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Zomangamanga zamasangweji zimagwiritsidwa ntchito kwambiri m'mafakitale ambiri chifukwa cha makina awo apamwamba. Kuphatikizika kwazinthu izi ndizofunikira kwambiri pakuwongolera ndikuwongolera makina awo pamakina osiyanasiyana. Ma concave lattice ndiabwino kwambiri kuti agwiritsidwe ntchito ngati zolumikizirana pamasangweji otere pazifukwa zingapo, monga kuwongolera kukhazikika kwake (mwachitsanzo, chiŵerengero cha Poisson ndi kuuma kolimba) ndi ductility (mwachitsanzo, kusungunuka kwakukulu) kuti zikhale zosavuta. Mphamvu ya mphamvu ndi kulemera kwa chiwerengero imapindula mwa kusintha zinthu zokhazokha za geometric zomwe zimapanga selo la unit. Apa, tikufufuza momwe masangweji a 3-layer concave core sangweji amagwiritsa ntchito analytical (ie, zigzag theory), computational (ie, finite element) ndi mayeso oyesera. Tidasanthulanso momwe ma geometric amitundu yosiyanasiyana amapangidwira (monga ngodya, makulidwe, kutalika kwa ma cell ndi kutalika) pamachitidwe onse amakanikidwe a masangweji. Tapeza kuti zomangira zapakati zomwe zimakhala ndi machitidwe auxetic (ie negative Poisson's ratio) zimawonetsa mphamvu zosunthika komanso kumeta ubweya wocheperako poyerekeza ndi ma grating wamba. Zomwe tapeza zitha kutsegulira njira yopangira zida zapamwamba zamitundu ingapo zokhala ndi ma lattice omangira apamlengalenga ndi ntchito zamankhwala.
Chifukwa cha mphamvu zawo zazikulu komanso kulemera kwake, masangweji amagwiritsidwa ntchito kwambiri m'mafakitale ambiri, kuphatikiza kapangidwe ka zida zamakina ndi masewera, zam'madzi, zamlengalenga, komanso uinjiniya wa biomedical. Zomangamanga za concave lattice ndi m'modzi yemwe angathe kuganiziridwa ngati zigawo zazikuluzikulu zamagulu ophatikizika chifukwa cha mphamvu zawo zapamwamba zamayamwidwe amphamvu komanso kuchuluka kwamphamvu kwa kulemera kwamphamvu1,2,3. M'mbuyomu, kuyesetsa kwakukulu kudapangidwa kupanga masangweji opepuka okhala ndi ma concave lattice kuti apititse patsogolo luso lamakina. Zitsanzo za mapangidwe oterewa ndi monga kukwezedwa kwakukulu m'mabwalo a sitima zapamadzi ndi zotsekera m'magalimoto4,5. Chifukwa chomwe mawonekedwe a concave latisi ndi otchuka kwambiri, apadera komanso oyenera kumanga gulu la masangweji ndikutha kuyimba mopanda mphamvu zake za elastomechanical (mwachitsanzo kuuma zotanuka ndi kufananiza kwa Poisson). Chimodzi mwazinthu zosangalatsa zotere ndi khalidwe la auxetic (kapena chiŵerengero choyipa cha Poisson), chomwe chimatanthawuza kukulitsa kwamtundu wa lattice pamene atatambasulidwa motalika. Khalidwe lachilendoli ndi logwirizana ndi kapangidwe kake kakang'ono ka ma cell ake oyambira7,8,9.
Kuyambira kafukufuku woyamba wa Lakes pakupanga thovu la auxetic, kuyesetsa kwakukulu kwapangidwa kuti apange ma porous porous ratio10,11 ya Poisson. Ma geometries angapo aperekedwa kuti akwaniritse cholinga ichi, monga ma cell, olimba, komanso okhazikika, 12 onse omwe amawonetsa machitidwe owoneka bwino. Kubwera kwaukadaulo wopanga zowonjezera (AM, yomwe imadziwikanso kuti 3D printing) yathandiziranso kukhazikitsidwa kwa 2D kapena 3D auxetic structures13.
