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Sandwich mapaneru zvimiro anoshandiswa zvakanyanya mumaindasitiri mazhinji nekuda kweakakwirira makina zvivakwa. Iyo interlayer yezvivakwa izvi chinhu chakakosha kwazvo mukudzora nekuvandudza ma mechanical zvinhu pasi pemamiriro akasiyana ekurodha. Concave lattice zvimiro ndivo vakatanhamara vakwikwidzi vekushandiswa sevanopindirana mune akadaro masangweji zvimiro nekuda kwezvikonzero zvakati, zvinoti kugadzirisa elasticity yavo (semuenzaniso, chiyero chePoisson uye elastic kuomarara kukosha) uye ductility (semuenzaniso, yakakwirira elasticity) kuti zvive nyore. Simba-ku-kurema reshiyo yezvivakwa inowanikwa nekugadzirisa chete zvinhu zvejometri zvinoumba unit cell. Pano, isu tinoongorora kushanduka kwemhinduro ye 3-layer concave core sandwich panel tichishandisa analytical (kureva, zigzag theory), computational (kureva, finite element) uye bvunzo dzekuyedza. Isu takaongororawo mabatiro eakasiyana geometric paramita eiyo concave lattice chimiro (semuenzaniso angle, ukobvu, unit sero kureba kusvika kureba reshiyo) pane yakazara mechanic maitiro eiyo sandwich chimiro. Isu takaona kuti zvimiro zvepakati zvine auxetic maitiro (kureva yakaipa Poisson's ratio) inoratidza yakakwirira flexural simba uye kushoma kwekunze-kwendege shear stress kana ichienzaniswa neyakajairwa gratings. Zvatinowana zvinogona kuvhura nzira yekuvandudzwa kweazvino mainjiniya akawanda ezvivakwa ane architectural core lattices yeaerospace uye biomedical application.
Nekuda kwesimba ravo rakakwirira uye huremu hwakaderera, zvimiro zvesangweji zvinoshandiswa zvakanyanya mumaindasitiri mazhinji, kusanganisira dhizaini yemuchina uye yemitambo dhizaini, marine, aerospace, uye biomedical engineering. Concave lattice zvimiro mumwe angangove mumiriri ari kutariswa sematanho epakati muzvimiro zvakaumbwa zvakadaro nekuda kwehukuru hwavo hwekunyudza simba uye yakakwirira-kusvika-huremu reshiyo zvivakwa1,2,3. Munguva yakapfuura, kuedza kukuru kwakaitwa kugadzira zvimiro zvemasangweji akareruka ane concave lattices kuti aenderere mberi nekuvandudza michina. Mienzaniso yemagadzirirwo akadai anosanganisira kurema kwakanyanya mumidziyo yengarava uye zvinobatisa zvekuvhundutsa mumotokari4,5. Chikonzero nei iyo concave lattice chimiro chakakurumbira, chakasarudzika uye chakakodzera sandwich panel kuvaka kugona kwayo kuzvimiririra tune yayo elastomechanical maitiro (eg elastic kuoma uye Poisson kuenzanisa). Imwe yakadaro inonakidza pfuma ndeye auxetic maitiro (kana yakaipa Poisson's ratio), iyo inoreva kuwedzera kwepashure kweiyo lattice chimiro kana yakatambanudzwa kureba. Aya maitiro asina kujairika ane hukama neiyo microstructural dhizaini yeayo ekutanga maseru7,8,9.
Kubva patsvakiridzo yekutanga yeLakes mukugadzirwa kweauxetic foams, kuedza kukuru kwakaitwa kugadzira zvimiro zveporous zvine reshiyo yakaipa yePoisson10,11. Mageometri akati wandei akakurudzirwa kuti azadzise chinangwa ichi, senge chiral, semi-rigid, uye akaomesesa anotenderera mayuniti maseru,12 ese anoratidza maitiro ehuxetic. Kuuya kwekuwedzera kwekugadzira (AM, inozivikanwawo se 3D kudhinda) matekinoroji akafambisawo kuitwa kweaya 2D kana 3D auxetic zvimiro13.
