Izisekelo
Umsebenzi wokuqina kwezinto uwukunquma ukuthi yimaphi amandla angaphandle angamelwa umzimba oqinile (isb., isakhiwo, ingxenye yesakhiwo noma umhlaba). Ukuze kuphendulwe lo mbuzo kusetshenziswa imiqathango emibili: ngakolunye uhlangothi, ama-stress akufanele adlule imikhawulo ethile encike ohlotsheni lwento, kanti ngakolunye uhlangothi, ibhalansi phakathi kwamandla angaphandle nangaphakathi kufanele izinzile. Ngokuhambisana nalokhu, zonke izinkinga zokuqina kwezinto zingahlukaniswa zibe “Izinkinga zama-stress” kanye “nezinkinga zokuzinza.
Ezindukwini nasezikhonkwaneni nasezithwalweni ezakhiwe ngazo (ama-truss, amafreyimu) ukunqunywa kwengcindezi kwenziwa ngezinyathelo ezimbili, ngaleyo ndlela okokuqala kususelwa emandleni angaphandle anikeziwe kubalwe i-resultant yamandla angaphakathi adluliswayo ngengxenye yokusikwa, bese kulezi “mibutho yesigaba” kunqunywa izingcindezi. Ingxenye yokuqala yale nqubo iyisigaba esikhethekile, esibanzi, i-statics yezakhiwo zobunjiniyela, enezindlela zayo ezithuthukisiwe futhi ngokuvamile ehlukaniswa nokumelana kwezinto, umsebenzi wayo omiswa ekunqumeni izingcindezi ezivela emandleni esigaba anikeziwe.
Imiqondo eyisisekelo yokumelana kwezinto
Encazelweni yokucindezeleka kufinyelelwa ngale mibono eyisisekelo elandelayo. Ake emzimbeni kusebenze uhlelo olulinganiselayo lwamandla angaphandle. Ake sicabange ukuthi umzimba siwuhlukanise ngephrofayili engahleliwe waba izingxenye ezimbili, bese sisusa enye yazo kanye namandla asebenza kuyo; khona-ke umthelela wayo engxenyeni esele, ukuze ukulingana kwamandla nokusabalala kokuguquka kuhlale kungashintshile, kufanele kushintshwe ngamandla angeziwe adluliselwa ngendawo yokunqamula. Lawa mandla “angaphakathi” asakazwa ngokuqhubekayo phezu kwendawo yokunqamula, ukuze isici ngasinye sendawo dF sibe namandla dβ. Uma kwakhiwa isilinganiso dβ dF bese kwenziwa ukudlula komkhawulo dF -> 0, khona-ke lesi sabelo sikhombisa inani lomkhawulo elibizwa ngokuthi ukucindezeleka. Ukucindezeleka engxenyeni ethile yendawo kungu, njengaku dβ, futhi kungahlukaniswa kube izingxenye ezijwayelekile nezithambekele ku-dF, ukucindezeleka okujwayelekile σ kanye nokucindezeleka kokugunda τ.
Uma kusikwa indawo efanayo ezindaweni ezihlukene ngokweziqondiso ezahlukene, kuzohambisana nazo izingcindezi ezahlukene. Ikakhulukazi uma kuhlukaniswa emzimbeni ikhyubhu eliyisisekelo, eliboniswe ku-sl. 1, ebusweni ngalunye oluyisithupha kuzosebenza i-vector yokucindezeleka engahlukaniswa ibe izingxenye ezintathu ngesiqondiso samazinga okuhlangana x, y z. Izingcindezi ezisebenza ezinhlangothini eziphambene zobuso ziyahluka, vele, kuphela ngokwe-differential, ngakho kufanele kuhlukaniswe 3 * 3 = 9 izingxenye zezingcindezi, ezimakwe kanje:
Emigudwini evamile σ kunikezwa inkomba ye-eksisi lapho ilele khona, futhi ibhekwa njengemihle uma ibangela ukweluleka, ibe mibi uma ibangela ukucindezela. Imigudu yokushefa τ ithola izinkomba ezimbili, eyokuqala yazo ifana nenkomba yomugudu ovamile ohambisanayo, kanti eyesibili ibhekisa ku-eksisi lapho umgudu wokushefa usebenza khona. Uma isiqondiso esihle somugudu ovamile ohambisanayo sisendleleni ye-eksisi yokuxhumanisa enhle (engalungile), nomgudu wokushefa nawo ubhekwa njengomuhle uma usebenza ngasendleleni ye-eksisi yokuxhumanisa enhle (engalungile).
Isithombe 1.
Ukuhambisana kwama-stress okuchelela
Uma, ku-prismatic block eyisisekelo, fig. 1, kubekwa isimo sokuthi i-moment yawo wonke amabutho maqondana ne-eksisi x ilingana no-zero, kutholakala τyz dx dz * dy = τzy dx dy * dz Kusukela lapha, kanye nasezibalo ezimbili ezihambisanayo zama-eksisi y no z, kutholakala ukuthi izingcindezi zokushefa ezinama-indeksi afanayo ziyalingana phakathi kwazo τxy = τyx, τyz = τzy, τzx = τxz (1)
Ukuguquguquka kwezinto eziyingxenye
Ukuthi izingcindezi ezichazwe ngenhla zinengqondo ngokomzimba kuvela ekuhlobeni kwazo nencazelo ethwalwa yiyo yonke imizimba ngaphansi kwethonya lamandla angaphandle. Sl. 2 ibonisa ikhubhu eliyisisekelo elilodwa, elaliyingunxande ngaphambi kokuguquka futhi linezilinganiso zemiphetho dx, dy, dz. Ubude bemiphetho ngemva kokuguquka singabubhala ngo dx + Δdx, dy, + Δdy, dz + Δdz izilinganiso εx = Δdx|dx, εy =Δdy|dy, εz = Δdz|dz zibizwa ngokuthi ama-dilatation. Lawa ngamanani angenasayizi, futhi kuzo zonke izinto ezingabhekwa kwezokwakha mancane uma kuqhathaniswa no 1. Ngaphandle kokwelulwa kwemiphetho, ikhubhu eliyisisekelo dx * dy * dz lingase libhekane nokushintsha kwama-engeli aqondile ayekade ekhona phakathi kwezinhlangothi zalo.
