Nheyo
Basa resimba rezvinhu nderekuona kuti masimba ekunze api anogona kutsungirirwa nemuviri wakasimba (semuenzaniso, chivako, chikamu chechimiro kana ivhu). Kuti tipindure mubvunzo uyu tinobva pamaitiro maviri: kune rimwe divi, zvinonetsa hazvifaniri kupfuura miganho yakati inobva parudzi rwezvinhu, uye kune rimwe divi, kuenzana pakati pemasimba ekunze neemukati kunofanira kuva kwakagadzikana. Zvinoenderana neizvi, matambudziko ose esimba rezvinhu anogona kupatsanurwa kuva “Matambudziko ekunetseka” uye “matambudziko ekugadzikana.”
Pamatanda nematanda makuru uye vatakuri vakavakwa nazvo (trusses, mafuremu) kuverengwa kwekushushikana kunoitwa muzvikamu zviviri, zvokutanga zvichiitwa nekuti kubva pamasimba ekunze akapiwa kuverengwa resultant yemasimba emukati anoendeswa nepakati pechikamu chemuchinjiko, uyezve kubva kune aya “masimba echikamu” ndimo munobva maverengwa kushushikana. Chikamu chekutanga chemaitiro chinomirira chirango chakaparadzana, chakakura, statics yezvivakwa zvekuvaka, chine nzira dzacho dzakagadzirwa uye chinowanzopatsanurwa kubva kuramba kwezvinhu, iro basa raro rinobva pakutsanangura kushushikana kubva pamasimba echikamu akapiwa.
Pfungwa dzinokosha dzekusimba kwemidziyo
Tsananguro yespaneti inowanikwa kuburikidza nepfungwa dzinotevera dzinokosha. Ngatiregei kuti pahuru panoshanda hurongwa hwekuenzana hwemasimba ekunze. Ngatifungidzirei kuti takakamura muviri nemucheka wega wega kuita zvikamu zviviri, uye kuti tabvisa chimwe chazvo pamwe chete nemasimba anoita pachiri; ipapo chiito chacho pachikamu chasara, kuti kuenzana kwemasimba nekurongwa kwekushanduka kurambe kusina kuchinjwa, chinofanira kutsiviwa nemasimba ekuwedzera anotakurwa pamusoro penzvimbo yekucheka. Aya masimba “emukati” anogara akagoverwa pamusoro penzvimbo yekucheka, zvekuti pane chimwe nechimwe chedenderedzwa dF panowirirana simba dβ. Kana chikamu dβ dF chikagadzirwa uye muganhu uchifambwa dF -> 0, ipapo chikamu ichi chinotarisira kukosha kwemuganhu kunonzi spaneti. Spaneti iri pachinhu chakati chepamusoro, sezvakaita dβ, uye rinogona kupatsanurwa kuita zvikamu zvinoti normal uye tangential ku dF, spaneti yakatwasuka σ uye spaneti yekusheara τ.
Kana zvikamu zvikatorwa nepakati pechimwe chete poindi nenzira dzakasiyana, zvinopesanawo nemasimba akasiyana. Kunyanya kana kubva mumuviri mukabviswa elemental prism, inoratidzwa pafig. 1, pane rimwe nerimwe remativi ayo matanhatu pachashanda vector yesimba inogona kupatsanurwa kuita zvikamu zvitatu munzira dzezviyero zvemakona x, y z. Masimba anoshanda pamativi anopikisana epamusoro anosiyana pakati pawo, hongu, chete ne differential, saka zvinofanirwa kusiyanisa 3 * 3 = 9 emasimba echikamu, ayo anoratidzwa nenzira inotevera:
Makonzero echiito chakatarisana σ anopiwa indekisi yedanda raanotevera uye anoonekwa seakanaka kana achikonzera kutambanuka, uye seasina kunaka kana achikonzera kudzvanywa. Matanho ekusheura τ anopiwa maindekisi maviri, wokutanga wavo wakafanana neindekisi yechiito chakatarisana chinoenderana, uye wechipiri unoreva danda rine nzira iyo chiito chekusheura chinoshanda. Kana nzira yakanaka yechiito chakatarisana inoenderana iri munzira yeakatsiga (asina kunaka) koordineti danda, ipapo chiito chekusheura chinoonekwawo seakanaka kana chichishanda munzira yeakatsiga (asina kunaka) koordineti danda.
Muf. 1.
Kudyidzana kwekushushikana kwekucheka
Kana nokuda kwechikwere chekutanga, mufananidzo 1, pakaiswa mamiriro ekuti nguva yemasimba ose maererano neaxis x iite zero, zvinobuda τyz dx dz * dy = τzy dx dy * dz Kubva pano, uye kubva muzviyero zviviri zvinoenderana zvemaoresa y ne z, zvinobuda kuti manikiro ekucheresa ane maindekisi akafanana akaenzana pakati pawo τxy = τyx, τyz = τzy, τzx = τxz (1)
Kukanganisika kwezvikamu
Kuti mamanikiro akatsanangurwa pamusoro apa ave nerevo yepanyama, zvinobuda kubva mukubatanidzwa kwawo netsananguro inotambirwa nemuviri wose pasi pesimba remauto ekunze. Muf. 2 unoratidza bhuroko rakapfava rimwe, iro risati raita deformashi raiva rechinhu chakakona uye raiva nemarefu emipendero dx, dy, dz. Marefu emipendero mushure me deformashi anogona kuratidzwa se dx + Δdx, dy + Δdy, dz + Δdz; zvikamu εx = Δdx|dx, εy = Δdy|dy, εz = Δdz|dz zvinonzi dilations. Aya ndiwo huwandu husina chiyero uye muzvinhu zvese zvinofungwa mukuvaka hudiki maererano ne1. Kunze kwekurebesa kwemipendero, bhuroko rakapfava dx * dy * dz rinogonawo kuchinjwa makona aro aimboita akatwasuka pakati pemativi aro.