Iyo auxetic maitiro inopa yakasarudzika michina zvivakwa. Semuyenzaniso, Lakes neElms14 zvakaratidza kuti auxetic furo dzine simba regoho repamusoro, simba rekutora simba rakanyanya, uye kuomarara kwakaderera pane zvakajairika. Nezve dynamic mechanical properties of auxetic foams, dzinoratidza kupikisa kwepamusoro pasi pesimba rekupwanya mitoro uye yakakwirira elongation pasi pesimba rakachena15. Mukuwedzera, kushandiswa kwe auxetic fibers sezvinhu zvinosimbisa mumakompositi zvichavandudza maitiro avo emagetsi16 uye kudzivisa kukanganisa kunokonzerwa nefiber stretch17.
Tsvagiridzo yakaratidzawo kuti kushandisa concave auxetic zvimiro senge musimboti weakakomberedzwa anoumbwa zvimiro zvinogona kuvandudza mashandiro avo ekunze kwendege, kusanganisira kuoma kwesimba uye simba18. Uchishandisa modhi yakaturikidzana, zvakaonekwa zvakare kuti auxetic core inogona kuwedzera kutsemuka kwesimba reanosanganiswa mapaneru. Macomposites ane auxetic fibers zvakare anodzivirira kutsemuka kupararira kana ichienzaniswa neyakajairika fibers20.
Zhang et al.21 vakatevedzera maitiro ekudhumhana kwemaitiro ekudzosa maseru. Vakaona kuti voltage uye kunyudzwa kwesimba kunogona kuvandudzwa nekuwedzera kona ye auxetic unit cell, zvichikonzera gireti ine imwe yakashata Poisson's ratio. Ivo vakakurudzirawo kuti auxetic sandwich mapaneru anogona kushandiswa sezvivakwa zvekudzivirira kubva kune yakakwira strain rate kukanganisa mitoro. Imbalzano et al.22 yakashumawo kuti auxetic composite sheets inogona kuparadza simba rakawanda (kureva zvakapetwa kaviri) kuburikidza neplastic deformation uye inogona kuderedza kukurumidza kwepamusoro kune reverse side ne70% kana ichienzaniswa nemapuranga ega ega.
Mumakore achangopfuura, kutarisisa kwakanyanya kwakabhadharwa kune nhamba uye yekuyedza zvidzidzo zvemasangweji zvimiro zvine auxetic filler. Zvidzidzo izvi zvinosimbisa nzira dzekuvandudza michina yezvimiro zvesangweji. Semuyenzaniso, kufunga zvakaringana gobvu auxetic layer sepakati pesangweji pani inogona kukonzera yakakwira inoshanda Yechidiki modulus pane yakaomesesa layer23. Uye zvakare, maitiro ekukotama emalaminated matanda makumi maviri nemana kana auxetic core chubhu 25 anogona kuvandudzwa neiyo optimization algorithm. Pane zvimwe zvidzidzo pamechani yekuyedza yeanowedzera epakati sandwich zvimiro pasi pemitoro yakaoma. Semuenzaniso, kumanikidza kuyedzwa kwekongiri kongiri ine auxetic aggregates, masangweji mapaneru ari pasi pezvinoputika mitoro27, kubhenda bvunzo28 uye yakaderera-velocity kukanganisa bvunzo29, pamwe nekuongorora kusiri-mutsara kupeta kwemasangweji mapaneru ane anoshanda akasiyana auxetic aggregates30.
