Iiseko
Umsebenzi wokuqina kwezinto kukuchonga ukuba zeziphi iintsimbi zangaphandle ezinokumelana nomzimba oqinileyo (umz., isakhiwo, inxalenye yolwakhiwo okanye umhlaba). Ukuze kunikwe impendulo kulo mbuzo kuqaliswa ngemigaqo emibini: kwelinye icala, iinyanzeliso akufuneki zidlule imida ethile exhomekeke kuhlobo lwento, yaye kwelinye icala ibhalansi phakathi kweentsimbi zangaphandle nezingaphakathi kufuneka ibe yizinzile. Ngokuhambelana noku, zonke iingxaki zokuqina kwezinto zinokwahlulwa zibe yi“Iingxaki zoxinzelelo” kunye ne“ingxaki yozinzo.”
Kwimivalo nakwiintsimbi zemijelo nakwizithwali ezenziwe ngazo (ii-truss, ii-frame) ukumiselwa koxinzelelo kwenziwa ngamanyathelo amabini, oko kukuthi kuqala kusetyenziswa imikhosi yangaphandle emiselweyo ukubala isiphumo semikhosi yangaphakathi egqithiselwa ngomnqamlezo, emva koko ukusuka kwezi “mikhosi yecandelo” kumiselwa uxinzelelo. Inxalenye yokuqala yale nkqubo yinkalo ekhethekileyo, ebanzi, i-statistics yezakhiwo, eneemethodi zayo eziphuhliswe kakuhle kwaye ngokuqhelekileyo yahlulwe kwityhefu yezinto, umsebenzi wayo uthi ga kukumisela uxinzelelo ukusuka kwimikhosi yecandelo enikiweyo.
Iingcamango ezisisiseko zokumelana kwezinto
Inkcazo yoxinzelelo ifunyanwa ngale mbono zisisiseko zilandelayo. Masithi emzimbeni kusebenza inkqubo elungeleleneyo yemikhosi yangaphandle. Masicinge ukuba siwuhlule umzimba ngomsiki ongazikhethelanga ube ngamacandelo amabini, saze sasusa elinye lala macandelo kunye nemikhosi esebenza kulo; ngoko ke impembelelo yalo kwelinye icandelo, ukuze ulungelelwano lwemikhosi nolwabiwo lweenguqu kuhlale lungatshintshanga, kufuneka itshintshwe ziimikhosi ezongezelelweyo ezidluliselwa kumphezulu wokusika. Le mikhosi ‘yangaphakathi’ isasazwa ngokuqhubekayo phezu komphezulu wokusika, ukuze into nganye yomphezulu dF ifumane amandla dβ. Ukuba kwenziwa isahlulo dβ dF kuze kwenziwe umda wokuguquka dF -> 0, ngoko eli xabiso lisondelela kwixabiso elingumda elibizwa ngokuba luxinzelelo. Uxinzelelo kwinto ethile yomphezulu lufana no dβ, yaye lungahlulwa lube zizithako ezithe nkqo nezijonge ecaleni ku dF, uxinezeleko oluthe nkqo σ noxinezeleko lokucheba τ.
Ukuba kumgama omnye kudluliswa amacandelo ngeendlela ezahlukeneyo, aya kuhambelana noxinzelelo olwahlukeneyo. Ngokukodwa xa emzimbeni kukhutshwa ikhabhathi esisiseko, eboniswe kwifig. 1, kwindawo nganye kwezo zintandathu kuya kusebenza i-vector yoxinzelelo enokwahlulwa ibe ziindawo ezintathu kwicala leendlela zokulungelelanisa x, y z. Uxinzelelo olusebenza kumacala ajongene ngokwahlukileyo luyahluka omnye komnye, kambe ke, kuphela ngediferenshali, ngoko ke kufuneka kwahlulwe 3 * 3 = 9 iinxalenye zoxinzelelo, eziphawulwa ngolu hlobo lulandelayo:
Kwiingcinezelo eziqhelekileyo σ kunikwa isalathiso se-axis apho zilele khona kwaye zijongwa njengezintle ukuba zibangela ukutsalwa, zibe zimbi ukuba zibangela uxinzelelo. Iingcinezelo zokucheba τ zifumana izalathiso ezimbini, eyokuqala iyafana nesalathiso sengcinezelo eqhelekileyo ehambelanayo, yaye eyesibini ibhekisa kwi-axis kwicala apho ingcinezelo yokucheba isebenza khona. Ukuba icala elilungileyo lengcinezelo eqhelekileyo ehambelanayo likwicala le-axis yolungelelwaniso olulungileyo (olubi), nengcinezelo yokucheba ithathwa njengeyilungileyo ukuba isebenza kwicala le-axis yolungelelwaniso olulungileyo (olubi).
Umfanekiso 1.
Ukudityaniswa koxinzelelo lwe-shear
Ukuba kwibhloko esisiseko, fig. 1, kusetyenzwa umqathango wokuba umzuzu wazo zonke iintsimbi ngokunxulumene ne-asi x ulingane noziro, kufumaneka τyz dx dz * dy = τzy dx dy * dz Ukusuka apha, nakwii-equations ezimbini ezihambelanayo zee-asi y ne-z, kufumaneka ukuba uxinzelelo lwashearing olunamanye ama-indeksi luyalingana omnye komnye τxy = τyx, τyz = τzy, τzx = τxz (1)
Iinguqu zecandelo
Ukuba iingcinezelo ezichazwe ngasentla zinentsingiselo yomzimba, oku kuvela kunxibelelwano lwazo nenkcazelo ethe yanyamezelwa ngumzimba ngamnye phantsi kwefuthe leentshukumo zangaphandle. Sl. 2 ibonisa i-cuboid esisiseko, eyayiyirekthangile ngaphambi kokuguquka yaye inobude bamacala dx, dy, dz. Ubude bamacala emva kokuguquka sinokubabhala ngo dx + Δdx, dy, + Δdy, dz + Δdz. Iingxunyi εx = Δdx|dx, εy =Δdy|dy, εz = Δdz|dz zibizwa ngokuba ziidilateshini. La ngamaxabiso angenamlinganiselo yaye kuzo zonke izinto ezityenziswa kulwakhiwo ziba zincinane ngokwemigaqo ye 1. Ngaphandle kokoluleka kwamacala, i-cuboid esisiseko dx * dy * dz inokufumana kwakhona utshintsho lwee-engile ezithe ngqo zangaphambili phakathi kwemiphezulu yayo.