Khalidwe la auxetic limapereka zinthu zapadera zamakina. Mwachitsanzo, Lakes ndi Elms14 awonetsa kuti thovu la auxetic lili ndi mphamvu zokolola zambiri, mphamvu yamphamvu yoyamwa mphamvu, komanso kuuma kochepa kuposa thovu wamba. Pankhani yamakina osinthika a thovu la auxetic, amawonetsa kukana kwakukulu pansi pa katundu wosweka komanso kukwezeka kwapamwamba pansi pa zovuta zoyera15. Kuphatikiza apo, kugwiritsa ntchito ulusi wa auxetic monga zida zolimbikitsira muzophatikizira kumawongolera mawotchi awo16 komanso kukana kuwonongeka komwe kumachitika chifukwa cha fiber stretch17.
Kafukufuku wawonetsanso kuti kugwiritsa ntchito zida za concave auxetic monga maziko a zopindika zopindika zimatha kupititsa patsogolo magwiridwe antchito awo akunja, kuphatikiza kuuma kwa flexural ndi mphamvu18. Pogwiritsa ntchito fanizo losanjikiza, zawonedwanso kuti pachimake cha auxetic chitha kukulitsa mphamvu yosweka ya mapanelo ophatikizika19. Zophatikizika zokhala ndi ulusi wa auxetic zimalepheretsanso kufalikira kwa ming'alu poyerekeza ndi ulusi wamba20.
Zhang et al.21 adatengera machitidwe akugundana kwamagulu obwerera. Iwo adapeza kuti mayamwidwe amagetsi ndi mphamvu amatha kupitilizidwa powonjezera mbali ya cell ya auxetic unit, zomwe zimapangitsa kuti grating ndi chiŵerengero choyipa cha Poisson. Ananenanso kuti mapanelo a masangweji auxetic atha kugwiritsidwa ntchito ngati zodzitetezera kuzinthu zowopsa kwambiri. Imbalzano et al.22 adanenanso kuti mapepala a auxetic composite amatha kutaya mphamvu zambiri (ie kawiri kawiri) kupyolera muzitsulo zapulasitiki ndipo zimatha kuchepetsa kuthamanga kwapamwamba kumbuyo ndi 70% poyerekeza ndi mapepala amodzi.
M'zaka zaposachedwa, chidwi chambiri chaperekedwa pamaphunziro owerengera komanso oyesera a masangweji okhala ndi auxetic filler. Maphunzirowa akuwunikira njira zosinthira makina a masangweji awa. Mwachitsanzo, kutengera gawo lokwanira la auxetic wosanjikiza ngati pachimake cha gulu la masangweji kumatha kubweretsa modulus yogwira mtima kwambiri ya Young kuposa wosanjikiza kwambiri23. Kuphatikiza apo, machitidwe opindika a matabwa a laminated 24 kapena auxetic core chubu 25 akhoza kusinthidwa ndi kukhathamiritsa kwa algorithm. Palinso maphunziro ena pakuyesa kwamakina amitundu yokulirapo ya masangweji apakati pazambiri zovuta. Mwachitsanzo, kuyesa kukanikiza kophatikiza konkriti yokhala ndi ma auxetic aggregates, mapanelo a masangweji pansi pa katundu wophulika27, mayeso opindika28 ndi mayeso otsika kwambiri29, komanso kusanthula kwapang'onopang'ono kwa mapanelo a masangweji okhala ndi ma auxetic aggregates30.
Chifukwa zoyerekeza zamakompyuta ndi zoyesa zoyeserera zamapangidwe otere nthawi zambiri zimawononga nthawi komanso zokwera mtengo, pakufunika kupanga njira zongoyerekeza zomwe zitha kupereka chidziwitso chofunikira popanga ma multilayer auxetic core core pamitu yotsitsa mosasamala. nthawi yoyenera. Komabe, njira zamakono zowunikira zili ndi malire angapo. Makamaka, malingalirowa sali olondola mokwanira kulosera momwe zinthu zimapangidwira komanso kusanthula zophatikizika zopangidwa ndi zinthu zingapo zokhala ndi zotanuka mosiyanasiyana.
