Amagobolondo abizwa ngokuthi yizithwali zobuso, indawo yawo ephakathi engesiyisicaba kodwa igqamile ngokusobala. Ukuziphatha kwawo kokuma kwesakhiwo kuhluka kakhulu kokwepulanga. Uma enesimo esifanele, ukucindezeleka kwawo kuba kuncane kakhulu, ukuqina kwawo kuba kukhulu ngokwezinga elifanele, kanti ukubala ezimweni eziningi kuba lula kakhulu.
Ukucindezeleka kwegobolondo ngalinye kungahlukaniswa kube izingxenye ezimbili: ukucindezeleka kwe-membrane nokugoba. Ukucindezeleka kwe-membrane, ngokufanayo nokucindezeleka kwepuleti elithwele ngaphakathi kwendiza yalo, kungavezwa ngamandla esigaba endaweni ethangential - isibonelo esigabeni x=const. amandla avamile _Nx=_σx*t kanye namandla okushefa _Nxy=_τxy*t, lapho t kuwugqinsi lwegobolondo. Ukucindezeleka ngenxa yokugoba kuyafana nokwezinye amapuleti futhi kungamelwa ngamamoment okugoba Mx, amamoment e-torsion Mxy kanye namandla okushefa Qx.
Izici ezibalulekile zamagobolondo zisekelwe eqinisweni lokuthi ngokuvamile ukucindezeleka ngenxa yokugoba akunabo ubukhulu noma ukubaluleka kokucindezeleka kwe-membrane, ngakho kungaba lula ukungakunaki ngokuphelele. Kulowo mehluko, konke ukucindezeleka kusatshalaliswa ngokulinganayo kuzo zonke izindawo zobukhulu begobolondo futhi kusebenza ngokuthambekele ebusweni obuphakathi. Izibalo ezisuselwa kule mibono zingena ngaphakathi komkhakha wethiyori ye-membrane yamagobolondo.
Ithiyori yegobolondo elijikeleze ngokulinganayo ngaphansi komthwalo ojikeleze ngokulinganayo
Amafomula ajwayelekile
Njengemigqa yokuxhumanisa kuthathwa ama-meridian kanye nemijikelezo ehambisanayo ebusweni obuphakathi begobolondo, ngakho-ke izixhumanisi yilezi: i-azimuth ϑ (“i-longitude ye-geographic”) kanye nokutsheka φ kwethanjana eliya ku-meridian maqondana nendiza eqondaniswe ne-axis yokulinganisa (umfanekiso 1a). Ngakho-ke amandla okusika yilezi: amandla avamile Nφ ngasemgqeni we-meridian kanye namandla avamile Nϑ emjikelezweni (umfanekiso 1b). Amandla okushefa Nφϑ awaveli ekucindezelweni okulingana ngokuzungezayo. Umthwalo ngeyunithi yendawo uvezwa kanje (umfanekiso 1b): Y ngokuthambekela ku-meridian, okuhle lapho φ ikhula, Z ivamile egobolondweni, okuhle ibheke ku-axis yokulinganisa.
Umd. 1
Fig. 2
Masiqonde ukuthi i-radius yokugoba kwe-meridian ngu r1. Iwumsebenzi we-engeli φ ngakho-ke ngesibalo _r1=r1(_φ) kunqunywa ukuma kwe-meridian. Lokhu kungabhekwa njengesibalo se-meridian futhi sithi, isb.
kwendingiliza r1=a=const.