Umfanekiso 2. ukuguquka kwecandelo
Makhe emva kokuguquka i-engile phakathi kweenqwelomoya ezidibana ngohlangothi OC ilingane 
kwaye ngokufanayo ukuncipha kwe-engile ethe tye ngohlangothi AO kulingane γyz, kunye nokuncipha ngohlangothi OB kulingane γzx. Ezi nguqu zintathu ze-engile γxy, γyz, γzx, zibizwa ngokuba kukutyibilika yaye nazo zisoloko zincinane ngokwe 1. Ngezinto ezintandathu ze-ε nezika-γ ukuguquka kwekhyubho yerhanti deformacija u malom kumiselwa ngokupheleleyo. Utshintsho lwento yomthamo d_V = dx * dy * dz_ ngu ΔdV = (dx + Δdx) (dy + Δdy) (dz + Δdz) - dx dy dz, apho, xa iimveliso zodlondlobalo zingahoywanga njengezinto ezincinane zodidi oluphezulu, kufumaneka udlondlobalo lwekhyubho ϱ = ΔdV|dV = εx, εy, εz (2)
Ukushenxiswa
Ukuguquka komzimba oqinileyo kunokuchazwa ngokupheleleyo nangale ndlela, ngokuba kwindawo nganye yawo kunikwe ukufuduswa okufunyenwe yileyo ndawo. Ukuba kususwa ekuqwalaselweni ukufuduswa kobukhulu obupheleleyo obuhambelana nokufuduswa komzimba oqinileyo, ngaloo ndlela, ukuba kuyimfuneko, kwibala lokubala kwamkelwe inkqubo yeekhonsepthi eshukumayo, ngoko ke neendawo zokufuduswa zeziqendu μ, ν, ω zihlala zincinci, kwaye iziphumo zazo ngokuthelekiswa neekhonsepthi zincinci xa zithelekiswa ne-1. Ngaphantsi kwale ngcinga, ngokomz. 3 ubude bento yomgca OA = dx emva kokuguquka
ke 
(3)
Ngendlela efanayo, kumz. 3 kubonakala ukuba ukutyibilika γxy γ1 + γ2: kwaye kwakhona
(4)
Umzobo 3 ukutyibilika
(5) 
(6)
Ezi ziqhagamshelo zibizwa ngokuba ziimeko zokuhambelana kwaye zibonisa ukuba izinto ezikhubazekileyo zinokudityaniswa njenge-mosaic ukuze isithuba sizaliswe ngokuqhubekayo, nto leyo engenakwenzeka ukuba ukukhubazeka kwezinto kungenamthetho. Iimeko zokuhambelana zizibalo ezahlulayo, ngoko ke, kuyacaca, onke amacandelo amathandathu okukhubazeka kwityhubhu nganye nganye azimele ngokwawo, kodwa ulungelelwaniso lwawo kulo naluphi na ummandla osasazeke ngokugqityiweyo lubotshelelwe ziimeko (5) kunye (6).
Kuba ezi meko zifunyenwe ngokwahlulahlula kwizibalo (3) kunye (4), xa zikhutshwa kulahleka inxalenye yeenkcukacha ezibandakanywe kwizibalo zokuqala. Ngoko ke akwanelanga ukuba kuzalisekiswe enye kuphela yezi nkqubo zimbini zezikali, koko zombini iinkqubo zezibalo kufuneka zaneliswe, ukuba kufuna ukuqinisekiswa ukuhambelana kokuguquka.
Izibalo ezahlukeneyo zenkqubo yokunwebeka
Ukuze kubalwe iintsimbi zoxinzelelo kunye nokuguquka kwemizimba e-elastic kusetyenziswa ezi zibalo zilandelayo:
Iimeko zokulingana kwento yevolyum. Iimeko zokuba imizuzu ejikeleze ii-asi ezintathu ilingane noziro sele zisetyenzisiwe ekukhutshweni kwenxaki (1). Iimeko zokulingana kwamandla zinika ngokomzobo 4
Umfanekiso 4
(7a-c)
Ukuba ngo X, Y, Z kuchazwa amacandelo emikhosi yevolumu (umz., ubunzima, umkhosi wesanti-centrifugal) kwiyunithi yevolumu. Ubudlelwane phakathi koxinzelelo nokonakala. Apha kuqondwa ubudlelwane phakathi koxinzelelo lwamacandelo kunye nokonakala kwamacandelo. Kwithiyori ye-elasticity ngokuqhelekileyo kuthathelwa ingqalelo kuphela ubudlelwane bomgca, obuchazwa ngumthetho kaHooke:
(8a-c)
(8d-f)
Ukuba iiequation (8a-c) zisonjululwa ngokweengxaki zoxinzelelo, kufunyanwa
(8 a)
kso kunye nezibalo ezimbini ezihambelanayo. Umthetho kaHooke ochazwe ngesiqendu (8) awumeli mthetho wendalo ozaliseka ngokungqongqo, koko yinto efanelekileyo esekwe kwindlela yokuziphatha yokwenene, eyahlukana nawo ngakumbi okanye ngaphantsi, kuxhomekeke kwizinto ezisetyenzisiweyo nakubukhulu bokuxinana. Ngenxa yokuba ukulawulwa kwezibalo kwengxaki yokuxhathisa kwezinto ezinezibophelelo ezinzima, ezingalandeleli mgca, phakathi koxinzelelo nokuguquka kuzisa ubunzima obukhulu kakhulu kwaye kunokwenziwa ngokwenene kuphela kwiimeko ezilula kakhulu, nasezintweni (ikonkriti!) apho ukuziphatha kwazo kuphambuka kakhulu kumthetho kaHooke, izibalo ezisekelwe kuwo kufuneka zisetyenziswe kuqala, yaye ubukhulu becala kube sisisombululo esimalunga kuphela, esithe kwakhona ngokuqhelekileyo siluncedo kakhulu kwaye sinika ukuqonda okungaphezulu kunokuba kukuba kuphela kwekwalithi. G = E|2 (1+μ).
