1、 -. I. -January 1,984 . , . Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-TECH LIBRARY KAFB, NM NASA Technical Paper 221 5 1984 National Aeronautics and Space Administration Scientific and Technical information Office 1984 00b7772 Buckling Loads of
2、 Stiffened Panels Subjected to Combined Longitudinal Compression and Shear: Results Obtained With PASCO, EAL, and STAGS Computer Programs W. Jefferson Stroud, William H. Greene, and Melvin S. Anderson Langley Research Center Hanapton, Virginia Provided by IHSNot for ResaleNo reproduction or networki
3、ng permitted without license from IHS-,-,-CONTENTS SUMMARY 1 INTRODUCTION 1 SYMBOLS 2 BUCKLING ANALYSIS IN PASCO FOR LOADINGS INVOLVING SHEAR . 4 VIPASA Buckling Analysis 5 Smeared Stiffener Solution 8 STIFFENED PANEL EXAMPLES 10 Example 1 . Composite Blade-Stiffened Panel 12 Panel description 12 PA
4、SCO input 13 EAL model . 14 STAGS model 14 Results . 16 Example 2 . Metal Blade-Stiffened Panel 23 Panel description 23 PASCO input 24 EAL and STAGS models 25 Results . 25 Example 3 . Heavily Loaded, Composite Blade-Stiffened Panel . 28 Panel description 28 PASCO input and EAL and STAGS models . 29
5、Results . 29 Example 4 . Metal Blade-Stiffened Panel With Thin Skin 33 Panel description 33 PASCO input and EAL and STAGS models . 33 Results . 33 Example 5 . Composite Hat-Stiffened Panel . 40 Panel description 40 PASCO input and EAL model 40 Results . 43 Example 6 . Composite Corrugated Panel 49 P
6、anel description 49 PASCO input and EAL model 50 Results . 51 Example 7 . Metal 2-Stiffened Panel . 56 Panel description 56 PASCO input and EAL model 57 Results . 57 iii 1.111111111 11111111 11111111 11111II11111111l IIII I1111 11111 II 11111 I I IIIIIIIIIIII I II IIII I Ill I II u I I U 11111111 II
7、III IIMIIIWI 1111111 1111 111 I 111 I1 II Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-RECENT DEVELOPMENTS . 62 CONCLUDING REMARKS 62 APPENDIX . EAL RUNSTREAMS USED FOR PANEL ANALYSES . 64 Runstream PANEL. BLADE . 64 Runstream PANEL. GEOM 65 Runst
8、ream PANEL. BUCK 65 REFERENCES 73 iv Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-SUMMARY The report examines several buckling analysis procedures for stiffened panels, presents accurate results for seven stiffened panels, and illustrates buckling
9、 modes with plots of buck- ling mode shapes. All panels are rectangular and have stiffeners in one direction - down the length of the panel. The buckling analyses used in PASCO are summarized with emphasis placed on the shear buckling analyses. PASCO buckling analyses include the basic VIPASA analys
10、is, which is essentially exact for longitudinal and transverse loads, and a smeared stiffener solution (equivalent orthotropic plate solution) that was added in an attempt to alleviate a shortcoming in the VIPASA analysis - underestimation of the shear buckling load for modes having a buck- ling hal
11、f-wavelength equal to the panel length. Such buckling modes are sometimes referred to as overall modes or general instability modes. Buckling results are then presented for seven stiffened panels loaded by combinations of longitudinal compression and shear. The buckling results were obtained with th
12、e PASCO, EAL, and STAGS computer programs. The EAL and STAGS solutions were obtained with a fine finite element mesh and are very accurate. These finite element solutions together with the PASCO results for pure longitudinal compres- sion provide benchmark calculations to evaluate other analysis pro
13、cedures. For each example, several figures illustrate buckling mode shapes for pure compression and pure shear loadings. It was concluded that the smeared stiffener solution should be used only with caution. INTRODUCTION Although buckling analysis procedures that are both fast and accurate have been
14、 devel- oped for stiffened panels subjected to longitudinal (N,) and transverse (Ny) loadings (for example, VIPASA, refs. 1 to 3, and BUCLASP2, ref. 4), no such procedure has been developed for analyzing stiffened panels subjected to loadings involving shear (Nxy). (See fig. 1.) VIPASA nearly meets
15、the dual objectives of speed and accuracy; however, when the loading involves shear, VIPASA underestimates the buckling load for the overall mode - that is, the mode for which the buckling half-wavelength in the direction of the stiffeners is equal to the panel length. VIPASA is generally accurate f
16、or loadings involving shear when the buckling half-wavelength in the direction of the stiffeners is less than one-third the panel length. Shear buckling analysis procedures in current use include the following modeling approaches: stiffeners modeled as linked plates with infinite panel length (VIPAS
17、A, ref. 1); hinges along plate element connections for local buckling and smeared stiffnesses for overall buckling (for example, ref. 5); approximations in which stiffeners are modeled as discrete lines of bending (EI) and twisting (GJ) stiffnesses on the panel skin; and general purpose finite eleme
18、nt approaches (for example, EAL, refs. 6 and 7, and STAGS, refs. 8 and 9). All these Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-Figure 1.- Loadings and orientations. approaches have shortcomings. The shortcoming of the approach used in VIPASA is