Nekuti kuenzanisa kwemakomputa uye kuyedzwa kwekuongorora kwezvigadziriso zvakadaro zvinowanzotora nguva uye zvinodhura, pane chikonzero chekugadzira nzira dzetioretical dzinogona kupa nemazvo uye nemazvo ruzivo runodiwa kugadzira multilayer auxetic core zvimiro pasi pemamiriro ekurodha zvisina tsarukano. nguva yakafanira. Zvisinei, nzira dzekuongorora dzemazuva ano dzine ganhuriro dzinoverengeka. Kunyanya, dzidziso idzi hadzina kurongeka zvekufanotaura hunhu hwezvinhu zvakakora zvakaumbwa uye kuongorora macomposites anoumbwa neakati wandei zvinhu zvine akasiyana siyana elastic properties.
Sezvo aya maodhisheni ekuongorora anoenderana nemitoro yakashandiswa uye mamiriro emuganho, pano isu tichatarisa pane inoshanduka maitiro e auxetic core sandwich mapaneru. Iyo yakaenzana single layer theory inoshandiswa pakuongorora kwakadaro haigone kufanotaura nemazvo shear uye axial kushushikana mune yakanyanya inhomogeneous laminates mune mwero ukobvu sandwich composite. Uyezve, mune dzimwe dzidziso (somuenzaniso, mune akaturikidzana dzidziso), nhamba kinematic variables (somuenzaniso, displacement, velocity, etc.) zvakasimba zvinoenderana nhamba akaturikidzana. Izvi zvinoreva kuti ndima yekufamba kwega yega yega inogona kutsanangurwa yakazvimirira, nepo ichigutsa zvimwe zvipingamupinyi zvekuenderera mberi kwemuviri. Nokudaro, izvi zvinotungamirira mukutora nhamba huru yezvakasiyana-siyana mumuenzaniso, izvo zvinoita kuti nzira iyi iwedzere kudhura. Kuti tikunde zvipimo izvi, isu tinopa nzira yakavakirwa pazigzag theory, yakasarudzika subclass ye multilevel theory. Iyo dzidziso inopa kuenderera kwekuveura kushushikana mukati mehupamhi hwelaminate, uchitora zigzag pateni ye-mu-ndege kusimuka. Nokudaro, iyo zigzag theory inopa nhamba imwechete yezvinyorwa zvekinematic pasinei nenhamba yezvikamu mu laminate.
Kuti tiratidze simba renzira yedu mukufanotaura maitiro emasangweji mapaneru ane concave cores ari pasi pemitoro inokotama, takaenzanisa zvatakawana nedzidziso dzechinyakare (kureva maitiro edu nemamodhi emakomputa (kureva zvinhu zvinogumira) uye data rekuyedza (kureva matatu-mapoindi kupeta kwe. 3D printed sandwich panels).Kuitira izvi, takatanga tatora hukama hwekutamiswa kwakavakirwa padzidziso yezigzag, tichibva tawana maequation equation tichishandisa iyo Hamilton musimboti tikaagadzirisa tichishandisa nzira yeGalerkin. Migumisiro yakawanikwa chishandiso chine simba chekugadzira zvinoenderana geometric parameters emasangweji mapaneru ane auxetic mafirita, achifambisa kutsvaga kwezvivakwa zvine akagadziridzwa makinika zvivakwa.
Funga nezvetatu-layer sandwich panel (Fig. 1). Geometric design parameters: top layer \({h}_{t}\), layer yepakati \({h}_{c}\) uye yezasi layer \({h}_{ b }\) ukobvu. Isu tinofungidzira kuti chiumbwa chepakati chine pitted lattice chimiro. Chimiro chacho chine masero ekutanga akarongwa padivi pemumwe nenzira yakarongeka. Nekushandura iyo geometric paramita ye concave chimiro, zvinokwanisika kushandura ma mechanic zvimiro (kureva, kukosha kweiyo Poisson's ratio uye elastic kuomarara). Iyo geometrical parameters yekutanga sero inoratidzwa muFig. 1 inosanganisira kona (θ), kureba (h), kureba (L) uye ukobvu hwekoramu (t).