Siphuma ngokuyimfuneko kubudlelwane phakathi koxinzelelo nokuguquka (8), kwiiequation zenguqu (16) zoxinzelelo nakwinkqubo ehambelanayo yeequation zokuguquka kweendawo. E no G zinemilinganiselo yoxinzelelo kwaye kuzo zonke izinto zokwakha zikhulu xa zithelekiswa noxinzelelo σ no τ olunokuthi luvele. Kodwa kule nyani kusekelwe ingcinga eyamkelwa kuyo yonke ithiyori ye-elasticity, yokuba ukuguquka kuncinci. I-coefficient yokwandiswa okuthe tye (inani likaPoisson) μ ayinamilinganiselo kwaye ihlala isoloko iphakathi kwe 0 kunye 1/2 .
Ubudlelwane phakathi kweenguqulo zamalungu nokuplacementsa. Obu budlelwane bunikezelwe ziiequation (3), (4). Zingobume obusulungekileyo bejiyometri. Ezi nkqubo zintathu zinika 3+6+6=15 yeequation ze 15 ezingaziwayo, oko kukuthi, ze 6 iindawo zoxinzelelo zamalungu, 6 iinguqulo zamalungu kunye 3 nokuplacementsa zamalungu. Ngoko ke zanele ekumiseleni ezi zingaziwayo. Ukuwulawula ngokwezibalo olu hlobo lukhulu lwenkqubo yeequation ezohlukeneyo, kambe ke, kunokwenzeka kuphela kwiimeko ezikhethekileyo. Ukuba kwi-equation (8) iinguqulo zamalungu zitshintshwa ngo placementsa zamalungu ngokweequation (3) kunye (4) yaye emva koko iindawo zoxinzelelo eziqhelekileyo σ kunye neendawo zoxinzelelo zokushelela τ, ngokweequation (8 d - f), zingeniswe kwiimeko zokulingana, jedn. (7), kufumaneka ii-equation ezohlukeneyo ezibizwa ngokuba ziiequation ezisisiseko zethiyori yokunwebeka.
(9)
apho 
kuboniswa umsebenzisi we-Laplace. Ngokujonga ku (2) ezi zizibalo ezintathu ezahlulayo ezineendawo ezintathu zokushenxiswa μ, ν, ω; kwezi ke, ngokwahlula-hlula ngokusekwe ku (3), (4) no (8) kunokufunyanwa zonke iindawo zoxinzelelo kunye neenguqulelo. Izibalo (9) zisoloko zingumgca wokuqala oluncedo kakhulu kuphononongo lweemeko ezikhethekileyo.
Umsebenzi wokuguqula
Inkcazo
Xa umthwali womthwalo ulayishwa, amanqaku okuhlaselwa ngamandla angaphandle afumana iintshukumo ezithambileyo yaye loo mandla enza umsebenzi othile. Ngale ndlela amandla angenisiweyo anokuguquka abe ziindlela ezahlukeneyo. Ukuba umthwalo ufakwa ngesiquphe, ukuze inkqubo yokuguquka ibe nesantya esikhulu, inxenye yala mandla iguquka ibe ngamandla e-kinetic, athi ekuhambeni kwexesha asasazeke, mhlawumbi ngale ndlela yokuba adluliselwe emhlabeni njengeliza elithambileyo elilahleka kwi-infinitiy, okanye ngokuba aguqulelwe bubuxhakaxhaka bangaphakathi abe bubushushu. Ukuba imithwalo ifakwa kancinci kangangokuba kungaveli nyuso ibonakalayo yamandla e-kinetic, oko kukuthi, imithwalo ekhula ngokuthe ngcembe iqala ku-zero kwaye ikwi-equilibrium eqhubekayo namandla angaphakathi, ngoko ngokucacileyo amandla asetyenziswa kuphela ekuguquleni umzimba aze ke abizwe ngokuba ngumsebenzi wokuguquka.
Ukubala umsebenzi wotshintsho siza kuqala sikubonise kwinxalenye ethwele umthwalo wokutsalwa kwicala elinye (sl. 5).
Masithi uxinzelelo olukhoyo σ kunye nokudilata okuhambelanayo ε zifumane izongezelelo dσ no dε. Ngoko ke amandla σdF endleleni dε * dl aya kwenza umsebenzi σdF * dεdl = σdεdV, ukuba i-dV imele umthamo wesiqwengana. Ukuba uxinzelelo luyanda ukusuka ku-zero lufikelele kwixabiso lalo lokugqibela yaye ukudilata ngokuhambelana nalo kusuka ku 0 kuye ku ε, umsebenzi opheleleyo owenziweyo ngeyunithi yomthamo uya kuba:
Ngendlela efanayo kunjalo nakwisixhobo esilayishwe ngoxinzelelo lokucheba τ (umz. 6) umsebenzi woguquko kwiyunithi yomthamo (umsebenzi othile woguquko, amandla agcinwe elastikini):
apho kuphela omnye wemikhosi emine τ * dF wenza umsebenzi.
Kwimeko jikelele, xa kukho onke amalungu amathandathu oxinzelelo olusebenza kwiqhekeza elincinane, kufunyanwa umsebenzi okhethekileyo wokuguquka ngokudibanisa imisebenzi yamalungu oxinzelelo ngalinye:
(10)
Ngokwahlulahlula ngokomda ophezulu ngamnye wolu dityaniso, kufumaneka ubudlelwane obusebenzayo kwelona tyala libanzi kakhulu:
(11)
kwaye ngokufanayo nakwezinye iinguqulelo zeendawo. Ukuba umzimba uyawela, kwisimo ngasinye esithile soxinzelelo kusoloko kuhambelana isimo esifanayo sokuguquka, kungakhathaliseki ukuba elo meko lifunyenwe ngexesha lokulayisha okanye lokukhulula. Emva koko phantsi kwee-integral kukho imisebenzi enesiphumo esinye, yaye amandla apheleleyo asetyenziswe ngexesha lokulayisha aze emva koko akhululwe ngokupheleleyo ngu a = 0, kuba kule meko imida ephezulu yee-integral iba nguziro. Ngoko ke amandla ewonke anikwe umzimba ngexesha lokulayisha abuyiselwa ngexesha lokukhululwa.