Popeza zitsanzo zowunikirazi zimadalira katundu wogwiritsidwa ntchito ndi malire, apa tiyang'ana kwambiri machitidwe osinthika a auxetic core sandwich panels. Chiphunzitso chofanana ndi cha single layer chomwe chimagwiritsidwa ntchito pofufuza motere sichingathe kuneneratu molondola za kumeta ubweya ndi axial m'ma laminates osagwirizana kwambiri m'magulu a masangweji apakati. Komanso, mu ziphunzitso zina (mwachitsanzo, mu chiphunzitso cha layered), chiwerengero cha zosinthika za kinematic (mwachitsanzo, kusamuka, kuthamanga, etc.) zimadalira kwambiri chiwerengero cha zigawo. Izi zikutanthauza kuti gawo la kayendetsedwe ka gawo lirilonse likhoza kufotokozedwa paokha, pamene likukwaniritsa zovuta zina za kupitiriza kwa thupi. Chifukwa chake, izi zimatsogolera pakuganizira kuchuluka kwamitundu yosiyanasiyana muzachitsanzo, zomwe zimapangitsa kuti njirayi ikhale yokwera mtengo. Kuti tigonjetse malirewa, tikupangira njira yozikidwa pa chiphunzitso cha zigzag, gulu laling'ono la chiphunzitso cha multilevel. Chiphunzitsochi chimapereka kupitiriza kwa kumeta ubweya wa ubweya mu makulidwe onse a laminate, potengera njira ya zigzag ya kusamuka kwa ndege. Choncho, chiphunzitso cha zigzag chimapereka chiwerengero chofanana cha kusintha kwa kinematic mosasamala kanthu za chiwerengero cha zigawo mu laminate.
Kuti tiwonetse mphamvu ya njira yathu polosera za machitidwe a masangweji okhala ndi ma concave cores pansi pa katundu wopindika, tidafanizira zotsatira zathu ndi malingaliro akale (mwachitsanzo, njira yathu ndi mitundu yowerengera (ie zinthu zomaliza) ndi data yoyesera (ie kupindika kwa mfundo zitatu za 3D printed sandwich panels).Kuti tikwaniritse izi, tidapeza koyamba ubale wakusamuka kutengera chiphunzitso cha zigzag, kenako tidapeza ma equation ogwirizira pogwiritsa ntchito mfundo ya Hamilton ndikuthana nawo pogwiritsa ntchito njira ya Galerkin. magawo a geometric a mapanelo a masangweji okhala ndi ma auxetic fillers, omwe amathandizira kusaka kwamapangidwe omwe ali ndi makina abwino.
Ganizirani gulu la masangweji atatu (mkuyu 1). Mapangidwe a geometric: pamwamba \({h}_{t}\), wosanjikiza wapakati \({h}_{c}\) ndi wosanjikiza wapansi \({h}_{b}\) makulidwe. Timalingalira kuti maziko ake amakhala ndi mazenera a lattice. Kapangidwe kake kamakhala ndi ma cell oyambira omwe amakonzedwa motsatira dongosolo. Posintha magawo a geometric pamapangidwe a concave, ndizotheka kusintha mawonekedwe ake amakina (mwachitsanzo, mayendedwe a Poisson ndi kuuma kolimba). Magawo a geometrical cell cell akuwonetsedwa mumkuyu. 1 kuphatikiza ngodya (θ), kutalika (h), kutalika (L) ndi makulidwe a mzati (t).
Lingaliro la zigzag limapereka maulosi olondola kwambiri a kupsinjika ndi kupsinjika kwamapangidwe amitundu yosiyanasiyana ya makulidwe apakati. Kusamuka kwamapangidwe mu chiphunzitso cha zigzag chili ndi magawo awiri. Gawo loyamba likuwonetsa khalidwe la sangweji yonse, pamene gawo lachiwiri likuyang'ana khalidwe pakati pa zigawo kuti zitsimikizire kuti kumeta ubweya wa ubweya kupitirirabe (kapena otchedwa zigzag ntchito). Kuonjezera apo, chinthu cha zigzag chimasowa kunja kwa laminate, osati mkati mwa wosanjikiza. Chifukwa chake, ntchito ya zigzag imatsimikizira kuti gawo lililonse limathandizira kusinthika kwathunthu kwa magawo. Kusiyana kofunikiraku kumapereka kugawa kwenikweni kwakuthupi kwa ntchito ya zigzag poyerekeza ndi ntchito zina za zigzag. Mtundu wa zigzag wosinthidwa wamakono sumapereka kupitilira kwa kukameta ubweya wodutsa pakati pawosanjikiza wapakatikati. Chifukwa chake, gawo lakusamuka kutengera chiphunzitso cha zigzag litha kulembedwa motere31.
