Umxholo wengcaphephe yooVimba: okubhaliweyo kunye neefomula zigqithisa inkcazo-ntetho yethiyori yembali kwaye ayiyoprojekthi, ubalo olungatshintshiyo, ukujonga umthamo wokuthwala umthwalo, uvavanyo lwento esele ikho, okanye imiyalelo yolwakhiwo okanye yokubuyisela kwisimo sangaphambili. Ukutyunjwa, uqikelelo kunye neepateni eziqikelelweyo kufuneka zihlolwe ngokuchasene nenkqubo ethile, imathiriyeli, ijometri, iimeko zemida kunye nemigangatho esebenzayo. Ukubalwa kwe-torsion, ukuzinza, ukudinwa, amajoyina kunye noxinzelelo ngenxa yokugoba okuthintelweyo kufuneka kwenziwe yinjineli enelayisensi, kunye nolawulo oluzimeleyo xa lufunwa.
Namhlanje, i-Savo Kusić igxile kwi ifestile zomthi, iifestile zomthi-aluminiyam, iifestile zesiko, umnyango kunye nezicelo zekoteyishini. Eli nqaku lihlala liyindawo yogcino lwembali kwaye alimele inkonzo yoyilo lolwakhiwo.
Ithiyori yeSaint-Venant ye-torsion (i-torsion yasimahla)
Umahluko wenxaki
Sl.1
Makulungiswe intonga ethe tye kwesinye seziphelo zayo x=0kwaye mayilayishwe kwelinye isiphelo kunye nomzuzu we-torsion M (umkhiwane.1). Emva koko ngalinye lamacandelo alo lijikeleza nge-engile ethile α(x) malunga nomgca othile ohambelana ne-axis yentonga, esiya kuyamkela njenge-x-axis. Ukuba onke amacandelo ayalingana omnye komnye, nawuphi na umgca othe tye ongqamene ne-x-axis uya kudlula kwikhoyili, kwaye i-engile α iya kulungelelana nomgama ukusuka kwisiphelo esisisigxina: α=ϑx, apho icandelo lokufuduka kwinqwelomoya yecandelo livela (Fig.2):
v = - r a isono__ψ = - ϑ x z,
w = r a cos__ψ = ϑ x y. (1a)
Ubungakanani ϑ kuthiwa yi-engile ye-torsion (umlinganiselo: ubude-1, ukujikeleza ngobude beyunithi). I-engile ye-torsion ilungelelaniswa nomzuzu we-torsion M:
ϑ = M/GJT. (2)
Fig. 2
I-proportionality factor GJT, ukuqina kwe-torsional, ilingana nemveliso ye-shear modulus G kunye ne-factor JT, emele umphumo wesimo kunye nobukhulu becandelo.
Oku kujikeleza kwecandelo akukuphela kokuguqulwa kwentonga. Ukongeza, kukho kwakhona ukugoba kwecandelo elinqamlezileyo, oko kukuthi ukufuduka u kwicala le-x-axis, enobukhulu obufanayo kumanqaku ahambelana nawo onke amacandelo anqamlezileyo kwaye ngoko ke ngumsebenzi wolungelelwaniso kwinqwelomoya yecandelo, kwaye ngenye indlela ilingana nomthwalo M_M___
u = u(y,z) = ϑ ∙ φ(y,z), dφ/dx=0. (1b)
Ukuba amagama angasentla aziswa kwi-equations yokufuduswa ehambelanayo, kufunyanwa ukuba ugxininiso olungundoqo oluqhelekileyo lulingana no-zero, kushiya kuphela uxinzelelo lwamacandelo amabini txy kunye txz:
Nye.3
Umahluko we-equation yengxaki ye-torsion ifunyenwe ngokusekelwe kwii-equations (3) ukubeka:
Nye.4kwaye nam4b
kunye nokusombulula ezinxaki zomahluko zokungaziwayo τxy kunye τxz ngokwazisa umsebenzi woxinzelelo F(y,z) ukuba:
τxy = - dF/dz, τxz = + dF/dy. (5)
Ngale nto, i-equation (4a) waneliseke ngokufanayo, nakunxaki (4b) Umahluko ofunekayo uyafunyanwa
d2F/dy2+ d2F/dz2=2G__ϑ (6)
Umda womda ofunekayo kwisisombululo esisodwa salo mlinganiso ufunyenwe kwimfuno yokuba akukho xinzelelo lwe-shear kwimvulophu yentonga, apho, ngenxa yendalo yokudibanisa yoxinzelelo lwe-shear, kulandele ukuba uxinzelelo kwi-plane yecandelo akufunekanga ibe necandelo elixhomekeke kuyo kunye ne-contour. Ukusuka apha, umkhiwane.2:
dy/dz = _τxy/_τxz = - (dF/dz) / (dF/dy)
ke ngoko
dF/dy dy + dF/dz dz =0,
o.t. umahluko uwonke womsebenzi F kufuneka abe nguziro, oko kukuthi, kufuneka abe F=const. ecaleni kwecontour.