Isithombe 2. ukugobeka kwengxenye
Kuze kube ngemva kokuguquka, i-engeli phakathi kwezindiza ezihlangana emaphethelweni e-OC ilingane no 
futhi ngokufanayo, ukuncipha kwe-engeli eqondile emaphethelweni AO kube ngu γyz, futhi ukuncipha emaphethelweni OB kube ngu γzx. Lezi zinguquko ezintathu zama-engeli γxy, γyz, γzx zibizwa ngokuthi ukushelela futhi nazo zihlale zincane kakhulu uma kuqhathaniswa no 1. Ngamakhomponenti ayisithupha e-ε no-γ, ukuguquka kwe-elementi yekhivhedrithi eliyinhlanganisela “ukuguquka okuncane” kuchazwa ngokuphelele. Ushintsho lwe-elementi yomthamo d_V = dx * dy * dz_ luthi ΔdV = (dx + Δdx) (dy + Δdy) (dz + Δdz) - dx dy dz, okusho ukuthi, lapho imikhiqizo yokwandisa inganakwa njengezincane zohlelo oluphezulu, kutholakala ukwanda kwe-cubic ϱ = ΔdV|dV = εx, εy, εz (2)
Ukususwa
Ukuguquka komzimba oqinile kungachazwa ngokuphelele nangale ndlela, ngokuthi kuzo zonke izindawo zawo kunikezwe ukuhamba leyo ndawo eye yayithola. Uma kususwa ekubhekweni ukunyakaza kobukhulu obuphelele obuhambisana nokunyakaza komzimba oqinile, ngaleyo ndlela, uma kudingeka, emsebenzini kwamukelwe uhlelo lwezixhumanisi oluhambayo, khona-ke nokunyakaza kwezingxenye μ, ν, ω kuhlala kuyizinga elincane, kanti okuphuma kwazo mayelana nezixhumanisi kuncane uma kuqhathaniswa no-1. Kule mbono, ngokomdwebo 3 ubude besici somugqa OA = dx ngemva kokuguquka
ngakho 
(3)
Ngendlela efanayo, kusuka kumfanekiso 3 kubonakala ukuthi ukushelela γxy γ1 + γ2: futhi futhi
(4)
Isithombe 3 ukushelela
(5) 
(6)
Lawa mabandlululo abizwa ngokuthi izimo zokuhambisana futhi abonisa ukuthi izakhi eziguqukile zingahlanganiswa njengemosaic ukuze isikhala sigcwaliswe ngaphandle kokuphazamiseka, okungeke kufezeke uma ukuguquka kwezinto kungahleliwe. Izimo zokuhambisana ziyizibalo ezihlukile, ngakho-ke, kusobala, zonke izingxenye eziyisithupha zokuguquka zekhiyubhu ngayinye zizimele komunye nomunye, kodwa ukuhleleka kwazo kunoma iyiphi indawo enwetshiwe elinganiselwe kuboshwe yizimo (5) kanye (6).
Njengoba lezi zimo zitholwe ngokwehlukanisa ezibalweni (3) no-(4), lapho zikhishwa kulahleka ingxenye yezixhumanisi ezikuwo amanani ezokuqala. Ngakho akwanele ukuba kugcwaliseke kuphela enye yalezi zinhlelo ezimbili zezibalo, kodwa zombili izinhlelo zezibalo kufanele zihlangatshezwe, uma kufunwa ukuthi ukuhambisana kokuguquka komumo kuqinisekiswe.
Izibalo ezihlukile zohlelo lokunwebeka
Ukuze kubalwe izingcindezi nokuguquka kwemizimba e-elastic kusetshenziswa ama-equation alandelayo:
Izimo zokulingana zesakhi esinobukhulu. Izimo zokuthi amamomenti mayelana nama-axis amathathu alingane noziro sezisetshenzisiwe kakade ekukhipheni isibalo (1). Izimo zokulingana kwamandla zinikeza ngokwesimo esiku sl. 4
Isithombe 4
(7a-c)
Uma izakhi zamandla omzimba (isib. isisindo, amandla e-centrifugal) zikhonjiswa ngo X, Y, Z ngeyunithi ngayinye yevolumu. Izixhumanisi phakathi kwezingcindezi nokukhubazeka. Ngaphansi kwalokhu kuqondwa isixhumanisi phakathi kwezingcindezi zezingxenye nokukhubazeka kwezingxenye. Emcabangweni we-elasticity ngokuvamile kubhekwa kuphela isixhumanisi esiqondile, esivezwa ngomthetho kaHooke:
(8a-c)
(8d-f)
Uma izibalo (8a-c) zixazululwa mayelana namazinga okucindezeleka, kutholakala
(8 a)
kso kanye nezibalo ezimbili ezihambisanayo. Umthetho ka-Hooke ovezwe ngesibalo (8) awumeleli umthetho wemvelo owenziwe ngokuphelele ngokuqinile, kodwa kuwukwenza kube lula ukuziphatha kwangempela, okuphambuka kuwo kancane noma kakhulu, kuye ngezinto ezisetshenziswayo nangobukhulu bokucindezelwa. Njengoba ukucubungula kwezibalo kwenkinga yokumelana kwezinto ezinobudlelwano obuyinkimbinkimbi, obungewona umugqa phakathi kokucindezeleka nokuguquka kudala ubunzima obukhulu kakhulu futhi empeleni kungasetshenziswa kuphela ezimeni ezilula kakhulu, ngisho nasezintweni (ukhonkolo!) ukuziphatha kwazo kuphambuka kakhulu emthethweni ka-Hooke, izibalo ezisuselwa kuwo kufanele zisetshenziswe njengesisombululo sokuqala, futhi ikakhulu sibe yiso sodwa esilinganiselwe, esingaphezulu kwalokho ngokuvamile sisebenziseka kakhulu futhi sinikeza ukuqonda okungaphezu kokuba kwekhwalithi kuphela. G = E|2 (1+μ).
