REG NASA-TR-R-30-1959 LOCAL INSTABILITY OF THE ELEMENTS OF A TRUSS-CORE SANDWICH PLATE.pdf

1、NASA TR R-30.(tg(, rolalioiisof o+ (n_: 3. Ihwklimz mo(h,s for singh,-t russ-coru s:m(l_ i(ht)lai(,.Of ell(h of the (ore (,h,lm,nls ills Z(FO rotation.11 is convenient to denote the slitrn(,sses #_ or #a as/“2 or Fa for the face sheels and as (2 or Ca for the(ore. Then, for rood(, A,For mode I,and f

2、or mode (,21“.,+(:-_ (3 0 (3)2F.2+(_+(_ (I (4)41 _ t a-r(_ 0 (5)Mode D involves a defle(tion l)attern that isnlore complicated than the previous ones, and thesolution may be el)rained as folh)ws: The momentat any joint wilh a rotation a may I)( ol)tainedSolving e(lualion (6) for a and substituting i

3、nto(,qualion (7) yiehls the following stal)ilitv criterionfor Inode I):, (3F,.,+F_+:(*.,-( 3= ) Is)Equalions (3) rod (4) are identi(al: therefore,I)u(kling will o(cur in modes A rod B at the saln(,stress h,v(,l. The stal)ilily criterion that giveslhe lowest vahle of lhe )u(l,:ling slress is lhe onet

4、hat al)l)lies for any given case. Cal(ulationsshow that niode A and inode C ar(, the onlyinodes that need be (onsidered. Y.Io(h, A is ap-lfiicabh, for iligh values (if tf a with the use of equation (12a) or (12t) andequations (10) and Ill). The actual mode shapes(a u t hen I)(, (onst rt,te(I and are

5、 given in figure 4 (b)fl)r equation (12a) and in figure 4(c) for equation(I 21). For this (oufiguration, lhe behavior of eachiriangh, is indel)en(lent of the rest; therefore, thissoluti(m also applies to a singh, triangle with twoi(h, nti(a| sides or to a configuration represented bythe tlt)i)er hal

6、f of ihe (Iout)le-truss-core sandwich.Note thai equation (12a) is idenlical io equal|on(3) and thai mode A in figure 3 is equivahm! tomode A in figure 4.If the (Ioll)h-trliss-(,Ol(, sandwich has unequalfaces, the parl with t:le thinner fa(e may buckleas in moite A (fig. 4(b). This mode would beindep

7、endent of the thicker face; hell(!e, equation(12a) is still applicable. For unequM-faee sand-withes, that |)uckh, similar to mode B, the use ofequation (12t) wouhl h,ad to SOllle (ITOI*. |O_.V-ever, if it is assumed that |)oth faces of the sand-wich have the salne thickness as the lhimwr face,equati

8、on (12b) will yield results which are onlyslightly conservative.ALTERNATE FORM OF STABILITY CRITERIAIn order to cahtflate buckling stresses with thepreviously derived stability criteria, values of theO. Ct _ D. X _Xpoorted(c)(a) General mod, shalw.(b) 3,lode A.(c) Mode B.FI(; VRE L-l_uckling modes f

9、or doul)le-truss-coro sitndwichl)htte.various stiffness factors must he known. Charlsgiving “alues of #z amt u3 are presented in reference3. It s sometimes convenient in calculations tohave slillnesses giveu in t at)ular forln as is donein refeJence 4. t lowever, v.3 is not tal)ulated inreferen,_e 4

10、, t)ut the rehltionshi 1) of _., and _3 to thestiffnes:;es given in reference 4 |nay be obtainedwith tle aid of exl)ressions (1) and (2) and the(h,filfiti, ms of the various slifflWSSeS.In re_er,nce 4, the stiffness of a member with asymme ri(a defh,(,ti(m is denoted as S_v; hence,4Sw _ #2 (13 )The