Ukuba icandelo linecontour enye kuphela, inokubekwa ngokulula F= kuyo0, kuba ngomsebenzi we-voltage, apho ngokwenene sinomdla kuphela kwi-derivatives, i-adbitrary additive constant ayidlali indima. Kumacandelo anecontour engaphezulu kwesinye, lo mba unzima kakhulu.
Njengoko kubonwa kwi-equation (5) isiphumo soxinzelelo lokucheba τxy kunye τxz kwindawo engadingekiyo yokunqumla ilingana ngobukhulu kumthamo woxinzelelo lomsebenzi F, kodwa iperpendicular kuyo, oko kukuthi, inomgca wetangenti kumgca F=const.
Ngokusombulula umahluko wenxaki (6)) amandla ombane τ njengemisebenzi ye y, z kunye ϑ ifunyenwe. Umsebenzi wokubala, ngokuqinisekileyo, ukuzimisela kwe-angle ye-torsion ϑ kunye noxinzelelo, ngokukodwa uxinzelelo oluphezulu njengomsebenzi wexesha lokuxhatshazwa, ngoko ke, ukumiselwa kokuqina kwecandelo JT ukusuka kwi-equation (2) kunye netorque yokumelana WT = Mmaxτ. Ukufumana ezi, kuyimfuneko kuphela ukuchaza M njengomsebenzi we-F:
Zombini izishwankathelo zalo mdibaniso, ekufuneka zithathwe kulo lonke icandelo, zinokutshintshwa ngokudityaniswa ngokuyinxenye. Ukuba, umzekelo, eyokuqala idibanisa kuqala emgceni z=const. ukusuka kwindawo yecontour y=y1 ukuya kwinqanaba y=y2 (ikhiwane.3) kwaye uthathele ingqalelo ukuba kuzo zombini ezi ngongoma F=0, ifunyenwe
Ixabiso elifanayo lifunyenwe kwi-indibaniselwano yesibini, ukuze
Nye.7
Sl.3
Ezinye iimeko zamacandelo apheleleyo
Umahluko wenxaki (6) yi-inhomogeneous equation yethiyori enokwenzeka. Ngoko ke, kwisisombululo sengxaki ye-torsion kwimeko ye-cross-section engafanelekanga, iindlela ze-theory ezinokuthi zifumaneke, ezenza ukuba zihlale zifumaneka. Ezi ndlela, nangona kunjalo, zintsonkothe kakhulu ukuba zingasetyenziswa kwiimeko ezizodwa ezivela ekusebenzeni. Ngoko ke, le theyibhile ilandelayo ibonisa iziphumo zezibalo ezinjalo kumacandelo amaninzi.
Kumacandelo anqamlezayo kufutshane nesetyhula, JT=F inokubekwa4/40_Ip_, apho F iyindawo kwaye Ip ngumzuzu wepolar we-inertia yecandelo.