19、 mentioned in the previous paragraph and is discussed in this report. When stiffnesses are smeared, local deformations that contribute to the overall buckling mode are lost. Some local deforma- tions are also lost when the stiffeners are modeled as E1 and GJ stiffeners. Finite ele- ment approaches c
20、an provide high accuracy by using detailed modeling and fine meshes; how- ever, to obtain accurate results, the computation costs may be high. Because of the shortcomings in VIPASA, the buckling analysis in PASCO (refs. 10 to 13), an alternate solution approach for predicting overall shear buckling
21、was explored and incorpo- rated in PASCO. That approach is based on smeared orthotropic stiffnesses. This report presents buckling results obtained with the computer programs PASCO (which includes both VIPASA and a smeared orthotropic solution), EAL, and STAGS for seven stiffened panels. For each pa
22、nel, results are presented for several combinations of inplane shear and longitudinal (stiffener direction) compression ranging from pure shear to pure longitudinal compression. The results serve three purposes. They help evaluate the shear buckling analyses in PASCO, they provide accurate benchmark
23、 calculations to evaluate other analysis procedures, and they help provide a better understanding of the buckling mechanism for stiffened panels through the numerous detailed plots of buckling mode shapes. SYMBOLS Values are given in both SI and U.S. Customary Units. The calculations were made in U.
24、S. Customary Units. b plate width D plate bending stiffness 2 Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-Dll,D22,D33 orthotropic stiffnesses defined in equation (2) Youngs modulus Youngls modulus of composite material in fiber direction and tran
25、sverse to fiber direction, respectively shear modulus of composite material in coordinate system defined by fiber direction bending stiffness of beam amplitude of bow-type imperfection at panel midlength twisting stiffness of beam panel length bending moment about line parallel to Y-axis (see fig. 2
26、) bending moment about line parallel to X-axis applied longitudinal compressive loading per unit length (see fig. 2) value of N, that causes buckling applied shear loading per unit length (see fig. 2) value of Nxy that causes buckling applied transverse loading per unit length (see fig. 2) lateral p
27、ressure buckling displacements panel width coordinate axes in longitudinal, transverse, and late.ra1 directions, respectively coordinates 3 Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-EX strain in x-direction e fiber orientation angle (see fig. 9
28、) A buckling half-wavelength I-L Poissons ratio IJ.1, I-L2 Poissons ratios of composite material in coordinate system defined by fiber direction, pl = p2 E2 Abbreviations: Anti indicates that buckling displacement w is antisymmetric with respect to a point at the center of the panel FACTOR eigenvalu
29、e, the product of FACTOR and applied load is buckling load S.S. simple support boundary conditions SYm indicates that buckling displacement w is symmetric with respect to a point at the center of the panel Computer programs: BUCLASP2 Buckling of - LAminated - Stiffened - Panels EAL - Engineering - A
30、nalysis - Language PASCO - Panel - Analysis and - Sizing - Code STAGS - STructural - Analysis of - General - Shells VIPASA - Vibration and - Instability of - Plate - Assemblies including - Shear and - Anisotropy BUCKLING ANALYSIS IN PASCO FOR LOADINGS INVOLVING SHEAR PASCO is a computer program for
31、analyzing and sizing uniaxially stiffened composite panels subject to the loadings shown in figure 2. PASCO is described in references 10 to 13. 4 Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-Figure 2.- Stiffened panel with initial bow, applied lo
32、ading, and coordinate system. As pointed out in the introduction, an important limitation of PASCO is that VIPASA (the buckling analysis in PASCO) underestimates the buckling load when the loading involves shear and the buckle mode is a general or overall skewed mode having a longitudinal buckle len
33、gth equal to the length of the panel. That limitation and an approximate analysis technique intended to overcome it are discussed in this section. VIPASA Buckling Analysis VIPASA, the buckling analysis program incorporated in PASCO, treats an arbitrary assemblage of plate elements with each plate el
34、ement i loaded by (Nx)i, (Ny)i, and (Nxy)i. The buckling analysis connects the individual plate elements and maintains continuity of the buckle pattern across the intersection of neighboring plate elements. The buckling displace- ment w assumed in VIPASA for each plate element is of the form w = fl(
35、y) cos x - f2(y) sin x 71X 7rX where h is the buckling half-wavelength. Similar expressions are assumed for the inplane displacements u and v. Because the buckling displacements are assumed to have a speci- fied form in the x-direction, the VIPASA solution is essentially a one-dimensional solution.