11、st ttness of a member with the far edgeclampoql is S aim may be ohtained as follows:4S -#2+#3 (14)2Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-LOCAL INSTABILITY OF THE ELEMENTS OF A TRUSS-COI,E SANDWICH PLATE 5The stiffness of a member with the f

12、ar edgesimply suPl)orted is S H aml is given by tile follow-ing equation:4S H= 2#_Ia3- (15),u2_ #jThe stability criterion nmy be written in thenotation of reference 4 when equations (13), (14),and (15) are (lsed. Equation (3) which was fotmtaiued l)y using the chartsor tal)les of referelwes 3 and 4,

13、 if ),/b and k are re-placed with the fottowing expressions:flll(lb . /k X“ - k_ - b 2(_9)(20)Equations (19) and (20) are euckling coefficientswill prol)al)ly l)e slightly lfigber llmll tbe theoreticalvalues given in figures 5 and 6, if the actual coreelements are curved rather than flat. The dis-co

14、ntitmit,y in the slop(, of the ctuves of figure 6marks the ransitioll flom one mode to the oilier.Equation (12a) applies to the upl)er portion ofthe curves a,nd equation (121) al)l)lies to thelower port, ion.Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IH

15、S-,-,-() TECHNICAL REP()RT t. 31) -NATIONAL AEt_.ONAUTICS AND SPACE AI)MINISTRATIONCare restrains facel:li!t!4 *5._“hklf.A-_zL,!77L2i_II N.: i i i!, t ii:!71ill _1 I ,J iiFace reslroins core!III III Iillill II I1liiJlliill(a) k_=0.k,_%E / t F_-I“i,:ilt_: 5. I,ocal huckling co(fftieielit lor siugle-t

16、 russ-core s ul,dwich pld, a 12( 1 ; /z_) _bf/ “_I ttt_-l-tIt t t t- +_# |i ; ;_d-LLif i , _ ; i i i!1!iililt!TIT_1iiiiiiiiiiiii,11Iiili_IllllllIIIIllIIIIIIllllIIIII. i iProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-LOCAL INSTABILITY OF THE ELEMENT

17、S OF A TRUSS-CORE SANI)WICH PLATE 7Core restroins foce(b) k_ 0.5.FIGURE 5.-Continued.Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-TE(_HNI(ALI_.EP()RTlt 30 -NATI()NAI,AER()NAUT:CSANI)SPACEA1)MIN1ST_.ATION(c)kl,=1.0.FIGURE5.-Conelu(i(:_.Provided by

18、IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-LOCALINSTABILITYOFTHEELEMENTSOFA TRUSS-CORESANDWICHPLATE 9*f* “ T “TLLL._-_t,_._ilil_:_t: :!i:;:_*“ Core restrains face+ t1 1:! if:!: i!ii iii! ii!i !i!:!: . i“i:!it i+ . _ 4. ,+-:_: :3 iiii,!:tii!iii:iitiii:t:/it!

19、N+:i! :i:!:i_ !ill: ,. r:l-t-t .9 .P tt:V_I: “t * _,: t(:T7 :f:t ,f:2:2 _? ,:Tt _.*, ,*,l + *+_*:T;,_t 7I!,2 ;A_: :I45 _ iii,+.455 gT:2X:i_4x/t_.t.o ;:1 t, t t t I + * _ : :t:t i:55 1_+ *+*4 II+ +,+.+_ *_,+* +.+* *_+11_ +,_* .+-_._. 70 _4.tT“ t-t ! _Ti2 : +*Face reslrams core(a) k_=O.k y-_l_: ( t_ _

20、“F,G,:RE 6. l,ocM h,ckli,g co,qlSch,t for do,tble-truss-core s.uM,ieh plate =19.(1 _-_. _),_. “t_f!.i,: !.+ +Iit:+*+.4_._t*.t.4t510724-60-2Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-_() TECHNICAL REP()RT R-30-NATIONAL AERONAUT CS AND SPACE AI)MI