** Qaphela kwiifomyula kunye neetheyibhile: ** iintetho kunye nexabiso kwimifanekiso eskeniweyo zigcinwa njengomthombo wembali. Okubhaliweyo kwe-OCR, amanqaku esalathiso kunye nokuskena azithembekanga ngokwaneleyo ukubala. Ngaphambi kokusetyenziswa, ifomyula nganye, iyunithi, i-coefficient kunye nendawo yobungqina kufuneka ihlolwe kumthombo ogunyazisiweyo wobuchwephesha kunye nomgangatho osebenzayo.
Isifaniso nenwebu
Uncedo olulungileyo lokuqikelela uxinzelelo lwe-torsional, kwaye kwangaxeshanye inkqubo yokuzimisela kwabo ngokuchanekileyo ibonelelwa ngumzekeliso phakathi komsebenzi woxinzelelo F wengxaki ye-torsional kunye nokuphambuka komthwalo onqamlezileyo wenwebu. Makubekho umndilili wokuvula kudonga olusicaba lwenqanawa oluhambelana necandelwana elinqumlayo lentonga elayishwe kwi-torsion. Xa inwebu yoluliwe phezu kolu vulo kunye noxinzelelo oluncinci olugqithisileyo p lubangelwa kwisitya, i-membrane iqhuma ngaphandle, ukuze ukuphambuka kwayo ξ(y,z) kwanelise i-equation yokwahlukana.
apho N kukuxinana komphezulu kwi-membrane okubangelwa amandla e-capillary (imilinganiselo: amandla ngobude beyunithi). Le nxaki ingqamana nenxaki (6), kunye nemeko yomda ξ=0iyafana naleyo yomsebenzi wombane. Ngale ndlela, umsebenzi we-voltage F (y, z) unokufumaneka ngokusebenzisa esi sibuko kunye ne-membrane kwaye ngaloo ndlela usombulule ingxaki ye-torsion. Uxinzelelo τ ihambelana nethambeka lenwebu ngokunxulumene y-z-indiza, ngoko ke eyona ndawo ingumnqantsa yileyo apho intonga evezwe kwi-torsion inoxinzelelo olukhulu lokucheba.
Sl.4
Sl.5
Le nkqubo ye-membrane ifaneleka ngokukodwa ukufumana iipateni eziqikelelweyo zamacandelo amancinci. Xa, umzekelo, i-I-section yahlulwe ngokomkhiwane.4kumaxande amathathu kwaye ngamnye kubo ufaniso kunye nenwebu lwenziwa ngokwahlukileyo, isixa semithamo yeziphumo ezibangelwayo ziya kuba ncinane kuphela kunomthamo ohambelana nomsebenzi wombane. Ngoko ke, xa ubukhulu bungu b1 kunye b2 encinci, malunga
JT =2JT1+ JT2,
apho JT1 kunye ne_JT2_ izinto zokuqina zoxande ngamnye ezinokubalwa ngokusekelwe kwitheyibhile1. Indlela engcono ifunyanwa xa JT ibekwe kubambo2 = a2b32/3, ke ngoko, xa ubambo luthathwa njengenxalenye yoxande olude kakhulu. Ixabiso elichaneke ngakumbi lifunyanwa ngokwe Trayer kunye March\ ukusuka
JT =2JT1+1/3a2b32+2 D4,
apho D yidayamitha yesangqa esikhulu esibhalwe njengoko kubonisiwe kwifig.4, kwaye α inokuthatyathwa kwifig.5. Kwicandelo le-T lifumaneka ngokufanayo
JT = JT1+JT2+ α D4,
apho JT2 isiqingatha sexabiso elibalwe ngokwetheyibhile1ye a=2_a2_, b=b2. Kumacandelo e-L (Fig.6) iyafana naleyo
JT = JT1+ JT2+ β D4
apho JT1 kuba ingalo engqindilili ithathwa ngokuthe ngqo etafileni1, ngelixa JT2 kuba umlenze omncinci ubalwa njenge-T-candelo, kwaye β ithathwa kwifig.7.
