esisilinda esiphakamileyo h sigcwaliswe ngamanzi (umz. 9), ngoko ke kumphakamo x ngaphezu kweziseko ezimbini zoxinzelelo lwamanzi luba p=γ(h-x). Ukuba kwalo mphakamo, kusetyenziswa iindawo ezimbini ezithe tye ezinomgama dx. kusikwa kwisingxobo iringi aze lo ringi wahlulwe ecaleni kwedayamitha enye ube ngamacandelo amabini, imeko yokulingana yelinye lawo inika amandla e-membrane kwiringi Nφ=pa. Ukuba ubukhulu besikhongozeli kule ndawo ngu t, ukudilata kwiringi ngu εφ=Nφ/Et yaye ngoko ukwanda kweradiyasi yesikhongozeli (ukugobeka) ngu
Kumda ongezantsi x=0 ngoko ke
Umz. 9
Akukho nanye kwezi zimbini ngokuqhelekileyo ehambelana neemeko ezisemda, kuba ukuguquka kodonga kuthintelwa ngenxa yokudibana nomzantsi wetanki. Kule meko, ekudibaneni phakathi komzantsi nodonga lwesilinda kuvela amandla anqamlezileyo Qx0 kunye nemizuzu Mx0 (umz. 11), ubungakanani bazo kufuneka bumiselwe ngendlela yokuba, kunye namandla emembrane asandul’ ukubalwa kwiqokobhe, zibangele olu guquko kumda weqokobhe oluvunyelwa ngumzantsi.
Umz. 10, 11, 12, ngokulandelelana kwazo
Kwi sl. 11 kuboniswe into yeqokobhe dx*a dφ namandla asebenza kuyo. Imeko yokulingana kwamandla kwicala elingqameneyo neqokobhe inika
dQx a dφ + Nφ dx dφ = p a dφ dx,
apho kufunyanwa khona ngokwahlula ngo dx dφ:
a Q’x + Nφ = p a.
Kusuka kwimeko yokuba umzuzu ojikeleze itangenti ethe tye kwisilinda ngu-zero kufumaneka oku:
dM/dx = M’x = Qx
Ngokuphelisa amandla ewela ngokuthe tye Qx kwezi zibini zeequations kulandela
a M’’x + Nφ = p a.
Iyun. 6
Kule equation ezi nguvu ezingaziwayo zokunqamla zingachazwa ngehexa w. Ku Nφ sele kufunyenwe Nφ=Etw/a, yaye i-moment ilingana nokugobileka kwe-meridian w’’, oko kukuthi Mx=Kw’’, apho, njengakwiipleyiti, K=Et3/12(1-μ2) kukuqina kweqokobhe, okunokutshintsha ngokuhambelana no x. Ukuba la magama eemikhosi ephakathi afakwa kwi-equation (6), kufumaneka i-equation eyahlukileyo yethiyori yetanki:
Kwitanki enobukhulu bodonga obungaguqukiyo, isisombululo sithi:
Nye.7
apho λ4=3(1-μ2)/a2t2. Ukuba λh inkulu (masithi, ingaphezulu ko 3), kulula ngakumbi ukusebenzisa imisebenzi ye-exponential endaweni yemisebenzi ye-hyperbolic, ngoko ke:
Nye.8
Ngelo xesha, zinokumiselwa ngokuzimeleyo omnye komnye amagaqa A1, B1 avela kwiimeko zomda kumda osezantsi, kwaye amagaqa A2, B2 avela kwiimeko zomda kumda ophezulu, apho ngokuqhelekileyo kufunyanwa A2=B2=0. Ngokusekelwe kwii-equations (8) kunye (7) kufunyanwa imikhosi yokusika, xa ubalo luqhutywa kwicala elibuyiselweyo kuze kuzo zonke iindawo kufakwe i-equation (8) kunye (7); ke, umzekelo, ku A2=B2=0:
Xa iindonga zetanki ziqiniswa ngokuqinileyo kwipleyiti, ezantsi kwetanki ekutyebile ngokwaneleyo ukuba kungathathwa njengokuqinileyo, iikonstanti A1, B1 kufuneka zimiswe kwiimeko zokuba x=0, w=0 kunye w’=0, ngoko ke kufunyanwa:
Ukuba isiseko setanki yipleyiti okanye iqokobhe elibhetyebhetye, amandla omnqamlezo Qx kunye neethemomenti Mx ecaleni kwesangqa somda phakathi kwesakhiwo esisezantsi nodonga lwesilinda kufuneka zimiselwe ngeendlela zethiyori yeenkqubo ezingamiselwanga ngokwamanani, ngokusekelwe kwimfuno yokuba Mx kunye w’ kumacandelo omabini zibe nexabiso elifanayo.