mu equation. (1), k=b, c ndi t amayimira zigawo zapansi, zapakati ndi zapamwamba, motsatana. Malo osunthika apandege yapakatikati motsatira Cartesian axis (x, y, z) ndi (u, v, w), ndipo kuzungulira kwa ndegeyo pafupi ndi (x, y) olamulira ndi \({\uptheta} _ {x}\) ndi \ ({\ uptheta}_{y}\). \({\psi}_{x}\) ndi \({\psi}_{y}\) ndi kuchuluka kwa malo a zigzag, ndi \({\phi}_{x}^{k}\ kumanzere ( z \kumanja)\) ndi \({\phi}_{y}^{k}\left(z\right)\) ndi ntchito za zigzag.
Kukula kwa zigzag ndi ntchito ya vector ya yankho lenileni la mbale ku katundu wogwiritsidwa ntchito. Amapereka makulitsidwe oyenera a ntchito ya zigzag, potero amawongolera zopereka zonse za zigzag pakusamuka kwa ndege. Kumeta ubweya wa ubweya pa makulidwe a mbale kumakhala ndi zigawo ziwiri. Gawo loyamba ndi kumeta ubweya wa ubweya, yunifolomu kudutsa makulidwe a laminate, ndipo gawo lachiwiri ndi ntchito yosalekeza, yofanana ndi makulidwe amtundu uliwonse. Malinga ndi ntchito zokhazikika izi, ntchito ya zigzag pagawo lililonse imatha kulembedwa motere:
mu equation. (2), \({c}_{11}^{k}\) ndi \({c}_{22}^{k}\) ndi zotsatika zokhazikika pagawo lililonse, ndipo h ndiye makulidwe onse a diski. Kuphatikiza apo, \({G}_{x}\) ndi \({G}_{y}\) ndi zolemetsa zapakati zouma zometa, zowonetsedwa ngati 31:
Ntchito ziwiri za zigzag matalikidwe (Equation (3)) ndi zotsalira zisanu zotsalira za kinematic (Equation (2)) za chiphunzitso choyamba cha kumeta ubweya wa ubweya zimapanga gulu la ma kinematics asanu ndi awiri okhudzana ndi kusintha kwa chiphunzitso cha zigzag. Kungotengera kudalira kwamtundu wa kusinthika ndikutengera chiphunzitso cha zigzag, gawo lopindika mu dongosolo la Cartesian coordinate litha kupezeka monga:
kumene \({\varepsilon}_{yy}\) ndi \({\varepsilon}_{xx}\) ndi zopindika bwino, ndi \({\gamma}_{yz},{\gamma}_{xz} \ ) ndi \({\gamma}_{xy}\) ndi zopindika zometa ubweya.
Pogwiritsa ntchito lamulo la Hooke ndikuganiziranso chiphunzitso cha zigzag, ubale womwe ulipo pakati pa kupsinjika ndi kupsinjika kwa mbale ya orthotropic yokhala ndi mawonekedwe a concave lattice atha kupezeka kuchokera ku equation (1). (5) 32 kumene \({c}_{ij}\) ndi kusinthasintha kosalekeza kwa matrix opanikizika.
kumene \({G}_{ij}^{k}\), \({E}_{ij}^{k}\) ndi \({v}_{ij}^{k}\) amadulidwa mphamvu ndi modulus mbali zosiyanasiyana, Young's modulus ndi Poisson's ratio. Ma coefficients awa ndi ofanana mbali zonse za gulu la isotopic. Kuonjezera apo, kwa ma nuclei obwerera a lattice, monga momwe tawonetsera mkuyu 1, katunduwa akhoza kulembedwanso ngati 33.
