1、 1/mFOR AERONAUTICSTECHNICAL NOTE 2679THE STABILITY UNDER LONGITUDINAL COMPRJ3SSION OF FLATSYMMETRIC CORRUGATED-CORE SANDWICH PIATES WITHSIMPLY SUPPORTED LOADED EDGES AND SIMPLYSUPF+3RTED OR C LA.MPED UNLOADED EDGESBy Paul SeideLangley Aeronautical Laboratory-Langley Field, Va.WashingtonApril 1952,(
2、. .”makes possible the determination of ttieelasticover-all buckling loads of flat corrugated-coresandwich plates withsymmtric corrugated cores. By over-all buckling is meant buckling of,. . -. -.-.-.- -.-. - . - - - -Provided by IHSNot for ResaleNo reproduction or networking permitted without licen
3、se from IHS-,-,-. - . . - - -.-. -2the sandwich plate as a whole, withoutfaces between corrugation crests or ofpresent paper the theory is applied tounder longitudinal compression of flatNACA TN 2679 . :,regard to local buckling of thethe corrugationwalls. In thethe problem of the stability , Bi Cia
4、bDQX Dc+EcEsh0coefficients inrespectively,1,SYMBOLS.expressions for w, , and ,for a plate with simply supportedunloaded edgescoefficients in expressions for w, C the bucklewave lengths of corrugated-core sandwichplates with infinite transverseshear stiffness D%, however, tend to increasewith decreas
5、ing transverseshear stiffness D . Calculations indicate that a corrugated-coresand-QYwith plate with zero transverse shear stiffness QY buckles in only onelongitudinal half wave, regardless of the plate aspect ratio. The bucklehalf wave lengths of infinitely long corrugated-coresandwich plates withs
6、imply supported edges remain relatively constant over a large range ofvalues of the transverse-shear-flexibilityparameter and flexural-stiffness ratio. The half wave length is approximately equal.to theptwidth for values of the transverse-shear-flexibilityparameterXZE+ varying from O to 1.0 and for
7、values of the flenral-stiffnessb2Dratio varying from O to 1.0. In this range the half wave length is 1.0to 1.3 times the plate width. For plates with clamped unloaded edges,the half wave length of buckle varies somewhat more (from 0.66 to1.2 times the plate width).EFFECT OF FINITE TRANSVERSE SHEAR S
8、TJHTZESS D%Although it is customary to assume in the analysis of corrugated-core sandwich plates that the transverse shear stiffness DQX isinfinite, little or no information as to the limits of validity of thisassumption is available. Calculationshave been made for the present. . -. . .- - - - - - .
9、 - - - - - - -.- - - . - - - - . - -. - -Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,- - . . ,8!1 aper to determine thetion of infinite D,)tnz:)+n2B2,+ 1P,.,(1- Ps 2qn+ z( )2 n2rx + ryp2k=” d(6)1-1- !JS n; +ps2+ (n2+l)-Mm,movement parallel to the
10、edgesSolutions of the differential equations (2) for the(8)middle-surface “deflection w and the shear forces Qx md Qy exist in the formW.sin= E Ai cosh aiQx = COS z iYBi cosh i(9)where values of ni, Ai, , and Ci are to be determined from thedifferential equations (2). Equations (2) are satisfiedby e
11、quations (9)if, for each value of i, the following set of simultaneous equationsis satisfied:m2()lb3kAi: Bi + ni 1()b38ES X ;ci=o82 Es%.(10a). .- .- . . .Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-lJilCTN 2679 15.( +$- ni2)J*wi01-1- W2+ 2 (10C)T
12、hethat is,vanish -condition that .i, Bi, and Ci have values other than zero -that the determinant of their coefficients in equations (10) .yields an equation for the determination of ni1$E+(- Ms+-lp- k.x) =o (11)4. . . . . . . . - . . . . “.- . . . -. .-. . - - - .- .-._ . . . . . -Provided by IHSNo