for the parabola r1=a/cos3__φ
_i-ellipse r1=a2b2(a2sin2__φ+b2cos2__φ)-3/2
Ukuze kubalwe amandla avamile N__φ ohlangothini lwe-meridian kudingeka kubekwe umbandela wokulingana kwengxenye yegobolondo elele ngaphezu kombuthano ohambisanayo φ (sl. 2). Umphumela R wemithwalo Y no Z ehlasela le ngxenye uthe nkqo, ngenxa yokufana. Ubukhulu bawo butholakala ngokuhlanganisa phezu kwendawo yegobolondo kusukela φ’=0 kuya ku φ’=φ. Indawo yengxenye yegobolondo ngu dF=r1d__φ’*rd__ϑ, ngakho ingxenye emile yomthwalo (Ysin__φ’+Zcos__φ’)dF. Kuyo yonke ingxenye eyindilinga yegobolondo elele phakathi kwemibuthano φ’ no φ’+dφ’ umphumela womthwalo wangaphandle uthi:
dR=2__πr (Ysin__φ’+Zcos__φ’) r1d__φ’,
lapho ngokuhlanganisa maqondana no-φ’ engxenyeni yegobolondo elele ngaphezu kwendilinga ehambisanayo φ’=φ kutholakala:
Isib. 1
Lo mthwalo uthwalwa amandla avamile aqondiswe e-meridian, asebenza emkhawulweni wendilinga ebonakalayo; ingxenye eqondile yomphumela walawa mandla ingu 2__πr * N__φ sin__φ, ngakho-ke ngokulinganisa kusuka lapha kutholakala amandla avamile afunwayo
Umth. 2
Uma igobolondo engxenyeni engenhla isikwe ngohlangothi lwesiyingi φ=φ0 (isib. imbobo yokukhanyisa ku-dome), umkhawulo ongezansi wokuhlanganisa uyiqiniso, φ0, hhayi zero. Uma emaphethelweni egobolondo elivele ngale ndlela kusebenza nomthwalo R0, nawo kufanele wengezwe kumphumela R (sl. 3).
Isith. 3
Ukuze kunqunywe amandla ajwayelekile N__ϑ kudingeka kubekwe umbandela wokulingana kwento yegobolondo eqondile endizeni ethangentiali (umz. 4). I-risitho yomthwalo wangaphandle kulo mqondiso inani layo lingu Z r1 d__φ r d__ϑ. Amandla N__φ*r d__ϑ alele endizeni ye-meridiyali enza phakathi kwawo i-engeli encane d__φ, ngakho-ke risitho yawo iqondiswe enormalini egobolondweni N__φ r d__ϑ*dφ. Ngokufanayo, namandla Nϑ r1 dφ alele endizeni yesiyingi esivundlile futhi enza phakathi kwawo i-engeli dϑ anerisitho Nϑ r1 dφ*dϑ nayo elele endizeni yesiyingi esivundlile, ngakho-ke enormalini egobolondweni enza i-engeli 0,5_π-φ_, ukuze embandelweni wokulingana kungene kuphela ingxenye yawo Nϑ r1 dφ dϑ*sinφ. Ngakho-ke umbandela wokulingana uthi
noma, lapho kuhlukaniswa ngo-r r1 dϑ dφ:
Eyodwa.3
Lapha nge-r2=r/sinφ kubhalwe irediyasi yesibili eyinhloko yokugobeka kwegobolondo.
Umfanekiso 4
Idomu eyindilinga
Uma umumo wemidiyane unikezwe ngokuhlaziya ngenkulumo r1=r1(φ) futhi uma ku-terete Y(φ) no Z(φ) kunikezwe izinkulumo ezihlaziywayo, amandla okusika egobolondweni angahlale anqunywa ngokuhlanganisa ngendlela evaliwe noma ngokwezibalo, kusetshenziswa umthetho ka_Simpson_. Ngedomu eliyindilinga elinobubanzi a kulandelayo kunikezwa amandla okusika kwezinye izimo zomthwalo:
Ifomula yokugcina, enikeza amandla okusika angenamkhawulo ku φ=0, isebenza kuphela ebangeni elithile ukusuka endaweni lapho amandla esebenza khona. Emkhakheni oseduze nendawo lapho amandla enza khona, ngisho noma asatshalaliswa phezu kwendawo yesiyingi sobubanzi obunqunyiwe kodwa obuncane, umthwalo uthwalwa kakhulu ngokugoba.
Amafomu amakhobokhombisi avulekele engxenyeni engenhla angatholakala kulawo angaphambilini, uma emthwalweni wangempela kufakwa umthwalo oqanjiwe P esicongweni, ubukhulu bawo bunqunywa kanje uma amandla avamile aphelele ohlangothini lwe-meridian asebenza onqenqemeni olungaphezulu lwekhobokhombiso φ=φ0 lingu Nφ=0, noma lilingana nenani elithile elinqunywe yizinga lamandla angaphandle lawa khobokhombiso awamukelayo lapha.