Kusukela ekuxhumaneni phakathi kwengcindezi nokuguquka (8), kusukela ezilinganisweni zokuguqula (16) zezingcindezi kanye nesistimu efanele yezilinganiso zokuguquka kwezingxenye E no G zinobukhulu bengcindezi futhi kuzo zonke izinto zokwakha zinkulu uma ziqhathaniswa nezingcindezi σ no τ ezingavela. Kodwa kuleli qiniso kusekelwe ukuqagela okwamukelwe kuyo yonke indawo emfundisweni yokunwebeka, ukuthi ukuguquka kuncane. I-coefficient yokunwebeka ngokuphambene (inombolo kaPoisson) μ ayinabukhulu futhi ihlala iphakathi kuka 0 no 1/2 .
Izixhumanisi phakathi kwezinhlanekezelo zezingxenye nokusuka endaweni. Lezi zixhumanisi zinikezwa izibalo (3), (4). Zingokwemvelo yejiyomethri kuphela. Lezi zinhlelo ezintathu zinikeza 3+6+6=15 izibalo ze-15 ezingaziwa, okungukuthi ze-6 izingcindezi zezingxenye, 6 izinhlanekezelo zezingxenye kanye 3 ukususwa kwezingxenye. Ngakho-ke zanele ukunquma lezi ezingaziwa. Ukunqoba kwezibalo ezihlukene ezibanzi kangaka kungenzeka, ngokwemvelo, kuphela ezimweni ezikhethekile. Uma esibalweni (8) izinhlanekezelo zezingxenye zifakwa esikhundleni sokususwa kwezingxenye ngokwezibalo (3) kanye (4) bese izingcindezi ezijwayelekile σ kanye nezingcindezi zokusika τ, ngokwezibalo (8 d - f), zifakwa ezimweni zokulingana, isib. (7), kutholakala izibalo ezihlukene ezibizwa ngokuthi izibalo eziyisisekelo zethiyori yokunwebeka.
(9)
lapho kuyi 
i-Laplace-ov operator echaziwe. Ngokubheka ku (2) lawa izibalo ezintathu ezihlukile ezineminyakazo emithathu yezingxenye μ, ν, ω; kulokhu-ke ngokuhlukanisa ngokusekelwe ku (3), (4) no (8) kungatholwa zonke izingcindezi neziphambeko zezingxenye. Izibalo (9) zimelela indawo yokuqala evame ukuba usizo yokutadisha izimo ezikhethekile.
Umsebenzi wokuguquka
Incazelo
Lapho isekelo silayishwa, amaphuzu okuhlasela kwamandla angaphandle abhekana nokunyakaza okunwebekayo futhi amandla enza umsebenzi othile. Ngale ndlela amandla alethwe angadlulela ezimeni ezihlukahlukene. ‚Uma umthwalo usetshenziswa ngokuzumayo, ukuze inqubo yokuguquka ibe nesivinini esikhulu, ingxenye yaleli amandla iguquka ibe amandla e-kinetic, lawo ngokuhamba kwesikhathi ahlakazeka, kungaba ngokudluliselwa emhlabathini njengamagagasi okunwebeka aphela ekungapheli, noma ngokuguqulwa abe ukushisa ngenxa yokungqubuzana kwangaphakathi. Uma imithwalo ibekwa kancane kangangokuthi akukho ukwanda okubonakalayo kwamandla e-kinetic, ngakho-ke imithwalo ekhula kancane kusukela ku-zero isesimweni sokulinganisela okuqhubekayo namandla angaphakathi, amandla kusobala ukuthi asetshenziswa kuphela ekuguquleni umzimba futhi lapho abizwa ngokuthi umsebenzi wokuguquka.
Ukubalwa komsebenzi wokuguquka kuqala sizokubonisa engxenyeni encane elayishwe ngokudonswa ohlangothini olulodwa (fig. 5).
Ake sithi ukucindezeleka okukhona σ kanye nokunwebeka okuhambisanayo ε kuthole ukwanda dσ no dε. Khona-ke amandla σdF endleleni engu dε * dl azokwenza umsebenzi σdF * dεdl = σdεdV, uma u-dV umele ivolumu yengxenye encane. Uma ukucindezeleka kukhuphuka kusukela ku-zero kuya enanini lalo lokugcina futhi ukunwebeka ngokufanayo kusukela ku-0 kuya ku-ε, umsebenzi ophelele owenziwe ngeyunithi ngayinye yevolumu uzoba:
Ngokufanayo nakwiselementi ethwele ingcindezi yokusika τ (sl. 6) umsebenzi wokuguquka ngevolumu ngayinye (umsebenzi othile wokuguquka, amandla agcinwayo e-elastic):
lapho amandla amane τ * dF eyodwa kuphela enza umsebenzi.
Ngokuvamile, lapho yonke imithwalo emithathu yesimo sokucindezeleka ihlasela ingxenye eyisisekelo, kutholakala umsebenzi othile wokuguquka komumo ngokuhlanganisa imisebenzi yemithwalo ngayinye yesimo sokucindezeleka:
(10)
Ngokuhlukanisa ngasemkhawulweni ongaphezulu womunye nomunye walezi zinhlekelele, kutholakala ubudlelwano obusebenzayo esimweni esijwayelekile kakhulu:
(11)
nokunye okufanayo nakwezinye izinguquko zamakomponenti. Uma umzimba u-elastic, esimweni ngasinye esithile sokucindezeleka kuhambisana njalo isimo esifanayo sokuguquka, kungakhathaliseki ukuthi leso simo sifinyelelwe ngesikhathi sokulayisha noma sokukhipha umthwalo. Khona-ke ngaphansi kwama-integral kukhona imisebenzi enencazelo eyodwa, futhi amandla aphelele asetshenziswa ngesikhathi sokulayisha bese kukhululwa ngokuphelele ngu a = 0, njengoba kulesi simo imikhawulo ephezulu yama-integral iba ngu-zero. Ngakho-ke amandla aphelele alethwa emzimbeni ngesikhathi sokulayisha abuyiselwa ngesikhathi sokukhipha umthwalo.