Umfanekiso 6
Umfanekiso 7
Kumzimba ongaphelelanga ngokwe-elastic, ubudlelwane phakathi kweengcinezelo kunye nokukhubazeka kuyo yonke inkqubo yokulayisha nokukhulula bunomumo oboniswe ngokusondeleyo kwi-sl. 7 ngemigca O A B. Amandla 
aziswa ngexesha lokulayisha alingana nommandla OAA, kwaye amandla abuyiselweyo ngexesha lokukhulula alingana nommandla ABA, ngoko ke kulahleka (kuguqulelwa kubushushu) umsebenzi ohambelana nommandla owenziwe ngemigca ethe nkqo. Ukuba kwinkqubo ye-oscillation ingcinezelo itshintsha ngamaxesha athile phakathi kwexabiso lomda elilungileyo 
kunye nexabiso lomda elingalunganga, 
ukukhubazeka okungelastic kuqhubeka ngendlela efanayo naleyo iboniswe ngemigca enqamlekileyo kwi-sl. 7 kwaye ngexesha ngalinye lesiqingatha somjikelo we-oscillation kuguqulwa kube bubushushu, ngokweyunithi yomthamo, amandla DABCD. Ukuziphatha okunjalo ngexesha lokukhubazeka, apho ukukhubazeka kushiyeka emva koxinzelelo, kubizwa ngokuba elastični histeresis, yaye igophe DABCD libizwa ngokuba yiloop ye-hysteresis.
Umsebenzi wenguqu kunye nomthetho kaHooke
Ukuba kumaithegrali kwiequation (10) kufakwe umthetho kaHooke, kunokwenziwa ukuhlanganisa, yaye ngenxa yomsebenzi othile wokuguquka kufumaneka iintetho:
(12a)
(12b)
(12c)
Ukuba ifom yesibini kwezi ifakwa kwilingano (11), kufunyanwa kwakhona umthetho kaHooke, iilinganiso (8), ngendlela esonjululwe ngokwemfutho. Ingxelo yokuba umsebenzi wokuguquka uxhomekeke kumacandelo okuguquka, njengoko kuboniswe ngelingano (12b), ngoko ke iyalingana nomthetho kaHooke. Xa ilingano (12c) lihluthwa ngokwemfutho, kufunyanwa
(13)
Ezi fom, ngokungafaniyo neefom (11), zisebenza kuphela kwimizimba eziphatha ngokomthetho kaHooke yaye azinakusetyenziswa xa ubudlelwane phakathi koxinzelelo nokuguquka buhlukile. Kuyacaca ukuba kwicala lasekunene leequation (13) kukho kuphela ukuguquka kwecandelo okubangelwa ziingcinezelo, kwaye kuyashiywa ngaphandle zonke ezinye ezinokuthi zibe zavela ngenxa yotshintsho lobushushu, ukhukhumala, ukudumba, ukutshintsha kweekristale, njl.
IZIMVO EZIDITYANISIWEYO KWI-THETHI YE-ELASTICITY
Ukushenxiswa okubonakalayo. Umgaqo wamandla ombane anokubakho asezantsi
Njengoko umthetho kaHooke, izivakalisi (8) unokutshintshwa sisivakalisi esinye (12b), ngokunjalo endaweni yeemeko zokulingana kunokungeniswa umgaqo weendawo ezishenxiswayo ezingeyonyani, njengomthetho osisiseko wemekhaniki osebenza ngokubanzi. Lo mthetho ubonisa ukuba iimeko zokulingana zibalaseleka kuba umsebenzi wonke owenziwe yawo onke amandla ngotshintsho oluncinci lwemeko yokuguquka ulingana no-zero. Ukuba utshintsho oluncinci lweendawo zokushenxiswa eziguquguqukayo sibalula δμ δν, δω, ke amandla omzimba achazwe sisivakalisi (7) enza umsebenzi wengqikelelo
kunye nemikhosi yomphezulu px, py, pz esebenza kwinto yesebe dF yomphezulu wangaphandle womzimba umsebenzi 
apho i-integrali ephindwe kathathu ibhekisa kuwo wonke umthamo, kanti ephindwe kabini ibhekisa kuwo wonke umphezulu wangaphandle womzimba. Ukubala umsebenzi owenziwa ngamandla angaphakathi kusetyenziswa umgca (12b), yaye umsebenzi ngomthamo ngamnye ufunyanwa
Umgaqo wokufuduswa okucwangcisekileyo okucingelwayo unika ke ngoko
(14)
Ukuba imithwalo X, Y, Z px, py., pz iqondwa njengezinto zentshukumo yomxhuzulane (ubunzima bazo kunye nomthwalo wangaphandle), ii-integral kwicala lasekunene zimela amandla anokubakho alahlekileyo zezi mithwalo, logama icala lasekhohlo limela ukwanda kwamandla anokubakho (elastic) omzimba, ngoko lo mgaqo ubonisa ukuba amandla anokubakho ewonke esithwali nomthwalo ose kulo kwimeko yokulingana anexabiso eligqithisileyo. Ukuba eli xabiso ligqithisileyo yincitshiso, ukulingana kuzinzile.