Dzidziso ye zigzag inopa kufanotaura kwakanyatso kujeka kwekushushikana uye kushushikana maitiro eakaturikidzana anoumbwa zvimiro zvepakati nepakati. Kuchinja kwemaitiro mune zigzag theory ine zvikamu zviviri. Chikamu chekutanga chinoratidza hunhu hwesangweji pazere, nepo chikamu chechipiri chinotarisa maitiro pakati pematanho kuti ive nechokwadi cheshear stress kuenderera (kana iyo inonzi zigzag basa). Mukuwedzera, iyo zigzag element inonyangarika pamusoro pekunze kwelaminate, uye kwete mukati meiyi danda. Saka, iyo zigzag basa inovimbisa kuti imwe neimwe nhanho inobatsira kune yakazara muchinjiko-chikamu deformation. Iyi misiyano yakakosha inopa kugovera kwechokwadi kwemuviri kweiyo zigzag basa richienzaniswa nemamwe mabasa egzag. Iyo yazvino yakagadziridzwa zigzag modhi haipe transverse shear kusagadzikana kuenderera pamwe neiyo yepakati layer. Naizvozvo, nzvimbo yekutamisa yakavakirwa pane zigzag theory inogona kunyorwa sezvizvi31.
mu equation. (1), k=b, c uye t zvinomiririra pasi, repakati nepamusoro matinji, zvichiteerana. Munda wekutama wendege inorehwa padivi peCartesian axis (x, y, z) iri (u, v, w), uye kutenderera kuri mundege nezve (x, y) axis iri \({\ uptheta} _ {x}\) uye \ ({\ uptheta}_{y}\). \({\psi}_{x}\) uye \({\psi}_{y}\) inzvimbo yehuwandu hwekutenderera kwezigzag, uye \({\phi}_{x}^{k}\ kuruboshwe ( z \kurudyi)\) uye \({\phi}_{y}^{k}\left(z\kurudyi)\) mabasa ezvigzag.
Iyo amplitude ye zigzag ndeye vector basa remhinduro chaiyo yeplate kumutoro wakaiswa. Ivo vanopa kuyera kwakakodzera kweiyo zigzag basa, nekudaro vachidzora mupiro weiyo zigzag kune kutamiswa mundege. Shear strain mukati mekukora kweplate ine zvikamu zviviri. Chikamu chekutanga ishear angle, yunifomu mukati meukobvu hwelaminate, uye chikamu chechipiri ibasa rinogara riripo, rakafanana pahukobvu hwega ega. Zvinoenderana neaya piecewise anogara achiita mabasa, iyo zigzag basa reimwe neimwe layer inogona kunyorwa se:
mu equation. (2), \({c}_{11}^{k}\) uye \({c}_{22}^{k}\) ndiwo machinjiro akasimba emutsetse wega wega, uye h ndiko kukora kwese kwe. disc. Pamusoro pezvo, \({G}_{x}\) uye \({G}_{y}\) ndiwo akayerwa avhareji yekuomarara kweshear, inotaridzwa se31:
Iwo maviri zigzag amplitude mabasa (Equation (3)) uye akasara mashanu kinematic variables (Equation (2)) yekutanga kurongeka shear deformation theory inoumba seti yenomwe kinematics yakabatana neiyi yakagadziridzwa zigzag plate theory variable. Tichifunga mutsara wekutsamira kweiyo deformation uye uchifunga nezve zigzag theory, iyo deformation munda muCartesian coordinate system inogona kuwanikwa se:
apo \({\varepsilon}_{yy}\) uye \({\varepsilon}_{xx}\) zviri zvinochinja, uye \({\gamma}_{yz},{\gamma}_{xz} \ ) uye \({\gamma}_{xy}\) kugera.