Isithombe 6
Isithombe 7
Kumzimba ongenawo ukuqina okuphelele ubudlelwano phakathi kwezingcindezi nokuguquka kuwo wonke umjikelezo wokulayisha nokukhipha umthwalo bunomumo oboniswe cishe ku-sl. 7 ngemigqa O A B. Amandla 
alethwa ngesikhathi sokulayisha alingana nendawo OAA, kanti amandla abuyiselwa ngesikhathi sokukhipha umthwalo angendawo ABA, ngakho umsebenzi ohambisana nendawo enomthunzi uyalahleka (uguquke ube ukushisa). Uma enqubweni ye-oscillation ingcindezi ishintsha ngezikhathi ezithile phakathi komkhawulo omuhle 
nomkhawulo ongemuhle, 
ukuguquka okungelona-elastic kuhamba ngendlela efana naleyo eboniswe ngemigqa edwetshelwe ku-sl. 7 futhi ngesikhathi sesigaba ngasinye sokudlidliza amandla DABCD aguqulwa abe ukushisa ngeyunithi yevolumu. Ukuziphatha okunjalo ngesikhathi sokuguquka, lapho ukuguquka kusalela ngemuva kwengcindezi, kubizwa ngokuthi elastični histeresis, kanti ijika DABCD liyiluphu ye-hysteresis.
Umsebenzi wokuguquka noMthetho kaHooke
Uma emihlanganweni ekubalweni (10) kufakwa umthetho kaHooke, kungenziwa ukuhlanganisa, bese kutholakala izisho zomsebenzi othile wokuguquka:
(12a)
(12b)
(12c)
Uma omunye wale mibono efakwa esibhalweni sokulinganisa (11), kuphinde kutholakale umthetho kaHooke, izibalo (8), ngendlela exazululiwe ngokwezingcindezi. Isitatimende sokuthi umsebenzi wokuguquka uncika ezingxenyeni zokuguquka, njengoba kuboniswe ngesibalo (12b), ngakho-ke uyalingana nomthetho kaHooke. Uma isibalo (12c) sihlukaniswa ngokwezingcindezi, kuyatholakala
(13)
Ovi obrasci, za razliku od obrazaca (11), važe samo za tela koja se ponašaju prema Hooke-ovom zakonu i ne mogu se primeniti kada su veze između napona i deformacija drukčije. Razume se da se na desnoj strani jednačina (13) nalaze samo komponentalne deformacije izazvane naponima, a isključuju se sve ostale koje su eventualno mogle nastati usled promene temperature, puženja, bubrenja, rekristalizacije, itd.
IZIMISO EZIHAMBELANA NGOKUHLANGANA OKUHLANGANAYO EMQONDO WOKUNWEBEKA
Ukufuduka okungokomfanekiso. Isimiso samandla angaba khona amancane kakhulu
Njengoba umthetho kaHooke, izibalo (8) zingashintshwa ngesibalo esisodwa (12b), kanjalo esikhundleni sezimo zokulingana kungangeniswa umgomo wokunyakaza okubonakalayo, njengomthetho oyisisekelo jikelele owamukelekayo wemishini. Lo mthetho uveza ukuthi izimo zokulingana zihlukaniswa ngokuthi kuzo umsebenzi ophelele owenziwa yawo wonke amandla ngesikhathi sokushintsha okuncane kwesimo sokuguquka ulingana noziro. Uma izinguquko ezincane zokunyakaza okunwebekayo sizibeka njenge δμ δν, δω, khona-ke amandla evolumu achazwe ngesibalo (7) enza umsebenzi obonakalayo
namandla angaphezulu px, py, pz asebenza ku-elementi dF yendawo engaphandle yomzimba umsebenzi 
lapho i-integral kathathu isho wonke umthamo, kanti i-integral kabili isho yonke indawo engaphandle yomzimba. Ukuze kubalwe umsebenzi owenziwa amandla angaphakathi kusetshenziswa i-equation (12b), ngakho ngomsebenzi ngeyunithi yomthamo kutholakala
Umgomo wokunyakaza okubonakalayo ngokusekelwe kulokho unikeza
(14)
Uma imithwalo X, Y, Z px, py., pz ithathwa njengezingxenye zamandla adonsela phansi (isisindo sayo kanye nomthwalo wangaphandle), ama-integral ohlangothini lwesokudla amele amandla angaba khona alahlekelwe yile mithwalo, kanti uhlangothi lwesobunxele lumele ukwanda kwamandla angaba khona (elastic) omzimba, ngakho-ke lo mthetho uveza ukuthi amandla angaba khona ewonke e-beam nemithwalo elele kuyo esimeni sokulingana anenani elingaphezulu noma elingaphansi elikhulu. Uma leli nani eliphezulu lingu- minimum, ukulingana kuzinzile.
Umgomo wesilinganiso esincane samandla angaba khona ovezwe ngesibalo (14), inkulumo (12b) yomsebenzi wokuguquka kanye nemibandela yokuhambisana kokuguquka (5), (6) zakha uhlelo lwezibalo olwanele ukwakha umbono wokunwebeka, futhi ngokuyisisekelo luyalingana nohlelo lwezibalo. Lolu hlelo lungaba lusizo ikakhulukazi ezimweni lapho ukwanelisa izibalo ezihlukile, (9) kuletha ubunzima bokubala futhi ngenxa yalokho kufanele kufunwe isixazululo esilinganiselwe, isb., ekususweni kusengaphambili kucatshangwe ifomu elifanele eliqukethe ama-constant ambalwa amahhala bese lawa enqunywa ngesidingo sokuthi isibalo (14) sibe sihlangatshezwa. Ngakho-ke empeleni akutholakali isixazululo esiqinile senkinga, kodwa kuphela isilinganiso esingcono kakhulu esingafinyelelwa ngefomu lesixazululo elikhethiwe. Ukuthi ukusondela kwanele yini kuncike okokuqala kuhlobo lwesixazululo olwamukelwe, futhi ukusetshenziswa ngempumelelo kwale ndlela kudinga ngenxa yalokho ubuciko nesipiliyoni.