Umgaqo wobuncinci bamandla anokubakho obuchazwe ngesibalo (14), intetho (12b) ngomsebenzi wokuguquka kunye neemeko zokuhambelana kweenguqu (5), (6) zenza inkqubo yezibalo eyanele ukwakha ithiyori ye-elastiki, kwaye ngokusisiseko iyalingana nenkqubo yezibalo. Le nkqubo inokuba luncedo ngakumbi kwiimeko apho ukuzalisekiswa kwezibalo ezahlulayo, jeclnačina (9) kuzisa ubunzima bokubala yaye ngenxa yoko kufuneka kufunwe isisombululo esisondeleyo, umzekelo, ukushenxiswa kucingelwa kwangaphambili ngendlela efanelekileyo equlethe iikonstanti ezimbalwa ezikhululekileyo, ze ezi zimiselwe kwiimfuno zokuba isibalo (14) saneliswe. Ngaloo ndlela ke akufumaneki isisombululo esingqongqo sengxaki, koko kufunyanwa kuphela eyona ndlela ilungileyo esondeleyo enokufezekiswa ngohlobo lwesisombululo olukhethiweyo. Nokuba ukusondela kwanele na, kuxhomekeke kuqala nokuphambili kuhlobo lwesisombululo olwamkelweyo, yaye ukusetyenziswa ngempumelelo kwale ndlela kufuna ke ubuchule namava.
Umgaqo kaCastigliano
Ngelixa kumgaqo wobuncinane bamandla anokubakho kuthelekiswa zonke iimeko zokuguquka ezizalisekisa iimeko zokuhambelana kokuwa, kuze phakathi kwazo kukhethwe ezo apho uxinzelelo oluhambelanayo luzalisekisa iimeko zokulingana, kumgaqo kaCastigliano kuthelekiswa zonke iimeko zoxinzelelo ezizalisekisa iimeko zokulingana, kuze phakathi kwazo kukhethwe ezo apho iinguqu ezihambelanayo zizalisekisa iimeko zokuhambelana kokuwa. Lo mgaqo uthi: kuzo zonke iimeko ezinokubakho zokulingana, eyona yenzekayo ngokwenene yeyona ihambelana nomsebenzi omncinane wenguqu. Umgaqo kaCastigliano kunye nenxaki (12c) yomsebenzi wenguqu kunye neemeko zokulingana zenza inkqubo yezinxaki eyaneleyo yokwakha ukuxhathisa kwezinto. Kuba lo mgaqo uqulethe umthetho kaHooke, ukusetyenziswa kwawo kuxhomekeke ekucingeni ukuba iinguqu zinokuchazwa ngokupheleleyo ngalo mthetho. Oku kufuna kungekuphela ukuziphatha oku-elastic komgca kwezinto, kodwa kukwakhuphela ngaphandle notshintsho lobushushu.
Ukuziphatha kwezinto ezingaphezu kwemida yokuqina
Iziganeko phantsi komthwalo omileyo
Ukuguquka kwesixhobo phantsi kwempembelelo yoxinzelelo yinto entsonkothileyo kakhulu, ngoko ke kufuneka yenziwe lula ngeendlela ezahlukeneyo ukuze iqondwe. Enye yezi zenzi-lula yinto yokuba imithwalo ifakwa ngokuthe ngcembe, njengoko kwenziwa, umzekelo, ngeesampuli ngexesha lovavanyo lokutsalwa nokucinezelwa.
Ukuba intonga yentsimbi etsalwa ngentshukumo yomthwalo otyhalayo isetyenziselwa umthwalo onyuka kancinci kancinci kwaye kulinganiswe ukolula kwayo ε, kufumaneka idayagram eboniswe kumz. 8. Ekuqaleni ukolula kuncinci kakhulu kwaye kungalingana noxinzelelo, njengoko kufunwa ngumthetho kaHooke. Ukususela kuxinzelelo oluthile, ubungakanani obulinganayo buyayeka kwaye ukolula kuqala ukwanda ngokukhawuleza. Indawo echanekileyo yomda wolu lungelelwano kunzima ukuyimisela. Okukhona umlinganiselo uchane ngakumbi, kokukhona lowo mda ufumaneka usezantsi. Kwiimathiriyeli ezininzi usekwi σ = 0, kwaye umthetho kaHooke umele ke kuphela uqikelelo lokuqala lokuziphatha okunyamezelayo, ilungu lokuqala lophuhliso kuthotho lukaTaylor lomsebenzi ε = ε (σ) kufuphi nemvelaphi yeekhonate.
Ukuba intonga iyakhululeka, kuqatshelwa ukuba, xa uxinzelelo lwalungekho lukhulu kakhulu, ukuguquka nako kuyanyamalala, ngokuhambelana nomthetho kaHooke. Kodwa nalo mba utshintsha xa kugqithiswa uxinzelelo oluthile olusondele kumda wokulingana, oko kukuthi umda wokunwebeka; ngelo xesha uguquko lulonke luquka inxalenye enwebekayo (ebuyayo) kunye nenxalenye enganwebekiyo (esisigxina). Nawo umda wokunwebeka awunakumiselwa ngokuchanekileyo, ufumaneka usezantsi ngakumbi kokukhona ukuchaneka kwemilinganiselo kuphezulu. Nangona kunjalo, kuba unentsingiselo enkulu yobugcisa, kuba umele umda obalulekileyo phantse kuzo zonke izibalo kumandla ezinto, yaye ngaxeshanye ngumda apho kuvela khona umonakalo wokuqala osisigxina, xa kuvavanywa iisampuli uchazwa ngokungqongqo ngandlela ethile yesivumelwano esamkelweyo, ngoko ke, umzekelo, njengomda 0.2% kuchazwa loo mthwalo apho ukwandiswa okusisigxina kufikelela ku 0.2%.
Ngokukhawuleza emva kokuba umda wokunwebeka ugqithisiwe, ukuguquka komzimba kunyuka ngesiquphe kwaye kunokubonwa ngeliso lenyama; phantsi koxinzelelo oluphantse luhlale lungatshintshi intonga iyaqhubeka ukoluleka. Olu xinzelelo lubizwa ngokuba ngumda wokuhamba. Kwimishini ye-hydraulic yokuvavanya izinto kunokuphinda kuqatshelwe, emva kokuqala kokuhamba, ukuhla koxinzelelo okungaphezulu okanye okungaphantsi okucacileyo; njengoko kubonisiwe kumz. 8 ngegophe eliqhawukileyo; apho ke ubuninzi bubizwa ngokuba ngumda ophezulu wokuhamba, kwaye uxinzelelo olungatshintshiyo lokuhamba oluthi lulandele lubizwa ngokuba ngumda osezantsi wokuhamba.