Mufananidzo 2. component deformation
Ngazvive kuti mushure mekushanduka kona iri pakati pendege dzinosangana pamwe chete nemupendero OC ive yakaenzana ne 
uye zvakafanana kuderera kwekona yakarurama parutivi AO kuve γyz, uye kuderera parutivi OB kuve γzx. Shanduko idzi nhatu dzemakona γxy, γyz, γzx, dzinonzi kutsvedza uye dzinogarawo dziri diki zvichienzaniswa ne1. Nemakomhonenti matanhatu ε uye γ, kushanduka kweelementi yeparalelepipedhi yekutanga kunotsanangurwa zvizere se“deformation duku”. Kuchinja kwechinhu chevoliyumu d_V = dx * dy * dz_ kuri ΔdV = (dx + Δdx) (dy + Δdy) (dz + Δdz) - dx dy dz, kubva ipapo, kana zvigadzirwa zvedilatation zvikaregeredzwa sezvidiki zvehurongwa hwepamusoro, kunowanikwa kubatana kwecubha ϱ = ΔdV|dV = εx, εy, εz (2)
Kutama
Kukanganisika kwechinhu chakasimba kunogonawo kutsanangurwa zvizere nenzira iyi, kuti panzvimbo imwe neimwe yacho ipiwe kufamba kwakaitika pairi. Kana kufamba kukuru kunoenderana nekufamba kwemuviri wakaoma kwabviswa mukufunga, nenzira yekuti, kana zvichidikanwa, sisitimu yekoordhinati inofambiswa inotorwa pakuverenga, ipapo zvikamu zvekufamba μ, ν, ω zvinogara zviri zvidiki, uye zvinobva pazvo maererano nemakoorodhinati zvidiki zvichienzaniswa ne1. Pasi peiyi pfungwa maererano nesl. 3 urefu hwe line element OA = dx mushure mekukanganisika
saka 
(3)
Nenzira yakafanana, kubva pamuf. 3 zvinoonekwa kuti kutsvedza γxy _γ1 + _γ2: uye zvakare
(4)
Mufananidzo 3 kutsvedza
(5) 
(6)
Aya hukama anonzi mamiriro ekuenderana uye anoratidza kuti zvinhu zvakaremara zvinogona kuiswa pamwechete seshongwe yemamoyisiki kuitira kuti nzvimbo irambe ichizadzwa pasina kukanganisika, izvo zvisingagoneke kana kukanganisika kwezvinhu kuri kwechisarudzo. Mamiriro ekuenderana iienzaniso dzemadiferenshiyari, saka, zviri pachena, zvikamu zvese zvitanhatu zvekukanganisika pakwerega rimwe nerimwe zvakazvimirira pakati pazvo, asi kurongeka kwazvo munzvimbo ipi neipi yakapararira yakaperera kunosungwa nemamiriro (5) ne (6).
Sezvo mamiriro aya akawanikwa nekusiyanisa kubva muequation (3) uye (4), pakuaumba anorasika chikamu chekubatana chirimo mumaequation ekutanga. Nokudaro hazvina kukwana kuti chete rimwe chete remaseti maviri aya emaequation rizadziswe, asi maseti maviri aya ose anofanira kugutsikana kana uchida kuti kuenderana kwekukanganisika kuve kwakavimbiswa.
Mienzaniso yesiyano yesystemi yeelastisiti
Kuti kuverengwe misungo nekushanduka kwemiviri yeelastiki, maequation anotevera anoshandiswa:
Mamiriro ekuenzana kwechinhu chevhoriyamu. Mamiriro ekuti ma moment pamusoro pematatu ese axis akaenzana ne zero akatotobatsirwa pakuburitsa equation (1). Mamiriro ekuenzana kwemasimba anobva maererano nesl. 4
Mufananidzo 4
(7a-c)
Kana zvikamu zvesimba remuviri (semuenzaniso uremu, simba recentrifugal) pariyuniti yevhoriyamu zvichiratidzwa ne X, Y, Z. Hukama pakati pekumanikidzwa nekushanduka-shanduka. Pano panorehwa hukama pakati pekumanikidzwa kwezvikamu nekushanduka-shanduka kwezvikamu. Mune dzidziso yeelastisiti, sezvo mutemo unowanzo funga hukama hwakatwasuka chete, hunoratidzwa nemutemo waHooke:
(8a-c)
(8d-f)
Kana maequation (8a-c) akagadziriswa maererano nekushushikana, zvinowanikwa
(8 a)
kso uye minda miviri inoenderana. Mutemo waHooke wakaratidzwa nekuenzanisa (8) hauunzi mutemo wechisikigo unozadzikiswa zvakasimba, asi idealization yemaitiro chaiwo, ayo anotsauka kubva pauri zvakanyanya kana zvishoma, zvichienderana nezvinhu uye ukuru hwekumanikidzwa. Tichitarisa kuti kugadziriswa kwemathematical kwedambudziko rekusimba kwezvinhu rine hukama hwakaoma, husiri hwemutsara pakati pamanikiro nekushanduka kunounza kuoma kukuru zvikuru uye kunogona kuitwa chaizvo muzviitiko zviri nyore chete, kunofanira kuitwawo kunyangwe kune izvo zvinhu (betoni!) maitiro awo anotsauka zvikuru kubva kuMutemo waHooke, kuverenga kwakavakirwa pauri kushandiswa sechokutanga, uye kazhinjiwo semhinduro imwe chete yekufungidzira, iyo zvimwewo inowanzobatsira zvikuru uye inopa ruzivo runopfuura kungova rwemhando. G = E|2 (1+μ).
