SAVIJANJE TANKOSTJENIH KOMPOZITNIH ŠTAPOVA OTVORENOG POPREČNOG PRESJEKA
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1 SAVIJANJE TANKOSTJENIH KOMPOZITNIH ŠTAPOVA OTVORENOG POPREČNOG PRESJEKA SEMINAR DOKTORANADA I POSLIJEDOKTORANADA Maro Vuaović Spli, 015.
2 Sadržaj 1. Uvod. Savijanje anojenih ompoinih šapova ovorenog poprečnog prejea (STKŠ) 3. Analia verialnih pomaa i rednjeg normalnog napreanja pri avijanju anojenih ompoinih šapova ovorenog poprečnog prejea 4. Zaljuča
3 Uvod Uvod u problemaiu: Tanojeni ompoini šapovi Kompoii (vlanima-ojačani lamina) 1 Analia ruurnog ponašanja anojenih ompoinih šapova ovorenog prejea Ravoj analiičog modela: uima e u obir ujecaj micanja e ororopija maerijala Analia pomaa i napreanja od avijanja i uvijanja anojenih ompoinih šapova ovorenog poprečnog prejea [1] E. Carrera: Mechanic of Mulilaered Compoie Srucure: Baic Concep and Advanced Theorie, Draf of lecure given a CISM, UDINE, Ocober 01 in he framewor of EU Socrae Program.
4 Savijanje anojenih ompoinih šapova ovorenog poprečnog prejea (STKŠ) Definiranje onfiguracije laminaa: - imerični, uravnoeženi laminai - lojevi u ojačani jednomjernim, oninuiranim vlanima (unidirecional lamina) - laminai od ojih u vlana paralelna udužnom oi (unidirecional laminae) laminai od ojih u vlana umjerena pod uevima i (cro-pl laminae) - laminai od ojih u vlana umjerena pod uevima i (angle-pl laminae) [] T. L. C. Chen, C. W. Ber: Deign of compoie-maerial plae for maimum uniaial compreive bucling load, Proceeding of he Olahoma Academ of Science, 56, , 1976.
5 Savijanje anojenih ompoinih šapova ovorenog poprečnog prejea (STKŠ) Pomaci i deformacija: - Udužni poma oče S rednje linije poprečnog prejea: dw u u d 0 - Duljina deformacija u mjeru ivodnice rednje plohe: Napreanja: - Koniuivne jednadžbe: - Pojednoavljenje oniuivnih iraa: Q11 Q1 Q 16 Q11 Q 16 Q1 Q Q6, Q16 Q6 Q 66 Q16 Q66 - a lučaj da je 0 : - a lučaj da je : - ranformirane reducirane ruoi 0 Q Q Q Q Q Q, Q Q, Q Q, Q Q, Q Q, Q Q Q Q Q Q ij u d w du 0 d
6 Savijanje anojenih ompoinih šapova ovorenog poprečnog prejea (STKŠ) - Normalno napreanje u -om loju: d w du Q11 d Q I jednadžbe ravnoeže odječa -og loja lijedi angencijalno napreanje: -loj laminaa 1,,..., N 3 Q 11 d w d u f S 3 A Q 16 0 d, S d A ; A = d A ; da d, d d, f Q 16 d 0 0
7 Savijanje anojenih ompoinih šapova ovorenog poprečnog prejea (STKŠ) - Kuna deformacija u rednjoj plohi: 3 1 d w S d u A d, 3 - Faor ujecaja maerijala na micanje definiran je : Q Q16 66 Q66, Q Q d 0 N N Tangencijalno napreanje u -om loju Q Q Q d d, Q Q Q 1 d d Q 11 d w d u d w S d u A f S 3 A Q Srednje angencijalno napreanje 3 1 d w S d u A, m d 3
8 Savijanje anojenih ompoinih šapova ovorenog poprečnog prejea (STKŠ) - Kruo laminaa je definirana : - Normalno napreanje u -om loju: - Srednje normalno napreanje: N N Q d Q d Q d w du d w S d u A d w S d u A Q11 Q 11 d d Q d d w du d w S d u A, m d d d. d
9 Savijanje anojenih ompoinih šapova ovorenog poprečnog prejea (STKŠ) Diferencijalne jednadžbe ravnoeže d 4 u d I 4 q p d, L w 0, q, Tangencijalno napreanje priaano preo unuarnjih ila L in d d Q, - Tangencijalno napreanje: Q I I da A 3 d w, 3 P S dq q p L h p. S d P Q11 S S Q16 Q16 S QS Q q q, m I I I I d d,
10 Savijanje anojenih ompoinih šapova ovorenog poprečnog prejea (STKŠ) Normalno napreanje iraženo preo unuarnjih ila L L d d 0, M d d, Seundarne omponene unuarnjih ila : d w du M I M, A N 0. I M q, N q LS, A Faori micanja : I S 1 A S A I A L S A A d, d A, Normalno napreanje: Q11 Q11 Q11 LS Q16 Q11 I A A I I 0 S M q q Q S q d, M S q q q d. I A A I LS, m 0