Xa kufikelelwa ukwandiswa okuthile, okuphantse kube ngokupheleleyo okungelulo-elastiki, uxinzelelo luqala kwakhona ukunyuka, izinto ziba lukhuni. Kule ndawo yomthwalo kuvela ukuncipha okuphawulekayo komnqamlezo wentonga ngenxa yocontraksi olulodwa olungelulo-elastiki, yaye ukuqhubeka kwediagram yoxinzelelo neenguqu kuxhomekeke kuqala kuyo yonke into ekubeni xa kubalwa uxinzelelo σ amandla okutsala P asebenza entongeni ahlulwe ngomnqamlezo wokuqala F0 okanye ngomnqamlezo wangoku F. Ngeenjongo zobugcisa, uxinzelelo P|F0 luyathandeka. Olu xinzelelo ludlula kwelona nqanaba liphezulu elibizwa ngokuba ngamandla ezinto, yaye xa elo nqanaba liphezulu sele lidlulile, intonga iyancipha kakhulu kwenye indawo ize ikrazuke. “Uxinzelelo lokwenene” P|F luyenyuka de kube kukophuka.
Umfanekiso 8.
Ukuziphatha kwezinye iintsimbi ezininzi kuyahluka kakhulu kule ichazwe apha. Ukuhamba akusoloko kubonakala, yaye ukuqina kuqala kwangoko emva kokudlula umda wokunwebeka. Kwizinto ezibrittle (ilitye, iglasi, ikhonkrithi) iinguqu ezingezizo ezolulayo ngokubanzi zincinci, yaye sele kunokwanda okuncinane kuvela ukophuka. Ukunwebeka okupheleleyo okunyamezelwa sisixhobo de kube sekophukeni ngumlinganiselo wokoluleka (ngokuchaseneyo: brittleness) wesixhobo, yaye oko, kwintsimbi, kumiselwe ngokuchanekileyo kwiimeko zobugcisa. Noko ke, njengoko ngaphambi kokophuka uguquko olungaphezulu lugxininisa kwiindawo ezikufuphi zecandelo elincitshisiweyo, kufunyanwa ixabiso elahlukileyo lokunwebeka ekophukeni, kuxhomekeka ekubeni ubude bomlinganiselo bamkelwa inxalenye enkulu okanye encinci yentonga, ngoko ukuze kufunyanwe iziphumo ezicacileyo nezithelekisekayo kufuneka kusengaphambili kwamkelwe isivumelwano esithile. Ukunwebeka ekophukeni ngokuqhelekileyo kulinganiswa ngokuthi kwintonga ejikeleze enobubanzi d ngaphambi kovavanyo kuphawulwe ubude bomlinganiselo Ι = 10 d kwaye kususela ekwandeni kwayo ΔΙ kubalwe ukunwebeka ekophukeni εs_Ι = ΔΙ|Ι ._ Ukuba kufuneka kuvavanywe iintonga zecandelo elahlukileyo, ubude bomlinganiselo bumiselwa ngokobubanzi bentonga yesilinda esingqukuva enendawo efanayo yecandelo elinqamlezayo.
Umthwalo wexesha elide
Kwikhondo lovavanyo lokutsalwa akubalulekanga kangako ukuba umthwalo ude kufikelele ekuqhekekeni wongezwa kwisithuba se-10 m imizuzu okanye iiyure ezimbalwa. Nangona kunjalo, ukuba umthwalo usebenza iminyaka okanye amashumi eminyaka, phantsi kweemeko ezithile kuqatshelwa ukuba naphantsi komda wokuhamba ukuma kukhula kancinci ngexesha phantsi koxinzelelo olungaguqukiyo. Kule nto, inxalenye e-elastic, oko kukuthi inxalenye leyo ephelayo xa kukhululwa ngokupheleleyo, ayitshintshi kakhulu. Olu nyuso lokuma okungelastiki olwenzeka ixesha elide lubizwa ngokuba kukukhasa. Kwizinyithi, ngaphandle kwelothe, ukukhasa kubalulekile kuphela kumaqondo obushushu aphezulu; nangona kunjalo, kunjiniyela wokwakha kudlala indima kwikhonkrithi, ethi phantsi koxinzelelo iyekele kancinci, ukuze uxinzelelo lonyuke kwi-armor eqinisiweyo ecinezelweyo, ukuba ikhona.
Umthwalo otshintshayo
Ukuze iimpawu zoomatshini zezinto, ezifunyenwe kuvavanyo lokutsalwa, zikwazi ukusetyenziswa njengomlinganiselo womthwalo ovumelekileyo wezakhiwo, imeko kukuba izinto zikwazi ukumelana, kuzo zonke iintlawulo kwakhona, noxinzelelo ebezalunqobile kanye ngaphandle komonakalo. Le meko ayifezekiswa ukuba izinto zivezwe kukuphindaphindwa rhoqo kokulayishwa nokukhululwa, njengoko kunjalo, umzekelo, kwimeko yeentsika ezithwele amandla e-inertia avela koomatshini abangalinganiswanga ngokupheleleyo. Ngokuphindaphindwa rhoqo ngokwaneleyo komthwalo, inxalenye yolwakhiwo inokuziswa ekugqabhukeni nakwinqanaba loxinzelelo elikude kakhulu ngaphantsi kwamandla ezinto amiselwe kuvavanyo oluqhelekileyo olungamileyo. Ukubonakala kolu hlobo lokusilela kubizwa ngokuba kukudumba ngenxa yokudinwa. Inani le n lemijikelo yomthwalo enokunyanyezelwa yinto lixhomekeke kubungakanani boxinzelelo σ, yaye liba likhulu ngakumbi xa uxinzelelo luncinane. Umzekelo oqhelekileyo wale ngxhomekeko ubonisiwe kumzobo 9, apho kubonakala khona ukuba kumandla ezinto kukho umda osezantsi, omelana nawo nakwinani elingenamda leemijikelo zomthwalo yaye obizwa ngokuba ngamandla ezinto angaguqukiyo. Iidayagram zolu hlobo (sl.9) zibizwa ngokuba ziigophe zikaWӧhler.
Umfanekiso 9.