Inobva zvirokwazvo pachibatanidzo pakati pekushushikana nekushanduka (8), kubva muequation dzekushandura (16) dzekushushikana uye hurongwa hweequation hwakakodzera hwekushanduka kwezvikamu. E na G zvine chiyero chekushushikana uye, pazvinhu zvese zvekuvaka, zvakakura zvichienzaniswa nekushushikana σ ne τ kunogona kuoneka. Asi pachokwadi ichi ndipo panovakirwa fungidziro inogamuchirwa kwese mudzidziso yeelastiki, kuti kushanduka kudiki. Coefficient yekuwedzera kweparutivi (Nhamba yaPoisson) μ haina chiyero uye inogara iri pakati pe 0 ne 1/2 .
Ukama pakati pekukanganisika kwezvikamu uye kufambiswa. Ukama uhwu hunopihwa nemaequation (3), (4). Aya ndeehunhu hwegeometry chete. Aya masisitimu matatu anopa 3+6+6=15 maequation ezvisingazivikanwi 15, kureva kuti zve 6 zvikamu zvekushushikana, 6 zvikamu zvekukanganisika uye 3 zvikamu zvekufambiswa. Naizvozvo anokwana pakutsanangura izvi zvisingazivikanwi. Kukurira zvemasvomhu sisitimu yakakura kudai yema differential equation kunobvira, sezviri pachena, chete mumamiriro akasarudzika. Kana muequation (8) zvikamu zvekukanganisika zvatsiviwa nezvikamu zvekufambiswa zvinoenderana nemaequation (3) uye (4) uyezve normal stresses σ nemashear stresses τ, zvinoenderana nemaequation (8 d - f), zvinoiswa mumamiriro ekuenzana, eq. (7), anowanikwa ma differential equations anonzi maequation ekutanga edzidziso ye elasticity.
(9)
apo 
panoratidzwa mushandisi weLaplace. Tichitarisa pa (2) aya ndiwo maequation matatu e differential ane kufamba kwecomponent katatu μ, ν, ω; kubva maariwo, nekusiyanisa zvichienderana na (3), (4) uye (8), zvinogona kuwanikwa kushushikana nekukanganisika kwese kwecomponent. Maequation (9) anomiririra kazhinji pakutanga pakanaka pakudzidza nyaya dzakakosha.
Basa rekushandura chimiro
Tsananguro
Kana mutakuri warongerwa mutoro, nzvimbo dzinoitirwa masimba ekunze dzinowana kufamba kweelastic uye masimba acho anoita rimwe basa ipapo. Simba rakaunzwa nenzira iyi rinogona kushanduka kuita mafomu akasiyana. Kana mutoro ukaiswa pakarepo, zvekuti nzira yekushanduka ine kumhanya kukuru, chikamu chesimba iri chinoshanduka kuita simba rekinetic, iro rinopararira nenguva, kungave nokutapurirwa pasi semafungu eelastic anonyangarika asinga peri, kana nokushandurwa kuita kupisa kuburikidza nekukwesana kwemukati. Kana mitoro ikaiswa zvinyoronyoro zvikuru zvekuti hapana kuwedzera kunoonekwa kwesimba rekinetic, kureva kuti mitoro inokura zvishoma nezvishoma ichibva pa zero iri mukuyanana nguva dzose nemasimba emukati, simba iri zviri pachena rinoshandiswa chete pakukanganisa muviri, uye panguva iyoyo rinonzi basa rekushanduka.
Kuverenga basa rekushanduka kwechimiro tichazviratidza kutanga pachidimbu chakaremerwa nekukweverwa munzira imwe chete (muf. 5).
Ngatifungidzirei kuti kushushikana kuripo σ uye kuwedzera kwakakodzera ε zvinowana kuwedzera dσ ne dε. Ipapo simba σdF parwendo rwe dε * dl richaita basa σdF * dεdl = σdεdV, kana vhoriyamu yechidimbu ichimiririrwa ne dV. Kana kushushikana kukwira kubva pa zero kusvika pakukosha kwayo kwekupedzisira uye kuwedzera zvinoenderana nazvo kubva 0 kusvika ku ε, basa rose raitwa paunit yevhoriyamu richava:
Saizvozvowo, kune chinhu chakaiswa pasi pekunetswa kwekuchekwa τ (fig. 6) basa rekuremara pauniti yevoliyamu (basa rekuremara rakananga, elastic potential):
apo paine simba rimwe chete pamasimba mana τ * dF rinoita basa.
Kazhinji, kana pane chikamu chidiki chiri kurohwa nemakomboni ese matanhatu ekudzvanywa, basa rekukanganisa rinoenderana rinowanikwa nekuwedzera mabasa emakomboni ega ega ekudzvanywa:
(10)
Nekudiferenshesa maererano neganhu repamusoro peimwe neimwe yeaya maindigirals, tinowana hukama hunoshanda panguva yakanyanya kazhinji:
(11)
nezvimwewo zvimwe zvinoshanduka zvekomponenti. Kana muviri uri elastiki, mamiriro ega ega akatsanangurwa emutoro anogara achienderana nemamiriro akafanana ekushanduka, zvisinei kuti mamiriro acho asvikwa pakukwidziridzwa kana pakuderedzwa kwemutoro. Ipapo pasi peintegrals panomira mabasa asina kusiyana uye simba rose rakashandiswa pakutakura uyezve pakuderedzwa kuzere kwemutoro ndi a = 0, tichifunga kuti panguva iyi miganho yepamusoro yeintegrals inova zero. Naizvozvo simba rose rinopinzwa mumuviri pakutakura rinodzokera panguva yekuburutsa.