Umgomo kaCastigliano-v
Nakuba emthethweni wesisindo esincane samandla angaba khona kuqhathaniswa zonke izimo zokuguquka ezihlangabezana nezimo zokuhambisana kokuguquka, bese kukhethwa lezo lapho izingcindezi ezihambisanayo zihlangabezana nezimo zokulingana, emthethweni ka-Castigliano kuqhathaniswa zonke izimo zokucindezeleka ezihlangabezana nezimo zokulingana bese kukhethwa lezo lapho ukuguquka okuhambisanayo kuhlangabezana nezimo zokuhambisana kokuguquka. Lo mthetho uthi: kuzo zonke izimo zokulingana ezingenzeka, kwenzeka ngempela leso esihambisana nomsebenzi omncane wokuguquka. Umthetho ka-Castigliano kanye nesibalo (12c) somsebenzi wokuguquka nezimo zokulingana kwakha uhlelo lwezibalo olwanele ekwakhiweni kokumelana kwezinto. Njengoba lo mthetho uqukethe umthetho ka-Hooke, kungenzeka ukuwusebenzisa kuhlobene nokuqagela ukuthi ukuguquka kungachazwa ngokuphelele ngalo mthetho. Lokhu kudinga hhayi kuphela ukuziphatha kwezinto okune-elastic okuqondile, kodwa futhi akuvumeli izinguquko zokushisa.
Ukuziphatha kwezinto ngaphezu kwemikhawulo yobunwebeka
Izimo lapho kunomthwalo omile
Ukuguquka kwezinto ngaphansi kwethonya lezingcindezi kuyisenzakalo esiyinkimbinkimbi kakhulu, ngakho kufanele senziwe sibe lula ngezindlela ezahlukene ukuze kuqondakale. Okunye kwalokhu kwenza kube lula wukucabanga ukuthi imithwalo ifakwa kancane kancane, njengoba kwenziwa, isibonelo, ngezibonelo ngesikhathi sokuhlolwa kokudonswa nokucindezelwa.
Uma induku yensimbi egqokwe umthwalo wokudonswa ibhekene nomthwalo okhula kancane kancane futhi kubhekwa ukunwebeka kwayo ε, kutholakala idayagramu eboniswe ku sl. 8. Ekuqaleni ukunwebeka kuncane kakhulu futhi kulingana nengcindezi, njengoba kudingwa umthetho ka Hooke. Kusukela ekucindezelekeni okuthile, ukulingana kuyaphela futhi ukunwebeka kukhula ngokushesha. Indawo eqondile yomkhawulo walokhu kulingana kunzima ukuyinqamula. Njengoba isilinganiso sinembe kakhulu, leli nani litholakala liphansi kakhulu. Ezintweni eziningi lise ku σ = 0, futhi umthetho ka Hooke uba khona-ke kuphela isilinganiso sokuqala sokuziphatha okunwebekayo, ilungu lokuqala lokuthuthuka ochungechungeni luka Taylor lomsebenzi ε = ε (σ) endaweni eseduze nemvelaphi yezixhumanisi.
Uma induku ikhululwa emthwalweni, kuyaqapheleka ukuthi, lapho ingcindezi ingeyona enkulu kakhulu, ukuguquka nakho kuyanyamalala, ngokuvumelana nomthetho kaHooke. Kodwa nalokhu kuyashintsha uma kudlulwa ingcindezi ethile eseduze komkhawulo wobulinganiso, okuthiwa umkhawulo wokunwebeka; khona-ke ukuguquka okuphelele kuqukethe ingxenye enwebekayo (ebuyayo) nengxenye engagudluki (ehlala njalo). Nomkhawulo wokunwebeka awukwazi ukunqunywa ngokunembile, utholakala kancane kakhulu lapho ukunemba kokulinganisa kuphakeme. Nokho, ngenxa yokuthi unokubaluleka okukhulu kwezobuchwepheshe, ngoba umelela umkhawulo wokubaluleka cishe kuzo zonke izibalo emandleni ezinto zokwakha, futhi ngesikhathi esifanayo uwumkhawulo lapho kuvela khona umonakalo wokuqala ohlala njalo, ekuhlolweni kwamasampula uchazwa ngokucacile ngomqondo othile owamukelwayo, ngakho-ke, isb., njengomkhawulo we-0.2% kubizwa lowo mthwalo lapho ukunweba okuhlala njalo kufinyelela ku-0.2%.
Ngokushesha nje lapho umkhawulo wokunwebeka wedlulile, ukuguquka komumo kukhula ngokuzumayo futhi kungabonakala ngeso lenyama; ngaphansi kokucindezeleka cishe okungaguquki induku iyaqhubeka nokweluka ibe yinde. Lokhu kucindezeleka kubizwa ngokuthi umkhawulo wokugeleza. Emishinini ye-hydraulic yokuhlola izinto kungabonakala futhi ngemva kokuqala kokugeleza ukwehla okubonakalayo kakhulu noma okuncane kwengcindezi; njengoba kubonisiwe esith. 8 ngomugqa odayiselwe; lapho-ke inani eliphezulu libizwa ngokuthi umkhawulo ophezulu wokugeleza, kanti ukucindezeleka kokugeleza okungaguquki okulandela khona kubizwa ngokuthi umkhawulo ophansi wokugeleza.