Ukhuseleko lwezakhiwo
Imithwalo emibini yomda ibalulekile kwizakhiwo: umthwalo apho kuvela khona umonakalo wokuqala osisigxina (umda wokunikezela), kunye nomthwalo apho umthamo wokuthwala wesakhiwo ugqityiwe, yaye saphuke (umda wokophuka). Kuba ngaphambi komda wokunikezela ubuncinane ngokusondeleyo zisebenza iingcinga zeendlela zokuxhathisa kwezinto (ukuhamba kuncinci, umthetho kaHooke), ukhuseleko ngokuchasene notshintsho olusisigxina lunokuhlolwa ngokuthembeka kuzo zonke iimeko apho kuyenzeka ukoyisa ubunzima bezibalo. Ukuba uxinzelelo lulingana nomthwalo, umlinganiselo woxinzelelo lokunikezela noxinzelelo oluphezulu olwenziwa kwisakhiwo ulingana nomlinganiselo phakathi komthwalo apho kuvela khona ukunikezela kunye nomthwalo wokwenene kwaye umele i-coefficient yokhuseleko ngokunikezela. Nangona kunjalo, kwiimeko ezininzi olu lwalamano lulula alukho: ukugoba xa kususwa ukutsalwa, uxinzelelo phakathi kwemiphezulu egobileyo, iinkqubo ezinesakhiwo esitshintshayo kwaye, nto leyo ingalunganga ngakumbi, ukugoba kunye namandla e-axial. Kuzo zonke ezi meko ukwanda okuncinci ngokuthelekiswa komthwalo kunokukhokelela ekwandeni okukhulu koxinzelelo, kwaye ngoko akwanelanga ukusebenzisa i-coefficient eqhelekileyo yokhuseleko kuxinzelelo, koko kufuneka isetyenziswe kumthwalo.
Izehlo ezenzeka emva kokugqitha komda wokunikezela ukuya ekwaphulweni, kwiimeko ezininzi, zinokulandelwa kuphela ngokomgangatho. Ukuba izinto zinemfudumalo yokolula, iindawo apho umda wokunikezela ufikelelwa kuqala, nezisazikhubaza phantsi koxinzelelo olungaguqukiyo okanye olo lonyuka kancinci, zinegalelo elincinci ekuthwaleni umthwalo ongakumbi, ukuze ezinye iindawo zesakhiwo ezixinezeleke kancinci, ukuba kunokwenzeka ngokwemeko yesakhiwo saso, zithwale ngakumbi. Kulo mzamo wokulinganisa iincopho zoxinzelelo kukho umthamo othile wokhuseleko, onokusetyenziswa ekubalweni ukuba ukuguquka okusisigxina kweendawo ezithile, okuveliswe ngumthwalo omkhulu kanye kuphela, akuyongozi (indlela yomthwalo womda).
Ukuba imathiriyeli ibhityile/ithe kratya, umonakalo wokuqala osisigxina ubonakala kwiintanda, apho kwindawo esesichengeni kubakho ukuxinana koxinzelelo okungakumbi, nto leyo ekhokelela kwangoko ekuqhekekeni. Ukuqhekeka ngenxa yokudinwa nasemathiriyelini anokutsalwa kunempawu zokuqhekeka okubhrukhileyo.
Ubudlelwane phakathi kweengxaki kumacandelo ahlukeneyo anqamlezayo
Izibalo zenguquko
Iingcinezelo ezisithoba ze-component ezikwis. 1, zinxulunyaniswa neemeko ezintathu zokulingana. Ezinye ezintandathu, σx, σy, σz τxy, τyz, τzx, zinokunikwa ixabiso elithanda ngokuzimeleyo omnye komnye njengoko kubonakala ekuphuhlisweni kweequations ezahlulayo zethiyori ye-elasticity. Nangona kunjalo, xa la maxabiso emisiwe, imeko yoxinzelelo kwindawo ethile yomzimba oqinileyo ichazwe ngokupheleleyo, oko kukuthi, xa iingcinezelo zeendawo ezintathu ezithe tye omnye komnye zisaziwa, kunokumiselwa ngokungathandabuzekiyo nengcinezelo yendawo yesine ethe tye egqitha kwelo nqanaba lichaziweyo kwaye ene-normal kwicala elithanda nantoni na.
Kumz. 10 kuboniswe itetrahedron OABC enamacala amathathu alungelelaniswe ngokuhambelana neenqwelomoya zenkqubo yolungelelwaniso x, y, z kanti eyesine imele into yomphezulu ejolise ngokungakhethiyo ABC = dF. Ukuze kuqatshelwe ulwalathiso lwayo nendlela yoxinzelelo olugqithiselwa ngayo ngayo, kusetyenziswa enye inkqubo yolungelelwaniso, apho i-ξ axis ime nkqo ku dF.