Mufananidzo 6
Mufananidzo 7
Kune muviri usinganyanyi kuva elastic, hukama pakati pekushushikana nekukanganisika pakutenderera kwese kwekuremedza nekuburutsa hunoita chimiro chinofananidzirwa pedyo pamuf. 7 nemitsara O A B. Simba 
rinounzwa pakuremedza rakaenzana nenzvimbo OAA, uye simba rinodzoserwa panguva yekuburutsa inzvimbo ABA, saka basa rinoenderana nenzvimbo yakatenderedzwa rinorasika (rinova kupisa). Kana mukuita kweoscillation kushushikana kuchichinja nguva nenguva pakati peukoshi hwepamusoro hwepamusoro 
neukoshi hwepamusoro hwepasi 
kukanganisika kusina elastic kunofamba zvakafanana sezvinoratidzwa nemitsetse yakaputsika pamuf. 7 uye panguva yega yega yeperiodi yeoscillation kunoshandurwa kuita kupisa pakuyuniti yevhoriyamu simba DABCD. Maitiro akadaro panguva yekukanganisika, apo kukanganisika kunosara shure kwekushushikana, anonzi elastic hysteresis, uye curve DABCD ihysteresis loop.
Basa rekushanduka uye mutemo waHooke
Kana mumaintegral muequation (10) ukaiswa mutemo waHooke, kugadzirisa kunogona kuitwa, uye nekuda kwespecific deformation work zvinobuda zvinotevera:
(12a)
(12b)
(12c)
Kana fomu rechipiri reaya rinoiswa muenzaniso (11), panobuda zvakare mutemo waHooke, maenzaniso (8), uri muchimiro chakagadziriswa maererano nemaforosi. Mashoko ekuti basa rekushanduka-shanduka rinotsamira panzvimbo dzose dzekushanduka, sezvinoratidzwa nemaenzaniso (12b), saka akaenzana nemutemo waHooke. Kana muenzaniso (12c) ukatsanangurwa maererano nemaforosi, zvinobuda
(13)
Mafomu aya, kusiyana nemafomu (11), anoshanda chete kumiviri inozvibata maererano nemutemo waHooke uye haagoni kushandiswa kana hukama pakati pemasimba nekushanduka hwakasiyana. Zvinonzwisisika kuti kurudyi rwemaequation (13) kunongova nekushanduka kwekomponenti kunokonzerwa nemasimba, uye zvese zvimwe zvinogona kunge zvakakonzerwa nekushanduka kwetembiricha, kukambaira, kuzvimba, rekristalizasi, nezvimwewo zvinobviswa.
MITEMO YEINTEGRAL MUTHEORY YEEKISITENSI
Kufamba kwekufungidzira. Nheyo yekuti simba rinogona kuva shoma zvikuru
Sezvo mutemo waHooke, maequation (8) uchikwanisa kutsiviwa neequation imwe chete (12b), saizvozvowo panzvimbo pemamiriro ekuenzana panogona kuunzwa musimboti wekutama kwechinguva, semutemo mukuru unoshanda wemakanika. Mutemo uyu unoratidza kuti mamiriro ekuenzana anozivikanwa nekuti basa rose rinoitwa nemasimba ose pakuchinja kudiki kwemamiriro ekukanganiswa rinoenzana ne zero. Kana kuchinja kudiki kwekutama kweelastiki tikaratidza δμ δν, δω, ipapo masimba emuviri anotsanangurwa neequation (7) anoita basa rechinguva
uye masimba epamusoro px, py, pz anoshanda panhengo dF yepamusoro rekunze remuviri basa 
apo integral yetatu inoreva vhoriyamu yose, uye integral kaviri inoreva pamusoro pekunze hwese hwemuviri. Pakuverenga basa rinoitwa nemasimba emukati unoshandiswa equation (12b), saka basa pachikamu chevhoriyamu rinowanikwa
Nheyo yekufamba kwekufungidzira inobva ipapo inopa
(14)
Kana mitoro X, Y, Z px, py., pz ikanzwisiswa sezvikamu zvesimba regiravhiti (uremu hwayo pachahwo nemutoro wekunze), maintegral ari kurudyi anomirira simba rekuwanikwa rakaraswa nemitoro iyi, nepo rutivi rwekuruboshwe ruchimirira kuwedzera kwesimba rekuwanikwa (reelastic) remuviri, saka nheyo iyi inoratidza kuti simba rose rekuwanikwa regwara uye remitoro yakarara pariri kana paine kuenzana rine kukosha kwakanyanya. Kana kukosha uku kwakanyanya kuri hushoma, kuenzana kwakagadzikana.
Nheyo ye hushoma hwepotential energy, inoratidzwa ne equation (14), chirevo (12b) chebasa rekukanganisika, pamwe nemamiriro ekuwirirana kwekukanganisika (5), (6) zvinoumba hurongwa hweequation hunokwana kuvaka dzidziso ye elasticity, uye hunonyanya kuenzana nehurongwa hweequation. Hurongwa uhu hunogona kubatsira zvikuru kunyanya pazviitiko apo kuzadzikisa differential equations (9) kunounza matambudziko ekuverenga, uye nokudaro mhinduro inofanira kutsvakwa nepadyo, semuenzaniso, pakufamba kwemutoro kufanofungidzirwa chimiro chakakodzera chine maconstant akati wandei akasununguka, obva atemerwa kubva kuchinodiwa chekuti equation (14) igutsikane. Nenzira iyi, hakuzi kuwanikwa mhinduro chaiyo yedambudziko, asi kungori kuenzanisa kwakanakisisa kunogona kuwanikwa nechimiro chemhinduro chakasarudzwa. Kana kuenzanisa kwakakwana here kana kwete, zvinoenderana kutanga kwezvose nechimiro chemhinduro chagamuchirwa, uye kushandiswa kunobudirira kwenzira iyi kunoda hunyanzvi uye ruzivo.