Lapho kufinyelelwa i-dilatation ethile, ecishe ingabi ne-elastic ngokuphelele, ingcindezi iqala futhi ukukhuphuka, okokusebenza kuyaqina. Kulesi sigaba somthwalo kuba khona ukuncipha okubonakalayo kwesigaba esiphambene senduku ngenxa yokuncipha eceleni okungelona i-elastic, futhi ukuqhubeka kwediyagramu yengcindezi nokuguquka kuxhomeke ngokuyinhloko ekutheni lapho kubalwa ingcindezi σ amandla okudonsa P asebenza endukwini ahlukaniswa ngengxenye yokuqala F0 noma ingxenye yamanje F. Ngezinhloso zobuchwepheshe, ingcindezi P|F0 iyona ebalulekile. Le ngcindezi idlula nge-maximum ebizwa ngokuthi amandla ezinto zokwakha, futhi uma le maximum idlulile, induku iba mncane kakhulu endaweni eyodwa bese iyaphuka. “Ingcindezi yangempela” P|F ikhuphuka kuze kube sekubhujisweni.
Isithombe 8.
Ukuziphatha kwezinye izinsimbi ezincibilikayo kuhluke kakhulu kulokhu okuchaziwe lapha. Ukugeleza kuvame ukungabi sobala, kanti ukuqina kuqala ngokushesha ngemva kokweqa umkhawulo wokunwebeka. Ezintweni ezibrittle (itshe, ingilazi, ukhonkolo) ukuguquguquka okungesikho okunwebekayo kuvame ukuba kuncane kakhulu futhi kakade ekunwebekeni okuncane kuza ekuqhekekeni. Ukunwebeka sekukonke okutholwa yinto kuze kube sekuphukeni kuyisilinganiso sokweluleka (okuphambene: ukuqina) kwento, futhi kwe-steel kuchazwa ngokunembile ezimeni zobuchwepheshe. Nokho, njengoba ngaphambi nje kokuphuka ukuguquguquka okuqhubekayo kugxila ezindaweni ezizungezile zesigaba esincishisiwe, kutholakala inani elihlukile lokunwebeka ekuphukeni, kuye ngokuthi ubude bokulinganisa buthathwa kanjani ingxenye enkulu noma encane yenduku, ukuze kutholakale imiphumela ecacile futhi engaqhathaniseka phakathi kwazo kumele kusengaphambili kwamukelwe umthetho othile. Ukunwebeka ekuphukeni ngokujwayelekile kulinganiswa ngokuthi endukwini eyindilinga enobubanzi d ngaphambi kokuhlolwa kumakwe ubude bokulinganisa Ι = 10 d futhi kusukela ekwelulweni kwayo ΔΙ kubalwe ukunwebeka ekuphukeni εs_Ι = ΔΙ|Ι ._ Uma kudingeka kuhlolwe izinduku zesigaba esihlukile, ubude bokulinganisa buchazwa ngokobubanzi benduku eyindilinga eyisilinda enendawo efanayo yesigaba esiwela.
Umthwalo wesikhathi eside
Ngokuqondene nenqubo yokuhlolwa kokudonswa, akubalulekile kangako ukuthi umthwalo ukhuphuka kuze kube ukuphuka phakathi nemizuzu engu-10 m noma amahora ambalwa. Nokho, uma umthwalo usebenza iminyaka noma amashumi eminyaka, ngaphansi kwezimo ezithile kuyabonakala ukuthi ngisho nangaphansi komkhawulo wokugeleza, ukuguquka komumo ngaphansi kwengcindezi engaguquki kuyanda kancane kancane ngokuhamba kwesikhathi. Ingxenye enwebekayo, okungukuthi ingxenye enyamalalayo lapho kuthululwa ngokuphelele, ayiguquki kakhulu. Lokhu kukhula kokuguquka okungelastiki okwenzeka phakathi nesikhathi eside kubizwa ngokuthi ukucwila kancane (creep). Ezinsimbini, ngaphandle kokuhola, ukucwila kancane kubalulekile kuphela emazingeni okushisa aphezulu, kodwa kubunjiniyela bezokwakha kudlala indima kukhonkolo othe ngaphansi kwengcindezi uyekethisa kancane, ukuze ingcindezi ikhuphuke ekusimeni okuqinisiwe okucindezelwe, uma lokho kukhona.
Umthwalo oguqukayo
Ukuze izici zobunjiniyela bezinto, ezitholwe ekuhlolweni kokudonswa, zikwazi ukusetshenziswa njengesisekelo somthwalo ovumelekile wezinhlelo, kudingeka ukuthi impahla ikwazi ukumelana nengcindezi eyake yayimela ngaphandle kokulimala lapho iphinde ilayishwa njalo. Lesi simo asihlangatshezwana naso uma impahla ichayeka ekuphindaphindweni kaningi kokulayishwa nokukhululwa, njengalokhu, isibonelo, kwenzeka emibhoshongweni elayishwa amandla e-inertial emishini engalinganiswanga kahle. Ngokuphindaphindwa ngokwanele kokulayishwa, ingxenye yesakhiwo ingafinyelela ekuqhekekeni ngisho naseqophelweni lengcindezi eliphansi kakhulu kunamandla ento anqunywe ukuhlolwa okujwayelekile okumile. Lesi simo sokuqhekeka sibizwa ngokuthi ukwehluleka ngenxa yokukhathala. Inani lezikhathi zokulayisha n umkhiqizo ongamelana nazo lincike ebukhulu bengcindezi σ, ngakho-ke iba nkulu kakhulu uma ingcindezi incane. Isibonelo esijwayelekile salokhu kuncika sikhonjiswe ku-fig. 9, lapho kubonakala khona ukuthi amandla ento anomkhawulo ophansi, owumelana nawo ngisho noma kunenani elikhulu kakhulu lezikhathi zokulayisha futhi obizwa ngokuthi amandla ento asezingeni eliguqukayo Amadiyagramu alolu hlobo (fig. 9) abizwa ngokuthi amajika ka-Wöhler.
Isithombe 9.