Umfanekiso 10
Imeko yokulingana kwamandla ahlasela le tetrahedron kwicala le-ξ axis inika
Ukuba kuthathelwa ingqalelo ukuba
iyafumaneka
kunye nokufanayo oko kusuka kwiimeko zokulingana kwicala le-axis η:
Ezi zii-equation ezisetyenziswa ekubaleni uxinzelelo xa kutshintshwa iikhoyinathi. Kubaluleke kakhulu ukuba kujongwe kuphela ezo zinto zomphezulu dF apho i-ξ-xis ihambelana ne-z-xis. Iimilo zale meko singazifumana ngokwenza lula iifom ezandulelayo okanye sizifunde ngokuthe ngqo kumz. 11:
Umfanekiso 11
Uxinzelelo oluqhelekileyo luthatha amaxabiso agqithisileyo kwiindlela α = α0 , apho dσξ/dα = 0. Ngokwahlulahlula kufunyanwa kwisibalo (16)
kwaye ngoko, xa eli binzana lilinganiswa no-zero
Uxinzelelo τξη nalo luya kuba luxinzelelo olupheleleyo lweshear kwezi ndawo, ukuba τyz = τzx = 0. Ngoko ke, nge-equation (17) kumiselwa izalathiso ezimbini ezithe nkqo omnye komnye apho: 1. uxinzelelo olupheleleyo lweshear lulingana noziro kwaye, 2. uxinzelelo oluqhelekileyo lunamaxabiso agqithisileyo (eliphezulu nelisezantsi). Ezi zikhokelo zibizwa ngokuba zizikhokelo zoxinzelelo oluphambili, kanti uxinzelelo oluhambelanayo lubizwa ngokuba lizi--principal stresses. Zimelwe ngo σ1 no σ2 kwaye zinokubalwa ngqo ukusuka kwifomula
Isangqa sikaMohr
Iziqulelelo (16) zinokuboniswa ngokomzobo ngendlela ecacileyo. Ngenxa yoko kufuneka ziguqulelwe zibe yimo:
Ezi zibalo zibonisa kwinkqubo yeekowudi σ, τ uhlobo lweparamitha lwesibalo sesangqa, esizotywe kumz. 12, enezilungelelaniso zembindi σ = 1/2 (σx + σy), τ = 0 kwaye erediyam yaso
Eli candelo libizwa ngokuba sisangqa sikaMohr. Ukuba ngomgca othe tye ongaphezulu oneparalelo neentsika x = const. utsalwa ngapha kwendawo x, apho kugqithiselwa khona uxinzelelo σx, τxy, lo mgca uya kusika isangqa kwindawo p, ebizwa ngokuba yipolo yesangqa sikaMohr. Wonke umgca othe tye pξ otsalwe ngale polo usika isangqa kwindawo ξ echaza uxinzelelo σξ, τξη olugqithiselwa ngapha kwesikweko esinokuthelekiswa no pξ.
Xa kuqwalaselwa uphawu loxinzelelo lwasika xa kuzotywa isangqa sikaMohr, kufuneka kuqatshelwe ukuba lubekwa phezulu ukuba lunendlela eboniswe kwi-sl. 12c. Ngoko ke, kwizixinzelelo ezimbini ezidityanisiweyo τxy, τyx, esinye sihlala silungile yaye esinye sibi.
Kumaxabiso omda σ1, σ2 oxinzelelo oluqhelekileyo ahambelana amanqaku 1 kunye 2 kwisangqa, yaye imigca _p_1 no _p_2 inika imikhombandlela yoxinzelelo oluphambili.
Ukuboniswa koxinzelelo olulele kwindiza x-y kusetyenziswa isangqa sikaMahr akuxhomekekanga nakwesiphi na ingqikelelo ngeengcinezelo σz, τxz, τyz ezithe nkqo kule ndiza.
Umzobo 12
Oko ke oku kuyasebenza nakwimeko yesona sinzima kakhulu soxinzelelo lwamacala amathathu, ukuba kuthelekiswa kuphela ezo ndawo zokusika zonke ezidlula kumgca omnye ofanayo, apha okhethwe ukuba ube ziiasi ze z ne ξ. Kuba, ngokwemigaqo jikelele yotshintsho (15), uxinzelelo oluqhelekileyo σ alunakuba lungenasiphelo nakweyiphi na indawo yokusika, kufuneka ke lube nenani elipheleleyo eliphezulu σ1 kwelinye iplani, kwaye kwelinye ubuncinane σ3, kokubini okunokuthi, ngokuqondakalayo, kube nokuba kube negative. Ukuba ngeevektha σ1 ne σ3 kutsalwa iplani ize izotywe isangqa sikaMohr (sl. 13)
Umfanekiso 13
kumaxinzelelo alala kweli caba (oko kukuthi zonke iindlela ezithe nkqo kweli caba), ngoko ke i-σ1 kunye ne-σ3 ngawona maxinzelelo amakhulu nancinci aqhelekileyo anokuvela, yaye ngoko kufuneka abe ngokuthe nkqo omnye komnye. Ukuba iindlela 1 kunye 3 zongezwa ngendlela 2, ukuze ezi ndlela zintathu zenze inkqubo yeekhonkrithi ezithe nkqo, yaye ukuba kuzotywa izangqa zikaMahr kwiicaba 1 ~2 kunye 2 ~ 3, ngoko ke i-σ2 kwesinye sezi zangqa ngowona mncinci, yaye kwelinye ngowona mgangatho uphambili omkhulu, yaye ngoko kwiindawo ezinqamlezayo ezithe nkqo kwiindlela 1, 2 no 3 uxinzelelo lokucheba lulingana noziro. Amathathu amaxinzelelo aqhelekileyo athe nkqo omnye komnye σ1, σ2 no σ3, apho kungenzeki maxinzelelo okucheba, abizwa ngokuba ngamaxinzelelo aphambili.
Umda wokuhamba kweplastiki kunye nomda wokuqhekeka phantsi kwimeko yendawo yoxinzelelo
Imeko yoxinzelelo ibizwa ngokuba ngumntu-mnye, mibini okanye mithathu-dimensional, ngenye indlela: yomgca, ethe tyaba okanye yesithuba, kuxhomekeka ekubeni iingozi eziphambili enye, ezimbini okanye zontathu zingalingani no-zero. Kwiindawo zesakhiwo ezisetyenziswa rhoqo, oko kukuthi kwintonga etsalwayo, ecinezelweyo nenegobileyo, imeko yoxinzelelo, ubuncinane kwiindawo ezixineneyo kakhulu, yinye-dimensional, kwaye kunjalo nakwiimvavanyo zokutsala, ukucinezela okanye ukugoba, ezisetyenziswa phantse ngokupheleleyo kuvavanyo lwezinto zokumisela uxinzelelo oluvumelekileyo. Ngokwahlukileyo koko, kwiipleyiti ezithwalwa ngaphakathi kwendiza yazo okanye ngokuthe nkqo kuyo, kwakunye kumaqokobhe, imeko yoxinzelelo iyimibini-dimensional, yaye kwezinye iimeko kuvela iimeko ezintathu-dimensional zoxinzelelo, ngoko ke kuyimfuneko ukuba, ngokusekelwe kumda wokunwenwa nokwaphuka, omiselwe kwimeko yoxinzelelo yinye-dimensional, kufunyanwe izigqibo ngokuziphatha kwento kwimeko yoxinzelelo yesithuba.