NASA Technical Memorandum 4770

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Thermal and Mechanical Buckling

Analysis of Hypersonic Aircraft HatStiffened Panels with Varying Face

Sheet Geometry and Fiber Orientation

William L. Ko

Dryden Flight Research Center

Edwards, California

National Aeronautics and

Space Administration

Office of Management

Scientific and Technical

Information Program

1996
NASA Technical Memorandum 4770

Thermal and Mechanical Buckling

Analysis of Hypersonic Aircraft HatStiffened Panels with Varying Face

Sheet Geometry and Fiber Orientation

William L. Ko

December 1996
Y
CONTENTS

ABSTRACT ....................................................................... 1

NOMENCLATURE ................................................................. 1

INTRODUCTION .................................................................. 3

DESCRIPTION OF PROBLEM ........................................................ 3

FINITE-ELEMENT MODELING ...................................................... 4

BOUNDARY CONDITIONS ......................................................... 4

Axial Buckling .................................................................. 5

Lateral Buckling ................................................................. 5

Shear Buckling .................................................................. 5

Thermal Buckling ................................................................ 5

APPLIED LOADS .................................................................. 5

Axial Buckling ................................................................... 5

Lateral Buckling ................................................................. 6

Shear Buckling .................................................................. 6

Thermal Buckling ................................................................ 6

BUCKLING LOADS AND TEMPERATURES ........................................... 7

NUMERICAL EXAMPLES ........................................................... 7

MATERIAL PROPERTY ITERATIONS ...... .......................................... 8

Monolithic Panels ................................................................ 8

Metal-Matrix Composite Panels ..................................................... 9

RESULTS ........................................................................ 10

Monolithic Panels ............................................................... 10

Metal-Matrix Composite Panels .................................................... 11

CONCLUDING REMARKS ......................................................... 13

REFERENCES .................................................................... 15

iii
TABLES

1. MMC layup combinations ......................................................... 4

2. Geometry of the hat-stiffened panel ................................................. 7

3. Temperature-dependent material properties for monolithic titanium (Ti-6A1-4V, ref. 15) ....... 8

4. Temperature-dependent material properties for metal-matrix composite ..................... 8

5. Buckling loads and buckling temperatures of monolithic hat-stiffened panels ............... 10

6. Buckling loads and buckling temperatures of MMC hat-stiffened panels with [90/0/0/90]

face sheet and [45/-45/-45/45] hat ................................................. 11

7. Buckling loads and buckling temperatures of MMC hat-stiffened panels with flat face sheets... 12

FIGURES

1. Hat-stiffened panel with flat, microdented, or microbulged face sheet ..................... 16

2. Three types of hat-stiffened panels ................................................. 17

3. Composite layups for hat-stiffened panels ........................................... 18

4. Unit strip of a hat-stiffened panel .................................................. 18

5. Quarter-unit strip finite-element model; microbulged face sheet .......................... 19

6. Full-unit strip finite-element model; microbulged face sheet ............................. 19

7. Constraint conditions for axial buckling ............................................. 20

8. Constraint conditions for lateral buckling ............................................ 20

9. Constraint conditions for shear buckling ............................................ 21

10. Constraint conditions for thermal buckling ........................................... 21

11. Distributions of applied compressive forces .......................................... 22

12. Temperature-dependent material properties; Ti-6A1-4V titanium alloy .................... 22

13. Iterations of buckling temperatures; monolithic hat-stiffened panel; microdented face sheet .... 23

14. Iterations of buckling temperatures; metal-matrix composite hat-stiffened panel; [90/0/0/90]

flat face sheet, [45/-45/-45/45] hat ................................................. 23

15. Buckled shapes of three types of hat-stiffened panels under axial compression;

monolithic panels .............................................................. 24

16. Buckled shapes of three types of hat-stiffened panels under lateral loading; monolithic panels.. 25

17. Buckled shapes of three types of hat-stiffened panels under shear loading; monolithic panels... 26

18. Buckled shapes of three types of hat-stiffened panels under uniform temperature loading;

four edges clamped; monolithic panels .............................................. 27

19. Buckling loads as functions of dent or bulge; monolithic hat-stiffened panels ............... 28

iv
Pa_a 

20. Increase of buckling temperatures with increase of dent or bulge; monolithic

hat-stiffened panels ............................................................. 28

21. Buckling loads as functions of dent or bulge; metal-matrix composite hat-stiffened

panels; [90/0/0/90] face sheet, [45/-45/45/45] hat .................................... 29

22. Increase of buckling temperatures with increase of dent or bulge; metal-matrix composite

hat-stiffened panel; [90/0/0/90] face sheet; [45/-45/-45/45] hat .......................... 29

23. Buckling loads as functions of hat fiber orientation angle; metal-matrix composite hat-stiffened

panels with three types of face-sheet layups; flat face sheet (d = 0) ........................ 30

24. Buckling temperatures as functions of hat fiber orientation; metal-matrix composite hat-stiffened

panels; flat face sheet (d = 0) ..................................................... 30

V

ABSTRACT

Mechanical and thermal buckling behavior of monolithic and metal-matrix composite hat-stiffened

panels were investigated. The panels have three types of face-sheet geometry: flat face sheet, microdented face sheet, and microbulged face sheet. The metal-matrix composite panels have three types of

face-sheet layups, each of which is combined with various types of hat composite layups. Finite-element

method was used in the eigenvalue extractions for both mechanical and thermal buckling. The thermal

buckling analysis required both eigenvalue and material property iterations. Graphical methods of the

dual iterations are shown. The mechanical and thermal buckling strengths of the hat-stiffened panels with

different face-sheet geometry are compared. It was found that by just microdenting or microbulging of

the face sheet, the axial, shear, and thermal buckling strengths of both types of hat-stiffened panels could

be enhanced considerably. This effect is more conspicuous for the monolithic panels. For the metalmatrix composite panels, the effect of fiber orientations on the panel buckling strengths was investigated

in great detail, and various composite layup combinations offering high panel buckling strengths are

presented. The axial buckling strength of the metal-matrix panel was sensitive to the change of hat fiber

orientation. However, the lateral, shear, and thermal buckling strengths were insensitive to the change of

hat fiber orientation.