Uchishandisa mutemo waHooke uye uchifunga nezveiyo zigzag theory, hukama pakati pekunetseka uye kunetsa kweiyo orthotropic plate ine concave lattice chimiro inogona kuwanikwa kubva kuequation (1). (5) 32 apo \({c}_{ij}\) inogara iri elastic yestress-strain matrix.
apo \({G}_{ij}^{k}\), \({E}_{ij}^{k}\) uye \({v}_{ij}^{k}\) zvinochekwa simba ndiyo modulus munzira dzakasiyana, Young's modulus uye Poisson's ratio. Aya ma coefficients akaenzana mumativi ese eiyo isotopic layer. Mukuwedzera, nokuda kweiyo nuclei inodzoka yelatiti, sezvinoratidzwa mumufananidzo 1, zvinhu izvi zvinogona kunyorwa zvakare se33.
Kushandiswa kwemusimboti waHamilton kune equation yekufamba kweplate yakawanda ine concave lattice core inopa iwo equation equation yedhizaini. Nheyo yaHamilton inogona kunyorwa se:
Pakati pawo, δ inomiririra mushandisi wekusiyanisa, U inomiririra simba rinogona kuita, uye W inomiririra basa rinoitwa nekunze kwesimba. Iyo yakazara inogona kunetsa simba rinowanikwa uchishandisa equation. (9), uko A iri dunhu rendege yepakati.
Kufunga kushandiswa kwakafanana kwemutoro (p) munzira z, basa resimba rekunze rinogona kuwanikwa kubva kune inotevera fomula:
Kutsiva equation (4) na (5) (9) wotsiva equation. (9) uye (10) (8) nekubatanidza pamusoro pekukora kweplate, iyo equation: (8) inogona kunyorwa zvakare se:
Indekisi \(\phi\) inomiririra basa rezigzag, \({N}_{ij}\) uye \({Q}_{iz}\) masimba anopinda nekubuda mundege, \({M} _{ij}\) inomiririra nguva yekukotama, uye fomula yekuverenga ndeyotevera:
Kushandisa kubatanidzwa nezvikamu kune equation. Kutsiva mufomula (12) uye kuverenga iyo coefficient yekusiyana, iyo inotsanangura equation yesandwich panel inogona kuwanikwa nenzira yefomati (12). (13).
Iwo musiyano wekutonga equations yeakatsigirwa zvakasununguka matatu-layer mahwendefa anogadziriswa neGalerkin nzira. Pasi pekufungidzira kwe quasi-static mamiriro, basa risingazivikanwi rinoonekwa sekuenzanisa: (14).
\({u}_{m,n}\), \({v}_{m,n}\), \({w}_{m,n}\),\({{\uptheta}_) {\mathrm {x}}}_{\mathrm {m} \zvinyorwa{,n}}\),\({{\ uptheta}_{\mathrm {y}}}_{\mathrm {m} \zvinyorwa {,n}}\), \({{\uppsi}_{\mathrm{x}}}_{\mathrm{m}\text{,n}}\) uye \({{\uppsi}_{ \mathrm{y}}}_{\mathrm{m}\text{,n}}\) zvimiro zvisingazivikanwe zvinogona kuwanikwa nekuderedza kukanganisa. \(\ overline{\ overline{u}} \kuruboshwe({x{\text{,y}}} \kurudyi)\), \(\ overline{\ overline{v}} \kuruboshwe({x{\text {,y}}} \kurudyi)\), \(\ overline{\ overline{w}} \kuruboshwe( {x{\text{,y}}} \kurudyi)\), \(\ overline{\ overline {{{\ uptheta}_{x}}}} \kuruboshwe({x{\text{,y}}} \kurudyi)\), \(\ overline{\ overline{{{\uptheta}_{y} }}} \kuruboshwe( {x{\text{,y}}} \kurudyi)\), \(\ overline{\ overline{{\psi_{x}}}} \left( {x{\text{, y}}} \kurudyi)\) uye \(\ overline{\ overline{{\psi_{y} }}} \left({x{\text{,y}}} \kurudyi)\) mabasa ekuedza, iyo inofanirwa kugutsa zvishoma zvinodiwa muganhu mamiriro. Kune anongotsigirwa mamiriro emuganho, basa rekuyedza rinogona kuverengerwa se:
Kutsiviwa kweequations kunopa algebraic equations. (14) kune equation yekutonga, iyo inogona kutungamirira pakuwana zvisingazivikanwi coefficients mu equation (14). (14).