Nheyo yaCastigliano
Kunyange pakurongwa kwehuwandu hushoma hwepotential energy tichienzanisa mamiriro ose ekuvhunduka anozadzisa mamiriro ekuenderana kwekuvhunduka uye tichibvisa pakati pawo ayo anopindirana ma stresses azadzisa mamiriro ekuenzana, paCastigliano principle tichienzanisa mamiriro ose e stresses anozadzisa mamiriro ekuenzana uye pakati pawo tobvisa ayo anopindirana deformation azadzisa mamiriro ekuenderana kwekuvhunduka. Iyi principle inoti: kubva pamamiriro ose anobvira ekuenzana, chaiwo anoitika ndiwo ane basa diki rekushanduka. Castigliano principle pamwe neequation (12c) yebasa rekushanduka nemamiriro ekuenzana zvinoumba hurongwa hweequation hwakakwana pakuvaka kusimba kwezvinhu. Sezvo iyi principle iine mutemo waHooke, kushandiswa kwayo kunobva pane pfungwa yekuti kushanduka kunogona kutsanangurwa zvizere nemutemo uyu. Izvi zvinoda kwete kungori maitiro elastiki ane mutsara ezvinhu chete, asiwo zvinobvisa shanduko dzetembiricha.
Maitiro emidziyo pamusoro pemiganho yeelastiki
Zvinoitika pakutakurwa kwakasimba
Kuchinja kwemaitiro emuviri pasi pesimba remasimba chinhu chakaoma kwazvo, saka kunofanira kurerutswa munzira dzakasiyana kuti kunzwisiswe. Imwe yeiyi kurerutsa ndiyo pfungwa yekuti mitoro inoiswa zvishoma nezvishoma, sezvinoitwa, semuenzaniso, nemasampuli pakuyedza kukweva nekutsikirira.
Kana tsvimbo yesimbi inotakurwa nekudhonzerwa ikaiswa pamutoro unokura zvishoma nezvishoma uye kuwedzera kwayo kweurefu ε kuchiyerwa, panowanikwa dhayagiramu inoratidzwa pafig. 8. Pakutanga kuwedzera uku kudiki zvikuru uye kunoenzana nekushushikana, sezvinodiwa nemutemo waHooke. Kubva pane imwe kushushikana yakati, kuenzana kunopera uye kuwedzera kunokura nekukurumidza. Nzvimbo chaiyo yemuganho wekuenzana uku inonetsa chaizvo kutsanangura. Kuyera kukarurama kukuru, ndipo panobuda kuri pasi. Kune zvinhu zvakawanda, inowanikwa pa σ = 0, uye mutemo waHooke unomirira ipapo kungori fungidziro yekutanga yemaitiro e-elastic, nhengo yekutanga yekukudziridzwa muTaylor series yebasa ε = ε (σ) pedyo nepakutanga kwekoodhineti.
Kana tsvimbo yaburitswa kubva pamutoro, zvinoonekwa kuti kana kushushikana kusina kukura zvakanyanya, deformation inonyangarika zvakare, maererano nemutemo waHooke. Asi izvi zvinoshandukawo kana kushushikana kwakati kwadarika kunosvika pedyo nemuganho weproportionality, unonzi muganhu weelasticity; ipapo deformation yose inosanganisira chikamu cheelastic (chinodzoka) nechisina elastic (chisingadzoki). Muganhu weelasticity haungagoniwo kutsanangurwa chaizvo, unowanikwa zvakaderera sezvo kunyatsoyerwa kuchiwedzera. Zvisinei, sezvo uine kukosha kukuru kwehunyanzvi, nokuti unomirira muganhu wekushanda muzvinenge zvese zviverengero zvekusimba kwezvinhu, uye panguva imwe chete muganhu panotanga kukuvara kusingadzoki, pakuedza masampuli unotsanangurwa zvakajeka nechibvumirano chakagamuchirwa, saka, semuenzaniso, seganhu re0.2% rinoratidza kushushikana uko kuderera kusingadzoki kunosvika 0.2%.
Pakangodarika muganhu weelastiki, kukanganisika kunokwira pakarepo uye kunogona kuonekwa neziso risina rubatsiro; pasi pekumanikidzwa kunenge kuchigara kwakafanana, tsvimbo inoreba isingamire. Kumanikidzwa uku kunonzi muganhu wekuyerera. Pamichina yehydraulic yekuongorora zvinhu, mushure mekutanga kwekuyerera panogonawo kuonekwa kuderera kwekumanikidzwa kwakanyanya kana kushoma; sezvinoratidzwa pafig. 8 negonzo rakaputsika; ipapo kukosha kukuru kunonzi muganhu wepamusoro wekuyerera, uye kumanikidzwa kwekuyerera kunoramba kuri kwakafanana kunobva kwatevera kunonzi muganhu wepasi wekuyerera.