Kugwiritsiridwa ntchito kwa mfundo ya Hamilton pa ma equation of motion plate multilayer plate yokhala ndi concave lattice core kumapereka ma equation oyambira pamapangidwewo. Mfundo ya Hamilton ikhoza kulembedwa motere:
Pakati pawo, δ imayimira wogwiritsa ntchito mosiyanasiyana, U imayimira mphamvu yomwe ingathe kuchitika, ndipo W imayimira ntchito yopangidwa ndi mphamvu yakunja. Mphamvu zonse zomwe zingatheke zimapezedwa pogwiritsa ntchito equation. (9), pomwe A ndi dera la ndege yapakatikati.
Kungoganiza kugwiritsa ntchito katundu wofanana (p) mbali ya z, ntchito ya mphamvu yakunja ingapezeke kuchokera ku njira iyi:
Kusintha ma equation (4) ndi (5) (9) ndikusintha equation. (9) ndi (10) (8) ndi kuphatikiza pa makulidwe a mbale, equation: (8) ikhoza kulembedwanso monga:
Mlozera \(\phi\) umayimira ntchito ya zigzag, \({N}_{ij}\) ndi \({Q}_{iz}\) ndi mphamvu zolowa ndi kutuluka mundege, \({M} _{ij}\) imayimira mphindi yopindika, ndipo chiŵerengero chowerengera chili motere:
Kugwiritsa ntchito kuphatikiza ndi magawo ku equation. Kulowa m'malo mwa formula (12) ndikuwerengera kuchuluka kwa kusiyanasiyana, tanthauzo la equation ya gulu la masangweji litha kupezeka mu fomula (12). (13).
Ma equation owongolera ma equation a mbale zosanjikiza zitatu mwaufulu amathetsedwa ndi njira ya Galerkin. Pansi pamalingaliro a quasi-static mikhalidwe, ntchito yosadziwika imatengedwa ngati equation: (14).
\({u}_{m,n}\), \({v}_{m,n}\), \({w}_{m,n}\),\({{\ uptheta}_ {\mathrm {x}}}_{\mathrm {m} \text{,n}}\),\({{\uptheta}_{\mathrm {y}}}_{\mathrm {m} \text {,n}}\), \({{\uppsi}_{\mathrm{x}}}_{\mathrm{m}\text{,n}}\) ndi \({{\uppsi}_{ \mathrm{y}}}_{\mathrm{m}\text{,n}}\) ndizokhazikika zosadziwika zomwe zingapezeke pochepetsa cholakwikacho. \(\ overline{\ overline{u}} \kumanzere({x{\text{,y}}} \kumanja)\), \(\ overline{\ overline{v}} \left({x{\text {,y}}} \ kumanja)\), \(\ overline{\ overline{w}} \kumanzere( {x{\ text{,y}}} \ kumanja)\), \(\ overline{\ overline {{{\ uptheta}_{x}}}} \kumanzere({x{\text{,y}}} \kumanja)\), \(\mzere{\mzere{{{\uptheta}_{y}} }}} \kumanzere( {x{\text{,y}}} \kumanja)\), \(\ overline{\ overline{{\psi_{x}}}} \left( {x{\text{, y}}} \kumanja)\) ndi \(\ overline{\ overline{{\psi_{y} }}} \left({x{\text{,y}}} \kumanja)\) ndi ntchito zoyesa, zomwe ziyenera kukwaniritsa malire ofunikira. Pazigawo zamalire zongothandizidwa, ntchito yoyeserera imatha kuwerengedwanso motere:
Kusintha kwa equations kumapereka ma equation a algebraic. (14) ku ma equation olamulira, omwe angayambitse kupeza ma coefficients osadziwika mu equation (14). (14).