Isu tinoshandisa finite element modelling (FEM) kuita komputa-kutevedzera kukotama kwesangweji inotsigirwa zvakasununguka ine concave lattice chimiro sepakati. Ongororo iyi yakaitwa mune yekutengeserana finite element kodhi (semuenzaniso, Abaqus vhezheni 6.12.1). 3D hexahedral solid elements (C3D8R) nekubatanidzwa kwakareruka kwakashandiswa kuenzanisira mativi epamusoro uye epasi, uye linear tetrahedral elements (C3D4) yakashandiswa kuenzanisira yepakati (concave) lattice structure. Takaita mesh senitivity ongororo yekuyedza kuchinjika kwe mesh uye tikagumisa kuti mibairo yekutamisa yakachinjika padiki diki chimiro pakati pematanho matatu. Iyo sandwich ndiro inotakurwa uchishandisa sinusoidal mutoro basa, uchifunga nezve yakasununguka inotsigirwa mamiriro emuganhu pamakona mana. Iyo mutsara elastic mechanical maitiro inoonekwa semhando yezvinhu yakagoverwa kune ese matara. Iko hakuna kushamwaridzana kwakananga pakati pematanho, iwo akabatana.
Takashandisa 3D nzira dzekudhinda kugadzira yedu prototype (kureva katatu akadhindwa auxetic core sandwich panel) uye inoenderana netsika yekumisikidza kuseta kuti uise akafanana kubhenda mamiriro (uniform load p pamwe ne z-direction) uye muganhu mamiriro (kureva. inofungidzirwa munzira yedu yekuongorora (Fig. 1).
Sandwich panel yakadhindwa pa 3D printer ine matehwe maviri (yekumusoro nezasi) uye concave lattice core, hukuru hwayo hunoratidzwa muTable 1, uye yakagadzirwa paUltimaker 3 3D printer (Italy) uchishandisa nzira yekuisa ( FDM). tekinoroji inoshandiswa mukuita kwayo. Isu 3D yakadhinda base plate uye main auxetic lattice chimiro pamwe chete, uye yakadhinda iyo yepamusoro layer yakaparadzana. Izvi zvinobatsira kudzivirira chero matambudziko panguva yerutsigiro yekubvisa maitiro kana iyo yose dhizaini inofanirwa kudhindwa kamwechete. Mushure mekudhinda kwe 3D, zvikamu zviviri zvakasiyana zvinonamirwa pamwechete uchishandisa superglue. Takadhinda zvinhu izvi tichishandisa polylactic acid (PLA) pakakwirira infill density (kureva 100%) kudzivirira chero kukanganisa kudhindwa kwenzvimbo.
Iyo tsika clamping system inoteedzera yakafanana yakapfava yekutsigira muganhu mamiriro akatorwa mune yedu yekuongorora modhi. Izvi zvinoreva kuti iyo inobata system inodzivirira bhodhi kuti isafambe nemumicheto yaro munzira x uye y, ichibvumira mipendero iyi kutenderera zvakasununguka kutenderedza x uye y axes. Izvi zvinoitwa nekufungisisa mafiritsi ane radius r = h / 2 pamakona mana ekubata system (Fig. 2). Iyi clamping system inovimbisawo kuti mutoro wakaiswa unotamiswa zvakazara kubva kumushini wekuyedza kuenda kune panhi uye wanoenderana nepakati mutsara wepaneru (fig. 2). Takashandisa multi-jet 3D kudhinda tekinoroji (ObjetJ735 Connex3, Stratasys® Ltd., USA) uye akaomesesa ekutengesa resins (akadai seVero series) kudhinda iyo grip system.