13、t for ResaleNo reproduction or networking permitted without license from IHS-,-,-.6 NACA TN 2679Thus ni has the values *n , k%, and 3, the six roo%s of equ6-tion (n). Only the positive roots need be considered.“Ech of the coefficients Bi and Ci may he given in terms of the correspondingcoefficient A
14、i. From equations (lOa) and (1OC), the following rela-tionsareohtained: . , “ .; , . . . :, .(12)where2 2 s+Ps k-:%2 P ,2 P2 x1- Ps #)l+psPS2 + 2 %ni r-ni y+- =2 2 l+l%hni -+fii=“ p2 2p2.x1-)w &_ ni2 ry+l+ lJs,ni2rx %p2 2Equation (9) may now he written as.qY- )“3YA2 cosh + A3 cosh , . . . . ,.(&.)?+
15、3 cosh ? i (13),. . . . . .Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-3C.!NACA TN 2679 17Equations (13) already satisfy the boundary conditions along thesimply supported edges (equation (3a). The boundary conditions alongthe clamped edges (equat
16、ion (8) must nowbe satisfied.of eqwtions (13) into equation (8) yields the following.ml Ymz lm3Al coshy+ A2 cosh+ A3 cosh = o2YuL l-ma 3UMThe substitution,set of equations:o(q+ $Fy)% si +. 0 JIn order to assure the existence of values of Al, A2, and A3 otherthan zero, the determinant of th6 coeffici
17、ents of Al, A2, and A3is set equal to zero. When the determinantisexpanded, the followingequation is obtained:3 o(% - q(n3 + ry3)ty= (15)Equation (15) in conjunction with equation (n) is the criterion for thecompressivebuckling of corrugated-coresandwich plates with simplysupported loaded edges and
18、clamped unloaded edges.When values of the compressive-buckling-load-parameter k are com-puted with equations (11) and (15), a trial and error process is used.For given vaiues ofand m is assignedgive the values ofinto equation (15).f!, rx)ry, and q, a value of k is assumedsome integral value. Equatio
19、n (n) is solved tonl? n2 and n3. These values are then substitutedIf the left-hand side of equation (15) does not. . - . . . - .- . . . . .- . - - G _ .- .Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-.- . 18 NACA TN 2679vanish, other values of k m
20、ust be chosen and the process repeated.Th$s procedure yields a series of values of k and correspondingvaluesof the left-hand side of equation (15). The correct value of k may .now be obtained by plotting these values as ordinate and abscissa andpicking off the value of k at which the left-hand side
21、of equation (15)tis equal to zero. The entire process is then repeated for other integralvalues of m until the lowest value of k is obtained.For the case of infinite D%, the followti stability criterion isobtained:nl l-ml( )talih-l- Kn12 21- %s2+ 22 Yn2 2 ( )tall-=1- PSIF 21-%2+ 2 7-%2%(16)where nl
22、and “ are the ositive values of -theroots Anl and +of the equation112 21+ nk -2+2(l+pJ i P2.The samevalues of. kprocedme is used in solving equations (16).and (17) foras is used for equations (l-l)and (15). .Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IH
23、S-,-,-NACA TN 2679.191.2*3.4.5*6.REFERENCESLiboye, Chqrles, and Batdorf, S. B.: A General Small-IkflectionTheory for Flat Sandwich Plates. NACA Rep. 899, 1948. (FormerlyNACA TN 1526.)Libove, Charles, and Hubka, Ralph E.: Elastic Constants forCorrugated-CoreSandwich Plates. NACA TN =89, 1951.Libove,