Timagwiritsa ntchito finite element modelling (FEM) kuti tiyesere pakompyuta kupindika kwa sangweji yothandizidwa mwaufulu yokhala ndi ma concave lattice ngati pachimake. Kusanthula kunachitika mu code yamalonda yomaliza (mwachitsanzo, Abaqus mtundu 6.12.1). 3D hexahedral solid elements (C3D8R) yokhala ndi kuphatikizika kosavuta idagwiritsidwa ntchito kufanizira zigawo zapamwamba ndi zapansi, ndipo zinthu zofananira za tetrahedral (C3D4) zidagwiritsidwa ntchito kufanizira mawonekedwe apakati (concave). Tidachita kusanthula kwa ma mesh kuti tiyese kulumikizana kwa ma mesh ndipo tidawona kuti zotsatira zakusamuka zidasintha pakukula kochepa kwambiri pakati pa zigawo zitatuzo. Sangweji mbale imadzazidwa ndi ntchito ya sinusoidal katundu, poganizira za malire omwe amathandizidwa mwaufulu m'mbali zinayi. Liniya yamakina otanuka amaganiziridwa ngati mtundu wazinthu zomwe zimaperekedwa pamagawo onse. Palibe kukhudzana kwapadera pakati pa zigawozo, zimagwirizanitsidwa.
Tidagwiritsa ntchito njira zosindikizira za 3D kupanga mawonekedwe athu (mwachitsanzo, gulu la masangweji osindikizidwa patatu) ndi kuyeserera kofananirako kuti tigwiritse ntchito mikhalidwe yopindika yofananira (uniform load p motsatira z-direction) ndi malire (ie . amaganiziridwa mu njira yathu yowunikira (mkuyu 1).
Sangweji gulu losindikizidwa pa chosindikizira cha 3D lili ndi zikopa ziwiri (kumtunda ndi kumunsi) ndi pakatikati pa lattice, miyeso yake yomwe ikuwonetsedwa mu Table 1, ndipo idapangidwa pa chosindikizira cha Ultimaker 3 3D (Italy) pogwiritsa ntchito njira yoyika ( FDM). ukadaulo umagwiritsidwa ntchito pochita. Tidasindikiza 3D mbale yoyambira ndi main auxetic lattice kapangidwe palimodzi, ndikusindikiza gawo lapamwamba padera. Izi zimathandiza kupewa zovuta zilizonse panthawi yochotsa chithandizo ngati mapangidwe onse ayenera kusindikizidwa nthawi imodzi. Pambuyo pa kusindikiza kwa 3D, magawo awiri osiyana amamatiridwa pamodzi pogwiritsa ntchito superglue. Tidasindikiza zidazi pogwiritsa ntchito polylactic acid (PLA) pakuchulukira kwambiri (ie 100%) kuti tipewe zolakwika zilizonse zosindikiza.
Kachitidwe ka clamping kamatengera momwe zimakhalira zosavuta zomwe zimatengera momwe timawerengera. Izi zikutanthauza kuti kachipangizo kameneka kamalepheretsa bolodi kusuntha m'mphepete mwake mumayendedwe a x ndi y, kulola kuti m'mphepete mwake muzizungulira momasuka ma ax ndi y. Izi zimachitika poganizira zamagulu okhala ndi radius r = h / 2 m'mphepete mwa njira zogwirira (mkuyu 2). Dongosolo la clampingli limatsimikiziranso kuti katundu wogwiritsidwa ntchito amasamutsidwa kwathunthu kuchokera pamakina oyesera kupita pagulu ndikugwirizana ndi mzere wapakati wa gululo (mkuyu 2). Tidagwiritsa ntchito ukadaulo wosindikiza wa 3D wamitundu yambiri (ObjetJ735 Connex3, Stratasys® Ltd., USA) ndi ma resin olimba amalonda (monga mndandanda wa Vero) kusindikiza makina ogwirira.
Chojambula chojambula cha 3D chosindikizira chosindikizira cha 3D ndi kamangidwe kake ndi 3D sandwich yosindikizidwa yokhala ndi auxetic core.
Timayesa kukakamiza koyendetsedwa moyendetsedwa ndi quasi-static pogwiritsa ntchito benchi yoyesera yamakina (Lloyd LR, load cell = 100 N) ndikusonkhanitsa mphamvu zamakina ndi kusamuka pazitsanzo za 20 Hz.