Schematic dhizaini ye3D yakadhindwa tsika yekubata system uye kuungana kwayo ine 3D yakadhindwa sandwich panel ine auxetic core.
Isu tinoita nhanho-inodzorwa-inodzorwa quasi-static compression bvunzo tichishandisa mechanical test bhenji (Lloyd LR, load cell = 100 N) uye tinounganidza mauto emuchina uye kutamiswa pamwero wesampling we20 Hz.
Ichi chikamu chinopa ongororo yenhamba yezvakarongwa sandwich chimiro. Isu tinofungidzira kuti iyo yepamusoro uye yepasi yakaturikidzana yakagadzirwa nekabhoni epoxy resin, uye iyo lattice chimiro cheiyo concave core inogadzirwa nepolymer. Iyo mechanical properties yezvinhu zvakashandiswa muchidzidzo ichi inoratidzwa muTebhu 2. Mukuwedzera, zviyero zvisingaverengeki zvemigumisiro yekutama uye minda yekushungurudzika inoratidzwa muTebhu 3.
Iyo yakanyanya vertical dimensionless displacement yeyakaenzana yakatakurwa yakasununguka yakatsigirwa ndiro yakaenzaniswa nemhedzisiro inowanikwa nenzira dzakasiyana (Table 4). Pane kubvumirana kwakanaka pakati pedzidziso yakarongwa, iyo inogumira chinhu nzira uye yekuongorora ongororo.
Takaenzanisa vertical displacement yemodified zigzag theory (RZT) ne 3D elasticity theory (Pagano), first order shear deformation theory (FSDT), uye migumisiro yeFEM (ona Fig. 3). Iyo yekutanga-odha yeshear theory, yakavakirwa padhiyagiramu yekutamisa yeakakora multilayer mahwendefa, anosiyana zvakanyanya kubva kune elastic mhinduro. Nekudaro, iyo yakagadziridzwa zigzag theory inofanotaura mhedzisiro chaiyo. Mukuwedzera, isu takafananidzawo kunze-kwe-ndege shear stress uye mu-ndege yakajairika kushushikana kwedzidziso dzakasiyana-siyana, pakati peiyo zigzag theory yakawana mhinduro dzakarurama kupfuura FSDT (Fig. 4).
Kuenzanisa kweyakajairika vertical strain yakaverengerwa uchishandisa dzidziso dzakasiyana pa y = b/2.
Shanduko mukuveura kushushikana (a) uye kushushikana kwakajairwa (b) kuyambuka ukobvu hwesangweji pani, inoverengerwa uchishandisa dzidziso dzakasiyana.
Tevere, isu takaongorora pesvedzero yejometri parameters yeyuniti cell ine concave musimboti pane yakazara mechanic zvimiro zvesangweji pani. Iyo unit cell angle ndiyo inonyanya kukosha geometric parameter mukugadzira reentrant lattice zvimiro34,35,36. Nokudaro, takaverenga simba rechikamu chesero chekona, pamwe chete nehupamhi kunze kwepakati, pane kutsauka kweplate (Fig. 5). Sezvo ukobvu hwemukati wepakati hunowedzera, iyo yakanyanya dimensionless deflection inoderera. Simba rekukombama rinowedzera kune dzakakora core layer uye kana \(\frac{{h}_{c}}{h}=1\) (kureva, kana paine imwe concave layer). Sandwich panels ane auxetic unit cell (kureva \ (\ theta = 70 ^\ circ\)) ane madiki ekudzingwa (Fig. 5). Izvi zvinoratidza kuti kupeta kusimba kweiyo auxetic core kwakakwira kupfuura yeyakajairika auxetic core, asi haina kunyatso shanda uye ine yakanaka Poisson's ratio.
Normalized maximum deflection ye concave lattice rod ine akasiyana unit cell angles uye kunze-kwe-ndege ukobvu.