Fig. 6
Sl.7
Xa ubala uxinezeleko, umzuzu we-torsional wahlulwe waba ngamaxande adibeneyo: inxalenye ewela kwiiflanges M1=M JT2/JT; Uxinzelelo lokucheba lubalwa kumbindi wecala elide loxande ngalunye ngokusekwe kwitafile1. Olona xinzelelo lukhulu kolu xinzelelo akufuneki lube lolona xinzelelo lukhulu lokucheba oluvela kwicandelo. Ngokufanelekileyo, ukuba i-engile yezehlo ayirhangqwanga, τ=∞ ifunyenwe kuloo ndawo, ukuze kwiradiyasi encinci kakhulu yokurhangqa, olona xinzelelo lokucheba lunokulindeleka apha.
Inqaku lobuNjineli: ubunye bemathematika be-engile egqibeleleyo ayilophepha-mvume lokuqikelela ezona nkcukacha ngale pateni iyodwa. Ijiyometri ejikelezayo yokwenene, ukunyamezela, iplastiki, iiwelds, uxinzelelo olushiyekileyo, ukuzinza kwendawo kunye nokudinwa kufuna imodeli efanelekileyo kunye nokuqinisekiswa kweengcali.
Kwi-engile enecala elinye nobukhulu becala layo t ngokutsho Trefftz\ ikwisangqa sedayamitha r:
apho nge τ0 iphawulwe ubuninzi bombane obaliweyo kumlenze ngamnye ngamnye ngokusekelwe kwinkqubo echazwe apha. Kwiradiyi enkulu esangqa, τ= inokwamkelwa2__τ0.
Imibhobho eneNdonga eNcinci (Iipatheni zeBradt)
Kwimibhobho enodonga oluncinci, i-membrane ekhukhulayo inesimo esiboniswe kumkhiwane.8, equkethe indiza engaphezulu kwendawo evulekileyo ngaphakathi kombhobho kunye nomgangatho ojikelezayo ojikelezayo kwaye ulele ngaphezu kwecandelo elisebenzayo lodonga lombhobho; lo mhlaba uthambekele kufuneka ube phezulu ukuba iindonga zombhobho zincinci kwindawo efanelekileyo. Kule meko, uxinzelelo lwe-shear lusasazwa ngokulinganayo phezu kobunzima beendonga kwaye luhambelana ngokungafaniyo nobukhulu beendonga, okt shear force T = τt ayitshintshi kunye nomjikelezo wecandelo.
Sl. 8
Isiqalelo somphezulu t_∙ds_ sifumana inxalenye yomzuzu wobunzima
dM = t_∙ds∙τ∙h,_
ngoko umzuzu uphelele
Nye.8
apho i-FR surface igqunywe ngumgca ophakathi ophawulwe ngemigca kunye namachaphaza kwifig.8. Ifumaneka apha
Nye.9- Eyokuqala Bredt\ ipateni
Ukuqina kwe-torsional kufumaneka ngokulula xa umsebenzi wokuguqula ubonakaliswe kwelinye icala nge-torsional moment kunye ne-orsion angle kwaye kwelinye icala ngoxinzelelo lokucheba. Ngale ndlela, ifunyenwe intonga yobude l
ngoko, ukwazisa ixabiso le τ ngokweequation (8),
oko kukuthi, ngokuthelekisa nenxaki (2):
Nye.10
Ukuba ubukhulu beendonga bufana macala onke, ngoko kulula (2. Ipateni ka-Bredt):
Nye.11
Uxinzelelo oluqhelekileyo kwi-torsion ngenxa yokugoba kwecandelo
Amagama asisiseko kunye nenxaki yokwahlukana
Ukususwa kwecandelo u, inxaki (1b), imisela ukugoba kwamacandelo kwiinqwelomoya zabo. Xa umzuzu we-torsion ungaguquki, oku kugoba kuyafana kuwo onke amacandelo kunye noxinzelelo oluqhelekileyo σx alubonakali.