Ukuphepha kwezakhiwo
Imithwalo emibili yomkhawulo ibalulekile ezakhiweni: umthwalo lapho kuqala khona ukonakala okungapheli (umkhawulo wokugeleza), kanye nomthwalo lapho amandla okuthwala esakhiwo eseqediwe, bese siphuka (umkhawulo wokuphuka). Njengoba ngaphambi komkhawulo wokugeleza okungenani cishe kusebenza izimiso zemishini yezinto (ukunyakaza okuncane, umthetho kaHooke), ukuphepha ngokumelene nokuguquka okungapheli kungahlolwa ngokuthembekile kuzo zonke izimo lapho kungenzeka ukunqoba ubunzima bezibalo. Uma ukucindezeleka kuhlobene nomthwalo ngokulingana, isilinganiso sokucindezeleka kokugeleza kuya ekucindezelekeni okukhulu kunakho konke okuvela esakhiweni silingana nesilinganiso phakathi komthwalo lapho kuvela khona ukugeleza nomthwalo wangempela futhi simela i-coefficient yokuphepha ngokumelene nokugeleza. Nokho, ezimweni eziningi lobu buhlobo obulula abukho: ukugoba lapho kudonswa khona ingxenye yokwelula, ukucindezelana phakathi kwezindawo eziqhumile, amasistimu anesakhiwo esiguqukayo futhi, okuyinto engathandeki ikakhulukazi, ukugoba kunamandla e-axial. Kuzo zonke lezi zimo ukwanda komthwalo okuncane ngokulingana kungaholela ekwandeni okukhulu kokucindezeleka, futhi lapho-ke akwanele ukusebenzisa i-coefficient yokuphepha ejwayelekile ekucindezelekeni, kodwa kufanele isetshenziswe emthwalweni.
Izenzakalo ezenzeka ngemva kokwedlula umkhawulo wokukha amandla kuze kufike ekuqhekekeni, ezimweni eziningi zingalandelwa kuphela ngokwekhwalithi. Uma impahla iyeluleka kalula, izingxenye lapho umkhawulo wokukha amandla usufinyelelwe khona kuqala, futhi eziqhubeka ziguquka ngaphansi kwengcindezi engaguquki noma ekhuphuka kancane, zifaka isandla kancane ekuthwaleni umthwalo oqhubekayo, ukuze ezinye izingxenye zesakhiwo ezicindezelwe kancane, uma lokhu kungenzeka ngokwesakhiwo saso, zibe nesabelo esikhulu ekuthwaleni. Kulesi sifiso sokulinganisa iziqongo zengcindezi kunomkhawulo othile wokuphepha, ongase usetshenziswe ngokomubalo uma ukuguquka okuhlala njalo kwezinye izingxenye, okuvele ngenxa yokulayishwa okukodwa okukhulu, kungalimazi (indlela yomthwalo womkhawulo).
Uma impahla iyashelelela, ukulimala kokuqala okuhlala unomphela kuvela emifantwini, ngenxa yayo endaweni esengcupheni kuba nokugxila kwengcindezi okukhulu nakakhulu, okuyinto ngokushesha ebangela ukuphuka. Ukuphuka ngenxa yokukhathala nakwizinto ezinokwelulwa kuveza izici zokuphuka okuphukile.
Ukuhlobana phakathi kwama-stress ezindizeni ezahlukene zokusika
Izibalo zokuguqula
Izingcindezi eziyisishiyagalolunye ezimakhomponenti esithombeni 1, ziboshelwe ezimfunekweni ezintathu zokulingana. Amanani ayisithupha asele σx, σy, σz τxy, τyz, τzx angathatha, ngokuzimela komunye nomunye, amanani okuzithandela njengoba kubonakala ekukhishweni kwezibalo ezihlukene zethiyori ye-elasticity. Nokho, lapho la manani enikeziwe, isimo sokucindezeleka endaweni ethile yomzimba oqinile sichazwa ngokuphelele, okungukuthi, lapho izingcindezi zaziwa ezindaweni ezintathu eziqondile komunye nomunye, kunganqunywa ngokungangabazeki nengcindezi yendiza yesine edlula ephuzwini elinikeziwe futhi onombindi wayo onendlela engafani.
Ku-mz 10 kuboniswe i-tetrahedra OABC lapho izinhlangothi ezintathu zifana nezindiza zesistimu yezixhumanisi x, y, z kanti eyesine imele into engaphezulu eqondiswe ngokuzikhethela ABC = dF. Ukuze kubhalwe indlela yayo nendlela yengcindezi edluliswa ngayo kuyo, kwethulwa enye isistimu yezixhumanisi, lapho i-eksisi ye-ξ ime mpo ku-dF.