Gawoli likupereka kafukufuku wamawerengero a kamangidwe ka masangweji. Timaganiza kuti zigawo zapamwamba ndi zapansi zimapangidwa ndi carbon epoxy resin, ndipo mawonekedwe a lattice a concave core amapangidwa ndi polima. Zomwe zimagwiritsidwa ntchito pamakina azinthu zomwe zimagwiritsidwa ntchito mu phunziroli zikuwonetsedwa mu Table 2. Kuonjezera apo, chiwerengero chopanda malire cha zotsatira za kusamuka ndi madera opanikizika akuwonetsedwa mu Table 3.
Kusamuka kwakukulu koyima kosasunthika kwa mbale yonyamulidwa momasuka kunafanizidwa ndi zotsatira zopezedwa ndi njira zosiyanasiyana (Table 4). Pali mgwirizano wabwino pakati pa chiphunzitsocho, njira yomaliza ndi zotsimikizira zoyesera.
Tinayerekezera kusuntha kosunthika kwa chiphunzitso cha zigzag chosinthidwa (RZT) ndi chiphunzitso cha 3D elasticity (Pagano), chiphunzitso choyamba cha shear deformation (FSDT), ndi zotsatira za FEM (onani mkuyu 3). Lingaliro loyamba la kumeta ubweya wa ubweya, kutengera zojambula zamitundu yambiri yamitundu yambiri, zimasiyana kwambiri ndi njira zotanuka. Komabe, chiphunzitso cha zigzag chosinthidwa chimaneneratu zotsatira zolondola kwambiri. Kuonjezera apo, tinkayerekezeranso kupsinjika kwa kunja kwa ndege ndi kupanikizika kwabwino mu ndege zamaganizo osiyanasiyana, zomwe chiphunzitso cha zigzag chinapeza zotsatira zolondola kuposa FSDT (mkuyu 4).
Kuyerekeza kwa kupsinjika koyima kokhazikika komwe kumawerengedwa pogwiritsa ntchito malingaliro osiyanasiyana pa y = b/2.
Kusintha kwa kumeta ubweya wa ubweya (a) ndi kupsinjika kwanthawi zonse (b) mu makulidwe a gulu la masangweji, kuwerengeredwa pogwiritsa ntchito malingaliro osiyanasiyana.
Kenako, tidasanthula mphamvu ya magawo a geometric a cell cell yokhala ndi concave pachimake pamakina onse a sangweji. Magawo a cell cell ndiye gawo lofunikira kwambiri la geometric pamapangidwe a ma reentrant lattice34,35,36. Choncho, ife anawerengera chikoka cha unit selo ngodya, komanso makulidwe kunja pachimake, pa okwana kupatuka kwa mbale (mkuyu. 5). Pamene makulidwe a wosanjikiza wapakatikati akuwonjezeka, kupatuka kopanda dimensionless kumachepa. Mphamvu yopindika pachibale imawonjezeka pazigawo zokhuthala komanso pamene \(\frac{{h}_{c}}{h}=1\) (ie, pakakhala wosanjikiza umodzi). Masangweji mapanelo okhala ndi auxetic unit cell (ie \(\theta =70^\circ\)) ali ndi zosuntha zazing'ono kwambiri (mkuyu 5). Izi zikuwonetsa kuti mphamvu yopindika ya pachimake cha auxetic ndiyokwera kwambiri kuposa yamtundu wamba wa auxetic, koma imakhala yocheperako ndipo imakhala ndi chiŵerengero chabwino cha Poisson.
Kupatuka kokhazikika kokhazikika kwa ndodo ya concave lattice yokhala ndi ngodya zosiyanasiyana zama cell ndi makulidwe akunja kwa ndege.
Makulidwe a pachimake cha grating auxetic ndi mawonekedwe (ie \ (\ theta = 70 ^\ circ \)) zimakhudza kusamuka kwakukulu kwa mbale ya sangweji (Chithunzi 6). Zitha kuwoneka kuti kupatuka kwakukulu kwa mbale kumawonjezeka ndi kuwonjezeka kwa h/l. Kuphatikiza apo, kukulitsa makulidwe a pachimake cha auxetic kumachepetsa porosity ya kapangidwe ka concave, potero kumawonjezera mphamvu yopindika ya kapangidwe kake.