11 Analia verialnih pomaa i rednjeg normalnog napreanja pri avijanju anojenih ompoinih šapova ovorenog poprečnog prejea q 1 N/mm bh50 mm; 0 1 h,08 mm. Verialni poma poprečnog prejea na redini rapona: A D 1 C b B 0 T,P 48 I 1, 5 Al 1 Maerijal (alo/epoi): E GPa; E E GPa; 1 3 G 3.45 GPa; G G 8.96 GPa; ; Srednje normalno napreanje u oči poja rua i pojaa:, Faori ujecaja micanja: A A/, w w m b M h I I A h 6A1 A , Al 1I 0, 0, A / A, b/ h, 0 1 A A 0 h 0. 1 b 1,
![5,96 5,07 5,434 5,31 [15/-15] 4 4,314 4,1 4,498 4,310 [30/-30] 4,990,918 3,65,911 [45/-45] 4,93,37,594,19 [60/-60] 4,090,8,7,030 [75/-75] 4,41,33,317,0 [±90] 4,43,40,474,4 [0/90] 4 3,864 3,804](/docs-images/80/80945031/images/12-1.jpg "3,914 3,833 Konfiguracija laganja Faori ujecaja micanja na pomae STKŠ MKE 0 0 0 0 [0] 16,546,514,590,536 [15/-15] 4,193,156,66,17 [30/-30] 4 1,716 1,690 1,876 1,67 [45/-45] 4 1,465 1,477 1,681")
12 Meoda onačnih elemenaa (MKE): ADINA ofware; 9-čvorni ljuai onačni elemen. Zglobno-olonjeni I-profil omjera l/h=3: Faori ujecaja micanja na verialne pomae a I-profil omjera l/h=3 i l/h=5: Konfiguracija laganja Faori ujecaja micanja na pomae STKŠ MKE [0] 16 5,96 5,07 5,434 5,31 [15/-15] 4 4,314 4,1 4,498 4,310 [30/-30] 4,990,918 3,65,911 [45/-45] 4,93,37,594,19 [60/-60] 4,090,8,7,030 [75/-75] 4,41,33,317,0 [±90] 4,43,40,474,4 [0/90] 4 3,864 3,804 3,914 3,833 Konfiguracija laganja Faori ujecaja micanja na pomae STKŠ MKE [0] 16,546,514,590,536 [15/-15] 4,193,156,66,17 [30/-30] 4 1,716 1,690 1,876 1,67 [45/-45] 4 1,465 1,477 1,681 1,40 [60/-60] 4 1,39 1,44 1,53 1,366 [75/-75] 4 1,447 1,479 1,499 1,436 [±90] 4 1,515 1,504 1,54 1,510 [0/90] 4,031,010,055,01
13 Promjena verialnih pomaa w orijenacijom maerijalnih oi vlaana: Faori ujecaja micanja na rednje normalno napreanje a I-profil omjera l/h=3 i l/h=5: Konfiguracija laganja Faori ujecaja micanja na napreanja STKŠ MKE 0 0 [0] 16 1,40 1,393 1,385 [15/-15] 4 1,310 1,300 1,301 [30/-30] 4 1,186 1,179 1,176 [45/-45] 4 1,11 1,14 1,110 [60/-60] 4 1,10 1,114 1,096 [75/-75] 4 1,116 1,14 1,113 [±90] 4 1,134 1,131 1,13 [0/90] 4 1,68 1,65 1,60 Konfiguracija laganja Faori ujecaja micanja na napreanja STKŠ MKE 0 0 [0] 16 1,144 1,141 1,14 [15/-15] 4 1,111 1,108 1,109 [30/-30] 4 1,067 1,064 1,063 [45/-45] 4 1,043 1,044 1,039 [60/-60] 4 1,036 1,041 1,034 [75/-75] 4 1,041 1,044 1,041 [±90] 4 1,048 1,047 1,047 [0/90] 4 1,096 1,094 1,094
14 Promjena rednjeg normalnog napreanja m, orijenacijom maerijalnih oi vlaana: Uporedba faora ujecaja micanja na rednje normalno napreanje a omjere l/h=3 i l/h=5: Konfiguracija laganja STKŠ-MKE 100 % MKE 0 0 [0] 16 1,06 0,600 [15/-15] 4 0,711-0,0 [30/-30] 4 0,836 0,61 [45/-45] 4 0,967 1,57 [60/-60] 4 0,585 1,768 [75/-75] 4 0,7 1,037 [±90] 4 0,00-0,046 [0/90] 4 0,634 0,190 Konfiguracija laganja STKŠ-MKE 100 % MKE 0 0 [0] 16 0,38-0,05 [15/-15] 4 0,74-0,035 [30/-30] 4 0,43 0,193 [45/-45] 4 0,407 0,519 [60/-60] 4 0,36 0,687 [75/-75] 4 0,1 0,416 [±90] 4 0,089-0,006 [0/90] 4 0,18 0,034
15 Zaljuča - Poavljeno je analiičo rješenje a lučaj avijanja anojenih ompoinih šapova ovorenog poprečnog prejea dvije oi imerije, -Faori ujecaja micanja dani u u paramearom obliu ao bi e uporedio ujecaj micanja na avijanje, -Smicanje načajno uječe na ruurno ponašanje anojenih ompoinih šapova operećenih na vijanje, -Ujecaj micanja ne može e anemarii nii a relaivno duge šapove, -Uporedbom vrijednoi verialnih pomaa oje daju ravijeni analiiči model e MKE dobivena u određena odupanja (a angle-pl laminae) ao poljedica vođenja ravninog anja napreanja na jednodimenionalno anje, -Uporedbom vrijednoi rednjeg normalnog napreanja oje daju ravijeni analiiči model e MKE dobiveno je ivrno laganje reulaa a ve onfiguracije laganja laminaa.
16 Hvala na pažnji!
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