21、NISTRATIONfttlttttt:tt-_+tl:+!il;:;:l;:!;I._*I+_.I+.4-5l,im_l!.,;l,ltit! : : :i:,:4 t:tttf:t: i:i_!iI!_!_:!;iiT“IIJ; +* !ilili i;_ t t+,+* + t* +t#“t+; *;-+ $;4;:; : .+: . .;tb): :t!0, . + ,i.,| ,i!ii2iL : _;iilX!zi , i ,t .: : 7: l!iiCore restrains face ti ti “t +, ;.t; .i“:l:t:t tt:iOt:_;:i :_:L:,

22、 “;L:_:_- gL:2 :_.: :.f:l:.:!_t i : :XJ/: “I : t t/+.,+_,+ . . ,_i. i| t +i_t 5I . +5J. ,I:_.;._. .;i_:_I :,Z:/+: _. :, _ : l : :,_+. L;-.P*; “: .i!N: :,t+t +_i“-D#T._.i:i:za_(I) A.,: 0.5.FI(IIRE 6. (_olll ilille(Provided by IHSNot for ResaleNo reproduction or networking permitted without license fr

23、om IHS-,-,-LOCALINSTABILITYOFTHEELEMENTSOFA TRUSS-CORESANDWICHPLATE 11Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-12 TECHNICAL REPORT R 30 -NATIONAL AERONAUTICS AND SPACE AI)MINISTRATIONhy30:.; . t1.5 : 11!;.+!I.,.I 5 ;T;T o T:i:iti . +-_i-.-:! !

24、 i,i,*_.4i i!2tilV-“(:It_E 7. -l,ocal bu(kling co_,fficim_t for both single- aud double-truss-core sandwich plates subject to transverse in-planekor%E f tf N-Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-LOCALINSTABILITYOFTHEELEMENTSOFA TRUSS-CORES

25、ANWWICHPLATE 13oI I1“ICVrtE _. McLhod of interi)olati(m (m :_ carpet plot.( t_ )If _ and 0 are given, _z llmy l)e found as illustrated.Examimnion of figures ,5 and (i indicates lhalthe buckling stress in the longitudimd directiot_will I)e appreciably reduced 1)y lhe l)res(,nc(, oftransverse loads in

26、 the p/an(, of the sandwich ifthe face sh(,els are primarily responsible forbuckling. If the cove (dements ave unstabh, Ihepresence of transverse loads does not aller ap-pr(,ciably tit(, longitu(timd lmcklittg str(,ss.The curves of figures ,5 lo 7 are also applicabh_to sandwi(,hos with uuequal faces

27、 if the ratio tjtris obtahwd from the thi(kmss of the core andlhe thickness of the thimwst face. In figure 6, inthe region below the dashed line (he charts will beslightly conservative for double-truss-core sand-withes wilh unequal faces.I, AN(;LEY _/NqEARCII (_/,NI/_R,NATIONAL AERONAUTICS A.NI) SPA

28、CE ADMNISTRATI_)N_LAN(:LEY FIEI.D, VA., April I0, 1958.REFERENCESI. Anderson, Melvin S: Optimum Proportions of Truss-Core :rod Wel)-(!ore Sandwich Phttps Loaded inCompression. NASA TN D-98, 1(.159.2. Cox, 11. L.: Comt)utalion of Initial Buckling Stressfor Slmet-Stiffener Comt)imtlions. Jour. ICA.S.,

29、 vo.58, no. 525, Sct)t. 1954, pp. 634 638.3. Anon.: )alt Slmcls Stressed Skin Slruclur_.s. Vol.II, Fifth _sue, Royal Aero. Sot., Jan. 1957, nos.02.01.28 to 02.01.37.1. Kroll, _V. D.: Td)les of Stiffness “rod Carry-OverFactor for :lat Rectatgular l)lat(_s Under Coml)res-sion. NACA WR L;_98, 943. (For

30、merly NACAAILR 31(27.)5. Shuleshko, P.: A R(luct.ion Method for BucklingProblems of ()rLholropic Plates. Aero. Quarterly,vol. VIII, pt. 2, May 1957, Pt). 145-156.Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-