Kana kusvikwa kudyika kwakati, uko kunenge kusingachinji zvikuru, kushushikana kunotanga kukwira zvakare, zvinhu zvinobva zvaoma. Munzvimbo iyi yekutakurwa kunoonekwa kuderera kunooneka kwechikamu chemuchinjikwa chetsvimbo nokuda kwekudzikira kweparutivi (kusingachinji), uye kuenderera mberi kwechati yekushushikana nekushanduka kunoenderana pakutanga nezvekuti pakuverenga kushushikana σ simba rekutambanudza P riri kushanda kutsvimbo rinopatsanurwa nepakutanga muchinjikwa F0 kana muchinjikwa wazvino F. Zvechinangwa zvehunyanzvi kushushikana P|F0 kunonakidza. Kushushikana uku kunopfuura nepamwero wepamusoro unonzi simba rezvinhu uye kana mwero uyu wadarika, tsvimbo inotetepa zvikuru pane imwe nzvimbo uye yobvaruka. “Kushushikana chaiko” P|F kunokwira kusvika pakundikana.
Mufananidzo 8.
Maitiro ezvimwe simbi dzinorema anosiyana zvikuru nezvakatsanangurwa pano. Kuyerera hakuwanzo kuoneka zvakajeka, uye kuoma kunotanga pakarepo mushure mekudarika muganhu wekuchinjika. Pazvinhu zvinotsemuka zviri nyore (dombo, girazi, kongiri), kuchinja kusiri kwekuchinjika kunowanzo kuva kudiki zvikuru uye kutotsemuka kunoitika kutokwana kuchinja kudiki. Kuwedzera kwese kunosangana nezvinhu kusvika pakutsemuka ndicho chiyero chekugona kutambanuka (zvakapesana: brittleness) kwechinhu uye izvi zvinotsanangurwa chaizvo muzvinodiwa zvehunyanzvi zvesimbi. Zvisinei, sezvo pakarepo usati watsemuka kumwe kuchinja kuchiunganidzwa panzvimbo dzakapoteredza dzine chikamu chakamanikana, kukosha kwekuwedzera pakutsemuka kunowanikwa kwakasiyana, zvichienderana nekuti pakureba kwekuyeresa panotorwa chikamu chikuru kana chidiki chetsvimbo, saka kuti tiwane mhedzisiro imwe chete uye inofananidzwa pakati pawo, panofanira kutambirwa kare tsika yakatarwa. Kuwedzera pakutsemuka kunoyerwa kazhinji nenzira yekuti patsvimbo yakatenderera ine dhayamita d, usati waita muedzo, kureba kwekuyeresa Ι = 10 d kunocherechedzwa uye kubva pakurebesa kwayo ΔΙ kunoverengwa kuwedzera pakutsemuka εs_Ι = ΔΙ|Ι ._ Kana zvichidiwa kuti dziongororwe tsvimbo dzechimwe chikamu chemuchinjiko, kureba kwekuyeresa kunosarudzwa maererano nedhayamita yetsvimbo yecylindrical yakatenderera ine nzvimbo imwe chete yechikamu chemuchinjiko.
Mutoro wakareba-nguva
Pakuitwa kweedzo yekutambanudza, hazvina kunyanya kusiyana kuti mutoro unokwidziridzwa kusvika pakuputsika mukati me10 mneti kana maawa mashomanana. Zvisinei, kana mutoro ukashanda kwemakore kana makumi emakore, pasi pemamwe mamiriro zvinoonekwa kuti kunyange pasi pemuganho wekuyerera, kushanduka pasi pekunetsekana kwakatarwa kunowedzera zvishoma nezvishoma nekufamba kwenguva. Panguva iyoyo, chikamu chekupfava, kureva chikamu chinonyangarika kana mutoro wabviswa pakupedzisira, hachichinji zvikuru. Kuwedzera uku kwekushanduka kusingadzokeri kunoitika panguva refu kunonzi kukambaira. Pamasimbi, kunze kwetungamusi, kukambaira kwakakosha chete patembiricha dzakakwirira, asi kumainjiniya ekuvaka kunobatawo kongiri inozvidzikisa zvishoma pasi pekumanikidzwa, zvokuti kushushikana kunokwira musimbi inosimbisa iri mukumanikidzwa, kana iripo.
Mutoro unochinja
Kuti maitiro emuchina echinhu, akawanikwa pakuongorora kwekudhonza, ashande sechiyero chemutoro unobvumirwa wezvivako, panodiwa kuti chinhu chiwane, pakuremerwa patsva kwega kwega, kusagadzikana kwachakambotakura kamwe pasina kukuvara. Chinodiwa ichi hachizadzikiswi kana chinhu chichiiswa mukuremerwa nekusunungurwa kazhinji, sezvinoitika, semuenzaniso, kumatanda anotakurwa nemasimba e inertia emichina isina kunyatsodzikamiswa. Nokudzokorora kuremerwa kakawanda zvakakwana, chikamu chechimiro chinogona kuputsika kunyange pakusagadzikana kuri kure zvikuru nesimba rechinhu rakatarwa nekuyedzwa kwakajairika kwestatiki. Chiitiko chekuputsika kwemhando iyi chinonzi kuputsika nekuda kwekuneta. Nhamba n yemacikoro ekuremerwa ayo chinhu chinogona kutsungirira inoenderana nekukura kwekusagadzikana σ, saka inowedzera kana kusagadzikana kwadzikira. Muenzaniso wakajairika wekuenderana uku unoratidzwa pamuf. 9, uko zvinoonekwa kuti kune simba rechinhu kune muganhu wezasi, unogona kutsungirirwa kunyange paine nhamba ipi zvayo huru yemacikoro ekuremerwa uye unonzi simba rinogara rechinhu Magirafu erudzi urwu (muf. 9) anonzi Wӧhler curves.
Mufananidzo 9.