Kwiimeko ezininzi, i-curvature ye-cross-section, ekufuneka ivele ngesiseko se-_St. Ithiyori kaVenant ayinakwenzeka. Ukuba umzuzu we-torsional uguquka ngokukhawuleza kwinqanaba elinye elinqamlezayo, ukugoba kobukhulu obuhlukeneyo kuya kwenzeka kumacala omabini ecandelo elinqamlezayo, kwaye ukuqhubeka kwe-deformation kuya kuphazamiseka. Esinye isiphelo sentonga sinokunyanzeliswa kangangokuba ukugoba kwecandelo kukhutshwe ngokupheleleyo kuloo ndawo. Kwiimeko ezinjalo, ulungiso kufuneka lwenziwe _St. Iithiyori zikaVenant. Uxinzelelo olongezelelweyo σx kwicala le-axis yentonga kunye ne-supplementary shear force T (uxinzelelo lokucheba T/t) luvela kwintonga, ezona ziphezulu kwicandelo apho ukuqhubela phambili kwe-deformation yaphukile kwaye ehla ngokukhawuleza kunye nomgama ukusuka kweli candelo. Kwimeko yeentonga eziqinileyo kunye neetyhubhu, le ngcamango iyinkimbinkimbi, kwaye i-voltages eyongezelelweyo iyancipha ngokukhawuleza kangangokuba ukuzimisela kwabo akufanelekile kwiimeko ezininzi. Kwiindonga zeprofayili evulekileyo, olu lungiso lubaluleke kakhulu kwaye lunokubalwa ngokulula.
Sl.9
Sl.9ibonisa umgca apho indawo ephakathi kwodonga kunye nendiza yecandelo idibanisa (umgca ophakathi wecandelo). O ngumbindi wojikelezo oluzalanayo lwamacandelo amabini ajongeneyo. Ukuba umgama wabo ngu- dx, i-angle ye-torsion ngu-ϑ dx, ngoko ke indawo engafanelekanga yomgca ophakathi idlula kwi-displacement u ϑ dx. Oku kugxothwa kunecandelo rt ϑ dx kwicala letangent ukuya kwicandelo, kwaye sisiliphu somgangatho ophakathi wodonga (uthathela ingqalelo ukuba _u=_φϑ):
γ=__ϑ (rt + d__φ/ds).
Ekubeni uxinzelelo lokucheba kwindawo ephakathi eludongeni ingu-zero, kufuneka kwakhona ibe ngu-γ=0, ngoko ke
Lo mzekelo uqulethe iiparamitha ezintathu ezichaseneyo: imvelaphi apho ubude be-arc s bubalwa kunye nolungelelwaniso lombindi wojikelezo oluhlobene O, apho rt ixhomekeke khona. Isiqalo apho ubude be-arc s bubalwa khona sinokukhethwa ukuze ixabiso eliphakathi kwegophe libe nguziro:
kwaye ulungelelwaniso lweziko O lunokumiselwa ngendlela yokuba ixesha lokugoba icandelo libe nguziro:
Ingaboniswa ukuba i-center of rotation igqitywe ngokungqamana neziko lokucheba eli apha ichazwe yaza yachazwa ngenye indlela.
Ukuba ukugoba kwecandelo elichazwe kwezi patheni kuthintelwe ngokupheleleyo okanye ngokuyinxenye, uxinzelelo oluqhelekileyo σx kwicala le-axis yentonga kufuneka luvele. Uphononongo olusondeleyo lubonisa ukuba olu xinzelelo lunokuthi luthathwe lulungelelanise nomsebenzi we-curvature φ: σx=k__φ, apho φ ixhomekeke kuphela kwi-s kunye ne-k kuphela kwi-x. Ngokomthetho kaHooke:
σx = E_∂u/∂x = Eφ dϑ/dx_, (12)
kufuneka k=E d__ϑ/dx. Uxinzelelo oluqhelekileyo σx lubizwa ngokuba luxinzelelo lokugoba lwecandelo. Ukuqwalasela ii-equations ngasentla, benza inkqubo yokulinganisa amandla kwicandelo ngalinye, inkqubo yemikhosi ngenxa yokugoba kwecandelo.
Itorque iyonke inamacandelo amabini: enye yazo M1=GJT__ϑ ivela ngenxa yoxinzelelo lokucheba olunikwa ngu-_St. Ithiyori kaVenant, kunye nenye M2 kwenzeka ngenxa yokugotywa kwecandelo:
Nye.13
Ukusukela okomzuzwana M unikiwe njengomsebenzi we x, le ntetho imele umahluko wenxaki ye-engile ye-torsion ϑ. Nje ukuba le nxaki isonjululwe, M ingabalwa1 kunye no_M2_, kwaye ke lonke uxinzelelo kunye noxinzelelo.