24、Charles: A Small-DeflectionTheory for Flexurally OrthotropicFlat Sandwich Plates. nom: Theory and Practice of SandwichConstruction in Aircraft. .A Symposium. l%eprint No. 165, S.M.F.Fund Paper, Inst. Aero. Sci., Jan. 1948, pp. 54-55.Anon.: Sandwich Construction for Aircraft. .&t II - MaterialsProper
25、ties and Design Criteria. ANC-23, Air Force-Navy-CivilSubcommittee on Aircraft Design Criteria, May 1951, pp. 75-81.Seide, Paul, and Stowll, Elbridge Z.: Elastic and Plastic Bucklingof Simply Supported Solid-Core Sandwich Plates in Compression.NACA Rep. 967, 1950. (FormsrlyNACA TN 1822.)Seide, Paul:
26、 Compressive Buckling of Flat Rectangular Metalite meSandwich Plates with Simply Supported Loaded Edges and ClampedUnloaded Edges (Revised). NACA TM 2637, 1952.- . -. - . - . - -. . . . . - . . . _ . . Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-
27、. .20 NACA TN 26790 .#c . . . .Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-(.a.,rbNL-IYEN-.a(a) Stiply supported unloaded edges. .(b) Clamped unloaded edges.Figure 1.- Flat symmetric corrugated-coresandwich-platebucklin problems-solved in the pre
28、sent paper.-. .- .-.7 -. . - -. - _ - . . . - - - -. -. - -. . - - - -Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-22 NACATN 26798 1- .2&6 b2DQY ,-4 .5- -1.o-2L ., . .-CO.1I t II 1 I I I 1 I I I I I 1 II!I11I1II11It0 +.8- “ 1.2 - 1.6 2.0:“(a) EC7C
29、 = .E&.11,1,1!1,1,1,1,1,1!1,1,1,1,1,1,1,1,1,1,1,0-.4.8 !.2 1.6 2.0g “ =is$Yb .Figure 2.- Compressive-buckling-loadparameters for corrugated-core sand-wich plates with simply supported unloaded edges.,. . . . . . - . Provided by IHSNot for ResaleNo reproduction or networking permitted without license
30、 from IHS-,-,-NACA TN 2679 23. .,a71b2NT2E&.8 T2E& .642 - aI I t I I I t 1t 1II1IIII,II11i1t1I1Ito. .(c)Figure.8 1.2= 1.().S*S2.- Concluded.1.6 2.086 Ecic&N “4 *T2E& .-2I I 1 1 I I I I 1 I I 1 1 I t t I I I I 1 I I , 1 I 1 I I ,0 .2 .8, -s3.6%QYFigure 3.- Compressive-buckling-load parameters for inf
31、initely longsimply supported corrugated-core sandwich plates. . .- .=. - - . . . . -.-.- - .- - - - -Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-24b2N7T2Es&Figure 4.-o .8Ec (a) =.Es “1.2 1.6 2.012_ 7r2Es&8 _ .l, “ “.254 .5l.oI II I II I II I II t
32、 II I II 1 II I II I II I II0 .4 .8 1.2 1.6 2.0.(b) m = 0.5.ESIS. .,Compressive-buckling-loadparameters for corrugated-coresandwich plates with clamped unloaded edges. - . - Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-, 4C NACA TN 2679 252*,12_8
33、_4I(c)Figure.8 1.2 1.6 2.0 -ba= 1.().ESS4.- Concluded.0,0 2 4 .6 .8 Lolrgb2 DQYFigure 5.- Compressive-buckling-load paramet,ers. for infinitely longclamped corrugated-core sandwich-plates.,-,. - .- - . , . .- -Provided by IHSNot for ResaleNo reproduction or networking permitted without license from
34、IHS-,-,-26 NACA TN 2679 .6 : 7a)20lo / 2 _ ? _ r QY! II 1 II t I 1 I I I f II I II I II I II I IIIIIo .2 4 .6T2E&b2DQY.8 1.06_a)20 7t?N#E& z2 l- , -Qx T QyI II I II I II I 1,1111 I II I II I I 1. I II 1 IIo .2 !4 .6 .8 LoT2E& if DQY.Figure 6.-Effect of finite transverse shear stiffness Qx on thecomp
35、ressive-buckling-loadparameters of infinitely long simplysupported corrugated-coresandwich plates. Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-NACA TN 2679,27t?N7T2E&6_4 -2 _f II I II I IIo .2(c)Figure!4 .66.- Concluded.8 1.0NACA-Ungley -4-16-62-1000- - - - %. -Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-