36、(The finite element solutions discussed subsequently are two-dimensional.) The functions fl(y) and fz(y) satisfy the differential equation of equilibrium and allow various boundary conditions to be prescribed on the lateral edges of the panel. Boundary conditions cannot be prescribed on the ends of
37、the panel. However, certain useful boundary conditions are implic- itly satisfied at the ends of the panel. VIPASA is, therefore, still effective for analyzing a broad spectrum of structural analysis problems. Boundary conditions at the ends of the panel 5 Provided by IHSNot for ResaleNo reproductio
38、n or networking permitted without license from IHS-,-,-and the effect of these boundary conditions on the predicted buckling load are discussed in the following paragraphs. For orthotropic plate elements with no shear loading, the solution given by equation (1) involves a series of node lines that a
39、re straight, perpendicular to the longitudinal panel axis, and spaced X apart, as shown in figure 3. Along each of these node lines, the buckling dis- placements satisfy simple support conditions. Therefore, for values of X given by X = L, L/2, L/3, ., L/m, where m is an integer and L is the panel l
40、ength, the nodal pat- tern shown in figure 3 satisfies simple support boundary conditions at the ends of a finite, rectangular, stiffened panel. For this case, the VIPASA solution is exact. “ Node lines t t t $. 1 i t NY I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I
41、 I I I r-y I I I I I I I I t Nx c Figure 3.- Node lines for orthotropic plate elements with no shear loading. For anisotropic plate elements and/or plate elements with a shear loading, the solution given by equation (1) involves node lines that are skewed and not straight, but the node lines are sti
42、ll spaced X apart, as shown in figure 4. (Because anisotropy generally has negligible effect on buckling loads for long-wavelength buckling modes and because it is these long- wavelength modes that are troublesome, reference to anisotropy is dropped in the following discussion.) Since node lines can
43、not coincide with the ends of the rectangular panel, the VIPASA solution for loadings involving shear is accurate only when many buckles form along the panel length, in which case boundary conditions at the ends are not important. An example in which h = L/4 is shown in figure 5. As X approaches L,
44、the VIPASA buckling analysis for a panel loaded by Nxy may underestimate the buckling load substantially. One explanation is as follows. As seen in fig- ure 5, the skewed nodal lines given by VIPASA in the case of shear do not coincide with the end edges. Forcing node lines to coincide with the end
45、edges produces buckling loads that are always higher than those determined by VIPASA. When only one buckle forms along the panel 6 Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-“ NY t t + t + Node lines Nw - c- - - - Figure 4.- Node lines for aniso
46、tropic plate elements and/or plate elements with shear loading. / / Figure 5.- Buckling of panel under shear loading. Mode shown is A = L/4. length, the effect of boundary conditions at the ends is much more important than when multiple buckles form along the length. For long-wavelength buckling mod
47、es, the buckling load for a panel satisfying the end boundary conditions can be more than twice the buckling load for a panel not satisfying the end boundary conditions. Such cases are illustrated in the examples discussed subsequently. 7 Provided by IHSNot for ResaleNo reproduction or networking pe
48、rmitted without license from IHS-,-,-In summary, for stiffened panels composed of orthotropic plate elements with no shear loading, the VIPASA solution is exact in the sense that it is the exact solution of the plate equations satisfying the Kirchhoff-Love hypothesis. However, for stiffened panels having a shear loading, the VIPASA solution can be very conservative for the case X = L. Because VIPASA is overly conservative in the case of long-wavelength buckling if a shear load is present, another easily adaptable analysis procedure based on smeared ortho- tropic