Isithombe 10
Umbandela wokulingana kwamandla ahlasela le tetrahedron ngakolunye uhlangothi lwe-ξ uthi
Uma kubhekwa ukuthi
kutholakala
futhi okufanayo kusukela ezimeni zokulingana ngase-axis η:
Lawa ama-equation asetshenziselwa ukubala ingcindezi lapho kushintshwa izixhumanisi. Kubaluleke kakhulu ukubheka kuphela lezo zici zobuso dF lapho i-eksisi ξ ihlangana khona ne-eksisi z. Amaphethini alolu cala singawathola ngokwenza kube lula amaphethini angaphambilini noma siwafunde ngqo esithombeni 11:
Isithombe 11
Izingcindezi ezijwayelekile zithatha amanani amakhulu kakhulu ezinkomba α = α0 , lapho dσξ/dα = 0. Ngokuhlukanisa ngokuthola okuphuma ku-equation (16) kutholakala
ngakho-ke, lapho le nkulumo ilinganiswa noziro
I-stress τξη izoba futhi yiyo yonke i-shear stress kulezi zindiza, uma τyz = τzx = 0. Khona-ke ngesibalo (17) kunqunywa izinkomba ezimbili eziqondane phakathi kwazo lapho: 1. i-total shear stress ingu-zero futhi, 2. i-normal stress inamanani ayisikhawu aphezulu kakhulu naphansi kakhulu. Lezi zinkomba zibizwa ngokuthi izinkomba zezinzuzo eziyinhloko, kanti izingcindezi ezihambisanayo izinzuzo eziyinhloko. Zimakwa ngo σ1 no σ2 futhi zingabalwa ngokuqondile kusukela kwifomula
Indilinga kaMohr
Izibalo (16) zingaboniswa ngokudweba ngendlela ecacile. Ngale njongo kufanele ziguqulwe zibe yifomu:
Lezi zibalo zimelela, ohlelweni lokuxhumanisa lwe-σ, τ, ifomu eliyipharamitha lesibalo sendilinga, edwetshwe ku-fig. 12, enezixhumanisi zesikhungo σ = 1/2 (σx + σy), τ = 0 futhi enobubanzi
Lo mbuthano ubizwa ngokuthi umjikelezo kaMohr. Uma ngomugqa odlula ephuzwini x kudwetshwa umugqa oqondile ohambisana nesigaba x =const., lapho kudluliselwa khona izingcindezi σx, τxy uzosika umjikelezo ephuzwini p, elibizwa ngokuthi isigxobo somjikelezo kaMohr. Wonke umugqa pξ odwetshwe ngaleli sigxobo usika umjikelezo ephuzwini ξ elichaza izingcindezi σξ, τξη ezidluliselwa ngesigaba esihambisana ne pξ.
Mayelana nophawu lwezingcindezi zokugunda lapho kudwetshwa indilinga kaMohr kufanele kucatshangelwe ukuthi zikhonjiswa zibheke phezulu uma zine ndlela eboniswe ku sl. 12c. Ngakho-ke, kwezingcindezi ezimbili ezihambisanayo τxy, τyx, eyodwa ihlale iyinhle kanti enye imbi.
Kumanani emingcele e-σ1, σ2 wezingcindezi ezivamile kuhambisana amaphuzu 1 no 2 kumbuthano, kanti imigqa _p_1 no _p_2 inika izinkomba zezingcindezi eziyinhloko.
Ukuboniswa kwezingcindezi ezisemkhakheni we x-y ngosizo lwendilinga kaMahr akuxhomekile kunoma yikuphi ukucabangela mayelana nezingcindezi σz, τxz, τyz eziqondile kule ndawo.
Isithombe 12
Ngakho-ke lokhu kusebenza nasendabeni ejwayelekile kakhulu yesimo sokucindezeleka esinezilinganiso ezintathu, uma kuqhathaniswa kuphela lezo zindiza zokunqamula zonke ezidlula emgqeni ofanayo, lapha okhethwe njenge-axis z ne ξ. Njengoba ngokwezibalo ezijwayelekile zokuguqulwa (15) ukucindezeleka okujwayelekile σ kungakwazi ukungena ekungapheli kunoma iyiphi indiza yokunqamula, kufanele kube nenani eliphezulu elilinganiselwe σ1 lendiza ethile, kanti kwenye kube nenani eliphansi σ3, womabili lawo, kuyacaca, angaba negethivu. Uma kudonswa indiza phakathi kwama-vector σ1 no σ3 bese kudwetshwa indilinga ka-Mohr (sl. 13)
Isithombe 13
kwizingcindezi ezilele kule ndawo (okungukuthi, zonke izinkomba ezimile kule ndawo), khona-ke ama-σ1 no-σ3 yizingcindezi ezinkulu nezincane kakhulu ezijwayelekile ezingavela futhi ngenxa yalokho kufanele zibe zimile ngokuphambene komunye nomunye. Uma izinkomba 1 no-3 zengezwa ngenkomba 2, ukuze lezi zinkomba ezintathu zakhe uhlelo lwezixhumanisi olune-engeli engakwesokudla, futhi uma kudwetshwa imibuthano kaMahr yama-plane 1 ~2 kanye 2 ~ 3, khona-ke i-σ2 kwenye yale mibuthano iyona enkulu, kanti kwenye iyona encane kakhulu ingcindezi ejwayelekile, ngakho-ke eziphambanweni ezime mpo ezinkombeni 1, 2 no-3 ingcindezi yokugunda ilingana noziro. Lezi zingcindezi ezintathu ezijwayelekile ezimile ngokuphambene komunye nomunye σ1, σ2 no-σ3, ezingahambelani nezingcindezi zokugunda, zibizwa ngokuthi izingcindezi eziyinhloko.
Umkhawulo wokukhiqiza kanye nomkhawulo wokuphuka esimweni sokucindezeleka esisemkhathini
Isimo sokucindezeleka sibizwa ngokuthi singobukhulu obubodwa, obubili noma obuthathu, ngenye indlela: umugqa, isicaba noma isikhala, ngokuthi ingabe okukodwa, okubili noma konke kokuthathu ukucindezeleka okuyinhloko kuhluke ku-zero. Ezingxenyeni zokwakha ezisetshenziswa kakhulu, okungukuthi, endukwini edonswayo, ecindezelwayo nakugobile, isimo sokucindezeleka, okungenani ezindaweni ezicindezelwe kakhulu, singobukhulu obubodwa, kanjalo nasezivivinyweni zokudonsa, ukucindezela noma ukugoba, ezisetshenziswa cishe kuphela ekuhlolweni kwezinto zokunquma izingcindezi ezivumelekile. Ngokuphambene nalokho, kumaqoqo alayishwe ngaphakathi kwendiza yawo noma aqondile kuyo, kanye nasemagobolondweni, isimo sokucindezeleka singobukhulu obubili, kanti kwezinye izimo kuvela nezimo zokucindezeleka zobukhulu obuthathu, ngakho-ke kudingeka ukuthi kususwe iziphetho mayelana nokuziphatha kwento esimweni sokucindezeleka sesikhala, ngokusekelwe emkhawulweni wokugeleza nokuphuka, okunqunywe esimweni sokucindezeleka sobukhulu obubodwa.