Igobolondo eliyikhoni
Umfanekiso. 5
Kod konusne ljuske se nagib meridijana φ ne može koristiti kao koordinata, jer on ima u svim tačkama istu vrednost. Umesto njega uvodi se odstojanje s od vrha kupole mereno duž izvodnice (sl. 5). Normalna sila u pravcu meridijana u skladu sa tim označava se sa Ns. Potrebni obrasci mogu se dobiti iz navedenih pod 1 kada se izvrši granični prelaz. Iz jednačine (2) dobija se na taj način
futhi kusukela esibalweni (3)
Nϑ = -r2 Z = -Z s ctga.
Ezimweni ezibaluleke kakhulu zomthwalo, kusetshenziswa lezi zifanekiso ezilandelayo:
Inqubo eyingcaca yesimo esingahleliwe se-meridiyeni
Fig. 6
Uma ijika le-meridian linganikezwanga ngesisho se-analytical, kodwa, ngokwesibonelo, ngokomfanekiso, ukunquma i-radius yokugoba kuba nzima kakhulu futhi kunganembi kakhulu. Kuleso simo kuwusizo kakhulu ukusebenzisa indlela yomfanekiso (sl. 6).
Igobolondo lihlukaniswa ngezindiza eziningi ezinkulu φ=const., kubalelwa izisindo Δ_R_ zezindawo eziyindilinga eziphakathi kwezindiza futhi kungcono ukuzihlukanisa ngokushesha ngo-2_π_. La mandla ΔR/2π afakwa emdwebeni wamandla (sl. 6b). Uma-ke, ngokwesibonelo, ngeduze kwephuzu lokuhlukanisa 7 kudwetshwa umugqa oqondile ohambisana ne-tangent ku-meridian ephuzwini le-meridian 7, khona-ke ukuvundlile okuhamba ngephuzu eliphezulu lomdwebo wamandla kuzolunqamula khona ngobude obungu R1/2π sinφ7 kuso, ngokusekelwe esibhalweni samandla (2), ngokuhlukanisa ngo-r efanele kutholakala amandla avamile afanele ohlangothini lwe-meridian.
Ukuze kunqunywe amandla emasongweni kusetshenziswa umbandela wokulingana kwamandla avundlile entweni eyodwa yegobolondo. Uma kusebenza imithwalo emi mpo kuphela, lo mbandela uthi (sl. 4):
Lapho lapha dφ kufakwa umehluko ophelile Δφ, ohambisana nokwahlukaniswa okwamukelwayo kwegobolondo, futhi lapho esikhundleni sika r1 dφ kufakwa ubude Δs besici se-meridian, kutholakala kanje
Kubakaki ohlangothini lwesokudla kunomchilo osika emugqeni ovundlile ohlelweni lwamandla. Ngakho-ke lonke uhlangothi lwesokudla lumelela izingxenye phakathi kwamaphuzu okuhlukanisa kulo mugqa. Ukuze sikwazi ukukufunda ngokwanele ngokunembile, uhlelo lwamandla kufanele ludwetshwe ngokucophelela nangokwesilinganiso esikhulu ngokwanele.
Izindandatho ezidonsiweyo nezicindezelweyo
Igobolondo ngalinye elilingana ngokuzungeza liboshelwe ngendilinga eyodwa noma emibili evundlile (isith. 7). Kule mibono, ngokomgomo lingamukela kuphela leyo mithwalo nokusabela kwezisekelo enomkhombandlela wethangenti kumeridiyeni. Uma amandla angaphandle enomkhombandlela ohlukile, njengomthwalo P ovela engxenyeni engenhla yesakhiwo noma ukusabela S kwesisekelo sethangi esiboniswe esith. 97, la mandla kufanele, njengoba kuboniswe esithombeni, ahlukaniswe abe izingxenye eziya ngendandatho evundlile kanye nethangenti kumeridiyeni. Ingxenye P/sinφ0 noma S/sinφu ilingana namandla avundlile ngomkhombandlela wommeridiyeni Nφ asebenza kuleyo ndawo, kanti ukuze kwamukelwe amandla avundlile Pctgφ0 noma Sctgφu kudingeka indandatho emukela ukudonsa, okungukuthi ukucindezelwa, futhi lapho lo mthwalo osuka phakathi nendawo udala amandla ajwayelekile + P r0 ctgφ0, okungukuthi -S ru ctgφu. Izindandatho ezinjalo, ngaphandle kwemiphetho yegobolondo, kufanele zifakwe nakuzo zonke izindawo lapho umugqa wommeridiyeni unokuphuka. Zihlala zidala ukuphazamiseka kwesimo sokucindezeleka se-membrane.