Isisombululo kunye nezicelo
Xa umzuzu we-torsion M uhlala, isisombululo ngokubanzi se-equation (13) yi:
Uhlanganiso lwezigxina C1, C2 mayimiselwe ukusuka kwimiqathango emibini yomda.
a) Isiphelo esicinezelwe ngokungqongqo x=0(ikhiwane.1)
Kwesi siphelo yi u≡0, ngoko kusekwe kwinxaki (1b) ϑ=0. Ukuba intonga yinde kakhulu (αl>>1), emva koko C1=0kunye no_C2_= -M/GJT. Kwimeko yeentonga ezimfutshane, ukubonakala koxinzelelo ngenxa yokugoba kwecandelo kuchaphazelekayo yimeko ekupheleni kwentonga. Ukuba ukugotywa kwecandelo akuthintelwanga kuloo ndawo, kuyakubakho σx≡0kunye dϑ/dx=0. Ifumaneka apha
b) Umthwalo we-Symmetrical torsion ngokomkhiwane.10
Kwisiqingatha sasekhohlo sentonga, umzuzu wokutya ngu -M/2, kwaye ekunene +M/2. Kwimeko ye-torsion yamahhala, amacandelo ukuya ngakwesobunxele nasekunene kumbindi wentonga aya kuguqulwa kwicala elichaseneyo, ngoko ke ukuqhubeka kwe-deformation akuyi kugcinwa. Ngoko ke, kwindawo x=0Umzuzu wonke wokutya kufuneka udluliselwe kuxinzelelo olwenzeka ngenxa yokugoba kwecandelo elinqamlezayo, kwaye ke ngoko kweli candelo linqamlezayo M1=0kwaye ke ϑ=0. Ngeli xesha, inkqubo yemikhosi isebenza ukuqinisekisa ukuba icandelo lihlala lithe tye, nangona amacandelo alele kude ukusuka kumbindi wentonga yentonga. Ukuba, ukongeza, kuyafuneka ukuba iziphelo zentonga zibe noxinzelelo σx≡0, omnye umda womda ufunyenwe kwisiqingatha ngasinye sentonga, ngoko ke isiqingatha esifanelekileyo
Fig. 10
c) Umzuzu wangaphandle M kwindawo engafanelekanga (fig.11)
Kule meko, isisombululo ϑ sawo omabini la malungu entonga kufuneka abhalwe ngokwahlukeneyo, ukuze kuvele itotali ezine eziguquguqukayo C.1, C2, C3, C4. Ukongeza, amaxesha e-torsion Ma, Mb awaziwa. Ii-equations ezintandathu ziyafumaneka: imeko yokuqhubekeka ye ϑ (echazwe ngu u) kunye ne dϑ/dx (ichazwe ngu σx) kwindawo yomthwalo, imeko enye ekupheleni kwentonga (umzekelo, ukuqina okuqinileyo ϑ=0, okanye ukugoba okungaphazanyiswa, dϑ/dx=0), imeko yokulinganisela ngemizuzu -Ma+Mb=M kwaye ekugqibeleni imeko yokuba amacandelo okugqibela angajikelezi ngokubhekiselele komnye nomnye: ∫ ϑdx =0.
Sl.11
** Inqaku lokugqibela: ** ukhetho lwemodeli ye-torsion luxhomekeke kwicandelo elivulekileyo okanye elivaliweyo, ubuncinci, indlela yokuxhasa, indawo yokufaka umzuzwana kunye nokwenzeka ukugoba ngokukhululekileyo. Kwinto yokwenyani, umda wokuthwala umthwalo kunye nenkonzo ithi, iinkcukacha zendawo, amajoyinti, ukudinwa nokuzinza kufuneka kuhlolwe, kungekuphela nje ifomyula eyodwa ephuma kwinqaku.