The pazipita kupatuka mapanelo masangweji chifukwa cha lattice nyumba ndi auxetic pachimake osiyanasiyana makulidwe ndi utali.
Kuphunzira za madera opsinjika ndi gawo losangalatsa lomwe lingafufuzidwe posintha magawo a geometric a cell cell kuti aphunzire njira zolephereka (mwachitsanzo, delamination) zamitundu yambiri. Chiŵerengero cha Poisson chimakhala ndi zotsatira zambiri pamunda wa kumeta ubweya wa kunja kwa ndege kusiyana ndi kupanikizika kwachibadwa (onani mkuyu 7). Komanso, zotsatirazi ndi inhomogeneous mbali zosiyanasiyana chifukwa cha orthotropic zimatha zinthu za gratings izi. Zina mwazinthu za geometric, monga makulidwe, kutalika, ndi kutalika kwa mapangidwe a concave, sizinakhudze gawo la kupsinjika maganizo, choncho sanafufuzidwe mu phunziroli.
Sinthani zigawo za kumeta ubweya wa ubweya m'magawo osiyanasiyana a sangweji yokhala ndi chodzaza ndi lattice chokhala ndi ngodya zosiyanasiyana.
Apa, mphamvu yopindika ya mbale ya multilayer yothandizidwa momasuka yokhala ndi nsonga ya concave lattice imafufuzidwa pogwiritsa ntchito chiphunzitso cha zigzag. Kapangidwe kameneka akuyerekezeredwa ndi ziphunzitso zina zakale, kuphatikiza chiphunzitso chamitundu itatu cha elasticity, chiphunzitso choyambirira cha kumeta ubweya wa ubweya, ndi FEM. Timatsimikiziranso njira yathu poyerekeza zotsatira zathu ndi zoyeserera pamapangidwe a masangweji osindikizidwa a 3D. Zotsatira zathu zikuwonetsa kuti chiphunzitso cha zigzag chimatha kulosera za kusinthika kwa masangweji amtundu wapakatikati pansi pa katundu wopindika. Kuphatikiza apo, chikoka cha magawo a geometric a kapangidwe ka concave lattice pamayendedwe amapindika a masangweji amawunikidwa. Zotsatira zikuwonetsa kuti pamene mulingo wa auxetic ukuwonjezeka (ie, θ <90), mphamvu yopindika imawonjezeka. Kuphatikiza apo, kukulitsa kuchuluka kwa mawonekedwe ndikuchepetsa makulidwe a pachimake kumachepetsa mphamvu yopindika ya gulu la sangweji. Pomaliza, zotsatira za chiŵerengero cha Poisson pa kupsinjika kwa kunja kwa ndege kumaphunziridwa, ndipo zimatsimikiziridwa kuti chiŵerengero cha Poisson chimakhala ndi chikoka chachikulu pa kumeta ubweya wa ubweya wopangidwa ndi makulidwe a mbale ya laminated. Mafomuwa ndi ziganizo zomwe zaperekedwa zitha kutsegulira njira yopangira ndi kukhathamiritsa kwa ma multilayer okhala ndi ma concave lattice fillers pansi pamikhalidwe yovuta kwambiri yotsitsa yofunikira kuti apange mapangidwe onyamula katundu muzamlengalenga ndiukadaulo wazomera.
Zolemba zomwe zagwiritsidwa ntchito ndi/kapena zowunikidwa mu kafukufuku wapano zikupezeka kuchokera kwa olemba omwe afunsidwa pazofunikira.
Aktai L., Johnson AF ndi Kreplin B. Kh. Nambala kayeseleledwe wa chiwonongeko makhalidwe a uchi pachimake. injiniya. fractal. ubweya. 75(9), 2616–2630 (2008).
Gibson LJ ndi Ashby MF Porous Solids: Kapangidwe ndi Katundu (Cambridge University Press, 1999).
Nthawi yotumiza: Aug-12-2023