Umfan. 7
Izingcindezi ngenxa yokugoba kumagobolondo anesimiso sokujikeleza esilinganayo
Obrasci membranske teorije ne sadrže dovoljan broj integracionih konstanata da bi se mogli ispuniti svi granični uslovi koji stvarno odgovaraju postavljenom zadatku. Posebno kod rotaciono simetričnih ljuski, nije moguće nekim pogodnim izborom integracionih konstanata postići da dilatacija εϑ = Nϑ/Et u pravcu prstena duž ivice ljuske bude jednaka odgovarajućoj dilataciji nekog drugog konstruktivnog dela koji je sa njom na tom mestu čvrsto vezan. Ovo isto važi i za ljuske kod kojih se duž jednog horizontalnog kruga skokovito menja krivina meridijana, debljina ljuske ili opterećenje po jedinici površine. I kada ljuska duž neke ivice nije ukrućena prstenom, ali je na ovom mestu opterećena silama koje imaju komponentu u pravcu normale na ljusku (npr. opterećenje P na sl. 7 kada se zamisli da je prsten uklonjen), ona ne može da primi ovakve terete samo preko membranskih sila. U ovakvim slučajevima smičuća sila i momenti savijanja (sl. 8) igraju bitnu ulogu pri rasporedu sila u ljusci, što se u statičkom proračunu mora uzeti u obzir.
Umdwebo 8
Ukubala okunembile kokugobeka kwegobolondo, ngaphandle kwesimo esikhethekile esilula kakhulu segobolondo lesilinda, kuwumsebenzi onzima kakhulu. Kwigobolondo elinezindonga ezincane kungakhiwa ithiyori elula kakhulu futhi ewusizo yokulinganisa, esekelwe eqinisweni elaziwayo othiyori eqinile, lokuthi izingcindezi ezivela ekugobekeni zikhawulelwa endaweni encane eduze komphetho futhi zehla ngokushesha njengoba ibanga ukusuka emaphethelweni likhula. Lokhu kwenza kube nokwenzeka ukuba inani elikhulu lamalungu esibalo esiqondile sokuhlukanisa linganakwa, ngakho leso sibalo sithola ifomu elenziwe lula.
Uma ngaphakathi kwephuzu lomngcele kuphela elithakazelisayo κ kufakwe inani eliphakathi, futhi lokhu cishe kuhlale kungenzeka, isisombululo sesibalo siyoba
Isib. 4 no 5
lapho a1, b1, a2, b2 kuyizinkinga zokuhlanganisa. Njengoba isixazululo sinentshisekelo kuphela eduze komkhawulo φ=φ0, kulungele ukwethula ibanga le-engeli ω=φ0-φ noma ω=φ-φ0 kulo mkhawulo njengokudidiyela, bese ngokuguqula isixazululo esishiwo ngenhla kutholakala isisho sesibili esishiwo. Lapha kuvela kuphela izinkinga zokuhlanganisa ezimbili A, B noma C, ψ, ngoba ingxenye yesibili yesixazululo equkethe isici eκω, futhi ngenxa yalokho njengoba ω ikhula ayinciphi, ingakhishwa ekucatshangelweni.