Ukobvu hwepakati peiyo auxetic grating uye aspect ratio (kureva \ (\ theta = 70 ^\ circ\)) inokanganisa kutama kukuru kwesangweji ndiro (Mufananidzo 6). Zvinogona kuonekwa kuti kukanganisa kwakanyanya kweplate kunowedzera nekuwedzera h / l. Uye zvakare, kuwedzera kukora kweiyo auxetic core kunoderedza porosity yeconcave chimiro, nekudaro kuwedzera kukombama kwesimba rechimiro.
Iyo yakanyanya kutsauka yesangweji mapaneru anokonzerwa nelattice zvimiro zvine auxetic musimboti weakasiyana makubvu uye kureba.
Chidzidzo cheminda yekushushikana inzvimbo inonakidza iyo inogona kuongororwa nekushandura geometric parameters yeyuniti cell kuti idzidze kukundikana modes (semuenzaniso, delamination) yeakawanda magadzirirwo. Chiyero chePoisson chine simba guru pamunda wekunze-kwe-ndege shear stresss kupfuura zvinowanzoitika (ona mufananidzo 7). Uye zvakare, mhedzisiro iyi inhomogeneous munzira dzakasiyana nekuda kweiyo orthotropic zvinhu zveiyo gratings. Zvimwe zvigadziriso zvejometri, zvakadai sehupamhi, kureba, uye kureba kwezvivakwa zveconcave, hazvina kukanganisa pandima yekushungurudzika, saka hazvina kuongororwa muchidzidzo ichi.
Shandura mushear stress components muzvikamu zvakasiyana zvesangweji panel ine lattice filler ine akasiyana concavity angles.
Pano, simba rekukotama replate yakatsigirwa yakasununguka ine concave lattice core inoongororwa uchishandisa zigzag theory. Kuumbwa kwakarongwa kunofananidzwa nedzimwe dzidziso dzekare, dzinosanganisira nhatu-dimensional elasticity theory, yekutanga-order shear deformation theory, uye FEM. Isu tinosimbisawo nzira yedu nekuenzanisa mibairo yedu nemhedzisiro yekuedza pane 3D yakadhindwa sandwich zvimiro. Mhedzisiro yedu inoratidza kuti iyo zigzag theory inokwanisa kufanotaura deformation yemasangweji zvimiro zvepakati nepakati ukobvu pasi pekukotama mitoro. Pamusoro pezvo, pesvedzero yejometri paramita yeconcave lattice chimiro pane kukotama maitiro emasangweji mapaneru akaongororwa. Zvigumisiro zvinoratidza kuti sezvo chiyero che auxetic chinowedzera (kureva, θ <90), simba rekukotama rinowedzera. Uye zvakare, kuwedzera chikamu chechiyero uye kudzikisira ukobvu hwepakati kunoderedza kukombama kwesimba resangweji. Pakupedzisira, mhedzisiro yechiyero chePoisson pane kunze-kwendege shear stress inodzidzwa, uye zvinosimbiswa kuti reshiyo yePoisson ine simba guru pane shear stress inogadzirwa neukobvu hweplate yakamanikana. Iyo yakatsanangurwa mafomula uye mhedziso zvinogona kuvhura nzira yekugadzira uye optimization yeakawanda zvimiro zvine concave lattice mafirita pasi peakanyanya kuomarara mamiriro ekurodha anodiwa pakugadzirwa kwezvimiro zvinotakura zvinhu muaerospace uye biomedical tekinoroji.
Iwo madhata akashandiswa uye/kana akaongororwa muchidzidzo chazvino anowanikwa kubva kuvanyori vakasiyana pakukumbira zvine musoro.
Aktai L., Johnson AF naKreplin B. Kh. Numerical simulation yekuparadza maitiro ehuchi cores. injiniya. fractal. fur. 75(9), 2616–2630 (2008).
Gibson LJ uye Ashby MF Porous Solids: Mamiriro uye Zvivakwa (Cambridge University Press, 1999).
Nguva yekutumira: Aug-12-2023