Kuchengetedzeka kwezvivako
Mitoro miviri yemuganhu inokosha kuzvivakwa: mutoro unokonzera kukuvara kwekutanga kusingachinji (muganhu wekuyera), uye mutoro uyo kugona kwechivako kutakura kunenge kwapera, zvobva zvatyoka (muganhu wekutyoka). Sezvo pamberi pemuganhu wekuyera fungidziro dzesainzi yemasimba ezvinhu dzichiri kushanda zvinenge zvizere (kufamba kudiki, mutemo waHooke), kuchengetedzeka pakuchinja kusingachinji kunogona kufungidzirwa zvine chivimbo muzviitiko zvose izvo matambudziko emasvomhu akakwanisa kugadziriswa. Kana kushushikana kuchienderana nemutoro, chiyero chekushushikana pamuganhu wekuyera kune kushushikana kukuru kunoonekwa muchivako chinoenzana nechiyero pakati pemutoro unokonzeresa kuyera nemutoro chaiwo uye chinomiririra coefficient yekuchengeteka pakuyera. Zvisinei, mune dzimwe nyaya hukama uhu huri nyore hahupo: kukotama kana kudhonza kwabviswa, kudzvanywa pakati penzvimbo dzakabudikira, masisitimu ane chimiro chinoshanduka uye, chinonyanya kusagadzikana, kukotama nesimba reaxial. Muzviitiko zvose izvi kuwedzera kudiki kwemutoro kunogona kutungamirira kukuwedzera kukuru kwekushushikana, uye ipapo hazvina kukwana kushandisa coefficient yekuchengeteka pane kushushikana, asi inofanira kushandiswa pamutoro.
Zvinoitika mushure mekudarika muganhu wekuyera kusvikira pakuputsika zvinogona kazhinji kucherechedzwa chete nenzira yemhando. Kana zvinhu zviri ductile, zvikamu zvakatanga kusvika pamuganhu wekuyera, uye zvinoramba zvichikanganiswa pasi pekumanikidzwa kusingachinji kana kunongowedzera zvishoma, zvinobatsira zvishoma mukutakura mutoro unotevera, zvekuti zvimwe zvikamu zvesangano zviri pasi pekumanikidzwa kushoma, kana zvichibvira tichitarisa chimiro charo, zvinotora chikamu chikuru mukutakura. Mune uku kuda kuenzanisa misoro yekumanikidzwa mune imwe chengetedzo yekuchengeteka, iyo inogona kushandiswa pakuverenga kana kukanganisika kusingagumi kwezvimwe zvikamu, kwakaitika pamutoro mukuru umwe chete, kusina kukuvadza (nzira yemutoro wemuganhu).
Kana chinhu chiri brittle, kukuvadzwa kwekutanga kunogara kuchiratidzwa nemapfundo, ayo anoita kuti paine nzvimbo iri munjodzi kuve nekusangana kukuru kwesimba, izvo zvinobva zvatokonzeresa kutsemuka. Kutsemuka nekuda kwekuneta kunyange muzvinhu zvinotambanuka kunoonekwa sekuputsika kwebrittle.
Kubatana pakati pekunetseka kwekudzvinyirirwa pamativi akasiyana echikamu
Miyedzo yeshanduko
Mapfumbamwe masimba echikamu ari panzira fig. 1, anosungwa nemitemo mitatu yekuenzanisa. Manhamba matanhatu asara σx, σy, σz τxy, τyz, τzx anogona, akazvimirira rimwe nerimwe, kuwana kukosha kupi zvako sezvinoonekwa mukubva kwemawenzani e-differential etheoriy yeelasticity. Zvisinei, kana kukosha uku kwapihwa, mamiriro ekushushikana pane imwe poindi yemuviri wakasimba anotsanangurwa zvizere, kureva kuti kana kushushikana kwemarwa matatu akatwasuka kune rimwe nerimwe kuchizikanwa, zvinogona kusarudzwa pasina kusava nechokwadi kushushikana kweimwe ndege yechina inopfuura nepapoindi yakapiwa uye normali yayo ine nzira ipi zvayo.
Panh. 10 inoratidzwa tetrahedra OABC ine mativi matatu akafanana nemaplane ehurongwa hwemakongiresi x, y, z uye chechina chinomiririra chimwe chinhu chesurface chakaiswa chero nzira ABC = dF. Kuti chiratidze nzira yacho uye nzira yekushushikana inopfuudzwa kuburikidza nacho, panoshandiswa imwe hurongwa hwemakongiresi, hune ξ axis iri perpendicular ku dF.
Mufananidzo 10
Mamiriro ekuti masimba ari kurwisa tetrahedron iyi achitevedza mhando yeξ anosangana nekuenzana anopa
Kana zvikanzi tichifunga kuti
inowanikwa
uye zvakafanana kubva pamamiriro ekuenzana munzira yeaxis η:
Aya ndiwo maequations anoshandiswa kuverenga kunetseka pakushandurwa kwemakorodinati. Chinokosha zvikuru ndechekutarisa chete zvinhu zvenzvimbo dF izvo ξ-axis inoenderana ne z-axis. Mienzaniso yenyaya iyi tinogona kuiwana nekurerutsa mienzaniso yapfuura kana kuiverenga zvakananga kubva pamuf. 11:
Muf. 11
Kushushikana kwakajairika kunotora kukosha kukuru nekudiki pamativi α = α0, ayo dσξ/dα = 0. Nekusiyanisa, kubva muequation (16) tinowana
uye saka, kana chirevo ichi chakaenzaniswa ne zero
Manikiro τξη achavawo total shear stress mumaplanes aya, kana τyz = τzx = 0. Ipapo, neequation (17), panotsanangurwa nzira mbiri dzakatarisana pakona, dzokuti: 1. total shear stress iri zero uye, 2. normal stress ine kukosha kwakanyanya uye kushoma (maximum uye minimum). Nzira idzi dzinonzi nzira dzemanikiro makuru, uye manikiro anoenderana anonzi manikiro makuru. Anoratidzwa ne σ1 uye σ2 uye anogona kuverengwa zvakananga kubva mufomura
Denderedzwa raMohr
Mienzaniso (16) inogona kuratidzwa nenzira inobatika zviri nyore. Nechinangwa ichi inofanira kushandurwa kuita chimiro:
Maequation aya anomirira muhurongwa hwemakorodhineti σ, τ chimiro cheparametric cheequation yedenderedzwa, rakadhirowewa mufig. 12, ane makorodhineti epakati σ = 1/2 (σx + σy), τ = 0 uye rine radius
Denderedzwa iri rinonzi denderedzwa raMohr. Kana kuburikidza nepfungwa x rikadhonzwa mutsetse wakafanana nepakati x =const., panopfuudzwa pakatipfuura zvinetso σx, τxy, mutsetse iwoyo uchacheka denderedzwa panzvimbo p, inonzi pol yekudenderedzwa raMohr. Mutsetse wose pξ wakadhonzwa kuburikidza nepol iyi unocheka denderedzwa panzvimbo ξ, iyo inoratidza zvinetso σξ, τξη zvinopfuudzwa nepakatipfuura yakafanana ne pξ.