Ngokusekelwe kusibalo 5 kutholakala amanani alandelayo wamandla asikelezayo kanye nokujikeleza κ kwe-tangenti ye-meridian:
Ukucindezeleka okubangelwa ukugoba emathangini esimo se-cylinder eyindilinga
Ake sithi ithangi eliyisilinda elinobude h ligcwele amanzi (umz. 9), khona-ke ebangeni elingu-x ngenhla kwamathangi amabili ingcindezi yamanzi ingu p=γ(h-x). Uma kuleli zinga kusuka ezindaweni ezimbili eziseceleni ezivundlile ezihlukaniswe ngo-dx. kusikwa iringi ethangini bese leyo ringi ihlukaniswa phakathi ngobude besibubanzi obubodwa ibe izingxenye ezimbili, umbandela wokulingana wenye yazo unikeza amandla e-membrane eringini Nφ=pa. Uma ugqinsi lwethangi kule ndawo lungu t, ukunwebeka eringini kungu εφ=Nφ/Et futhi ngenxa yalokho ukwanda kweradiyasi yethangi (ukugoba) kungu
Onqenqemeni olungezansi x=0 ngakho-ke
Umfanekiso 9
Nakuba kokubili ngokuvamile kungahambisani nemibandela yomngcele, ngoba ukuguquka kodonga kuvinjwe ngenxa yokuxhumana nesisekelo sethangi. Kulokhu, ekuxhumaneni phakathi kwesisekelo nodonga lwesilinda kuvela amandla transverse Qx0 namamomenti Mx0 (sl. 11), ubukhulu bawo kufanele bunqunywe ukuze, kanye namandla e-membrane asanda kubalwa egobeni, kubangele lokhu kuguquka emaphethelweni egobeni okuvunyelwa yisisekelo.
Sl. 10, 11, 12, ngokulandelana
Esithombeni. 11 kuboniswe into yegobolondo dx*a dφ enamandla asebenzayo kuyo. Isimo sokulingana kwamandla ohlangothini olujwayelekile kugobolondo sinikeza
dQx a dφ + Nφ dx dφ = p a dφ dx,
lapho-ke ngokuhlukanisa ngo dx dφ:
a Q’x + Nφ = p a.
Kusukela esimweni sokuthi umzuzu mayelana ne-tangente evundlile kusilinda ulingana noziro kutholakala:
dM/dx = M’x = Qx
Ngokususa amandla e-transversal Qx kulezi zibalo zombili kulandela
a M’’x + Nφ = p a.
Isib. 6
Kulesi sibalo lezi zixuku ezingaziwa zingavezwa ngosizo lokugoba w. Ku-Nφ sekuvele kutholakele Nφ=Etw/a, kanti umzuzu ulingana nokugobeka kommeridiyeni w’’, okungukuthi Mx=Kw’’, lapho njengoba nakumapuleti K=Et3/12(1-μ2) kuwukuqina kwegobolondo, okungashintsha nge-x. Uma lezi zinkulumo zamandla amaphakathi zifakwa esibalweni (6), kutholakala isibalo esingafaniyo sethiyori yetangi:
Ngakho-ke, ithangi elinobukhulu bodonga obungaguquki, isixazululo sithi:
Eyodwa.7
lapho λ4=3(1-μ2)/a2t2. Uma λh inkulu (ake sithi, ingaphezu kuka 3), kulula kakhulu ukwethula imisebenzi ye-exponential esikhundleni semisebenzi ye-hyperbolic, ngakho-ke:
Eyodwa.8
Tada se mogu nezavisno jedna od drugih odrediti konstante A1, B1 iz graničnih uslova na donjoj, a konstante A2, B2 iz graničnih uslova na gornjoj ivici, pri čemu se po pravilu dobija A2=B2=0. Na osnovu jednačine (8) i (7) dobijaju se presečne sile, kada se proračun sprovede u obrnutom pravcu i svuda uvede jednačina (8) i (7); tako je npr. za A2=B2=0:
Lapho izindonga zethangi ziboshwe ngokuqinile epuletini, phansi kwethangi okudele kakhulu ukuze kubhekwe njengokunganyakazi, izinkambiso A1, B1 kufanele zinqunywe kusukela ezimeni zokuthi x=0, w=0 no w’=0 bese kutholakala:
Uma phansi kwethangi kuyipuleti elinwebekayo noma igobolondo, amandla asika‑transverse Qx kanye namamomenti Mx eceleni komjikelezo onqenqemeni phakathi kwephansi nodonga lwesilinda kufanele kunqunywe ngezindlela zethiyori yamasistimu anganqunywa ngendlela yokumiswa ngokwesibalo, ngokusekelwe esidingweni sokuthi Mx kanye no w’ kuzo zombili izingxenye kube nenani elifanayo.