Kana zvasvika pachiratidzo chematsindiro ekugera pakudhirowa denderedzwa raMohr, zvinofanira kurangarirwa kuti anorongedzwa kumusoro kana aine gwara rakaratidzwa pamufig. 12c. Naizvozvo, pane matsindiro maviri akabatana τxy, τyx, rimwe rinogara riri rakanaka uye rimwe rakaipa.
Kukosha kwemuganhu kwe σ1, σ2 kwekushushikana kwakajairwa kunoenderana nemapoinzi 1 ne 2 padenderedzwa, uye mitsetse _p_1 ne _p_2 inopa mafambiro ekushushikana kukuru.
Kuratidza matsindiro ari mundege x-y kuburikidza nedenderedzwa raMahr hakuna kusungirirwa kune chero fungidziro pamusoro pematsindiro σz, τxz, τyz akatwasuka kune ndege iyi.
Mufananidzo 12
Naizvozvo izvi zvinoshanda zvakare kune chimiro chemukomboni chematatu-matatu chakasiyana-siyana chezvinetso zvemanikiro, kana kungofananidzwa chete ndege dzekutemesa dzose dzinopfuura nomutsetse mumwe chete, wakasarudzwa pano se z uye ξ axis. Sezvo maererano nemazhinji emafomura ekushandura (15) manikiro akatarisana σ asingagoni kuva asingaperi kune chero ndege yekutemesa, anofanira kuva nekune rimwe ndege nekuwanda kwepamusoro kwakaganhurirwa σ1, uye kune rimwe minimum σ3, zvose zviri zviviri, sezviri pachena, zvinogonawo kuva zvisina kunaka. Kana ndege ikapfuura nemivekitori σ1 na σ3 ndokuchetwa denderedzwa raMohr (sl. 13)
Mufananidzo 13
kune kushushikana kunogara munde iyi ndege (kureva, nzira dzese dziri perpendicular kune iyi ndege), ipapo σ1 ne σ3 ndidzo kushushikana kukuru ne kudiki kwepachinhu zvinogona kuonekwa uye naizvozvo zvinofanira kuva perpendicular kune mumwe nemumwe. Kana nzira dze1 ne3 dzikawedzerwa nenzira 2, kuti nzira nhatu idzi dzigadzire hurongwa hwepakona yakatwasuka, uye kana madenderedzwa aMahr adhirowewa pamativi 1 ~2 uye 2 ~ 3, ipapo σ2 kune rimwe remadenderedzwa aya ndiko kushushikana kukuru, uye kune rimwe ndiko kudiki, saka pamapindiro ari perpendicular kunzira 1, 2 uye 3 kushushikana kwekuchera kwakaenzana nezero. Kushushikana hutatu hwepachinhu hunoenderana uye perpendicular kune mumwe nemumwe σ1, σ2 ne σ3, uko kusina kushushikana kwekuchera kunoenderana nako, kunonzi kushushikana kukuru.
Muganho wekutanga kuyerera nemuganho wekutsemuka mumamiriro ematambudziko epamativi matatu
Mamiriro ematsindiro anonzi ane chimiro chimwe, zviviri kana zvitatu, kana kuti: lineari, flat kana spatial, zvichienderana nekuti rimwe, maviri kana ese matatu matsindiro makuru haana kuenzana nezero. Pazvikamu zvechimiro zvinonyanya kushandiswa, kureva tsvimbo inotambanudzwa, inotsikirirwa uye inokotamiswa, mamiriro ematsindiro, zvirinani panzvimbo dzinonyanya kushushikana, ane chimiro chimwe, uye zvakafanana zvakare pakuedzwa kwekutambanudza, kudzvanya kana kukotamisa, izvo pakuyedza zvinhu zvinenge zvichingoshandiswa kuona matsindiro anobvumidzwa. Kusiyana nazvo, pamaplate anokandirwa mutsetse wawo kana perpendicular pairi, pamwe nemagoko, mamiriro ematsindiro ane chimiro chezviviri, uye mune dzimwe nyaya panobuda mamiriro ematsindiro ane chimiro chetatu, saka zvakakosha kuti pahwaro hwemuganhu wekuyerera nekutyoka, wakatarwa panguva yemamiriro ematsindiro ane chimiro chimwe, kutorwa mhedziso pamusoro pemaitiro echinhu kana paine mamiriro ematsindiro enzvimbo.