A

Ai_ 1, A i

A h

a

b

d

E

Ell

E22

E43

F

X

G

G12

h

JLOC

Li_ 1, L i

MMC

N x

NOMENCLATURE

cross-sectional area of unit strip of hat-stiffened panel, in 2

cross-sectional areas of two adjacent finite elements at node i, in 2

cross-sectional area of hat finite element at juncture of face sheet and hat, in 2

one-half of hat base width, in.

one-half of hat top width, in.

amount of microdent or microbulge of face sheet, in.

Young's modulus of monolithic material, lb/in 2

longitudinal modulus of elasticity of metal-matrix composite lamina, lb/in 2

transverse modulus of elasticity of metal-matrix composite lamina, lb/in 2

quadrilateral combined membrane and bending element

axial compressive load, lb

shear modulus of monolithic material, lb/in 2

shear modulus of metal-matrix composite lamina, lb/in 2

depth of hat-stiffened panel, in.

joint location (node or grid point)

widths of two adjacent finite elements at node i, in.

metal-matrix composite

effective panel load in hat axial direction, lb/in.
Nxy

Ny

n

Pi

P

Qi

Ri

F

SPAR

T

T

a

T r

t c

t s

x, y, z

ZERO

(_11

_12

(_22

AT

e

_x

)_y

_'xy

_r

v

v12

15x

panel shear load, lb/in.

panel load transverse to hat axial direction, lb/in.

integer

axial compressive nodal force at node i, lb

half-width of unit hat strip, in.

lateral compressive nodal force at node i, lb

shear nodal force at node i, lb

radius of circular arc regions of hat corrugation leg, in.

structural performance and resizing finite-element computer program

temperature, °F

assumed temperature for materials, °F

room temperature (70 °F)

thickness of reinforcing hat, in.

thickness of face sheet, in.

rectangular Cartesian coordinates

SPAR program constraint command

coefficient of thermal expansion of monolithic material, in/in-°F

longitudinal coefficient of thermal expansion of metal-matrix composite lamina, in/in-°F

coefficient of thermal shear distortion of metal-matrix composite lamina, in/in-°F

transverse coefficient of thermal expansion of metal-matrix composite lamina, in/in-°F

temperature increase, °F

fiber orientation angle measured from x-axis, degree

eigenvalue at jth iteration

eigenvalue for axial buckling

eigenvalue for lateral buckling

eigenvalue for shear buckling

eigenvalue for thermal buckling

Poisson ratio of monolithic material

Poisson ratio of metal-matrix composite lamina

axial compressive stress distributed over the entire cross-sectional area of the unit strip of hatstiffened panel, lb/in 2
Subscripts

cr

fiat

critical value at buckling

value associated with fiat face sheet case

nth iteration for updating input material properties

INTRODUCTION

Structural panels for hypersonic flight vehicles are subjected to both aerodynamic load (mechanical

load) and aerodynamic heating (thermal load). The thermal load can be quite critical at hypersonic

velocities. Therefore, the hot-structural panels must be designed to maximize the stiffness and, at the

same time, to minimize the thermal expansion-induced problems. Several hot-structural panel concepts

considered and evaluated both theoretically and experimentally in the past include: (1) beaded panels

(ref. 1), (2) tubular panels (refs. 2 and 3) high-temperature alloy honeycomb-core sandwich panels

(refs. 3 through 6), and (4) hat-stiffened panels (refs. 7 through 13).

Recently, the hat-stiffened panels, fabricated with either monolithic titanium alloy or metal-matrix

composites (MMCs) were analyzed and tested extensively to understand their buckling characteristics

under different thermal environments (refs. 7 through 13). The face sheet of the test panels were either

flat or microbeaded (or microdented). The hat-stiffened panels with microbeaded face sheets offer

considerably higher buckling strength compared with the flat face sheet panels. However, further study

on the effect of various structural design parameters will help define an optimum structural configuration

for the hat-stiffened panel concept.

This report deals with the finite-element thermal and mechanical buckling analysis of a unit strip

of hat-stiffened panels fabricated with either monolithic titanium alloy or with MMC. The face-sheet

geometry analyzed is similar in construction to those considered in the past, with either flat or microdented

face sheets. Additionally, hat-stiffened panels with microbulged face sheets are explored. This report

presents the results of an investigation into the effects of both microdenting and microbulging of the face

sheet on the buckling strengths of the hat-stiffened panels. For MMC hat-stiffened panels with flat face

sheets, the effects of composite fiber orientation on the panel buckling strengths are studied, and various

composite layup combinations offering high panel buckling strengths are discussed.

DESCRIPTION OF PROBLEM

Figure 1 shows one of the hat-stiffened panels. The panel face sheet has three types of geometry: flat

face sheet, microdented face sheet, and microbulged face sheet. The panels are fabricated with either

monolithic or MMC material. Figure 2 shows the cross-sectional shapes of the unit strips of the three

types of the hat-stiffened panels. The unit strip has width 2p, depth h, and the face sheet and hat have

thicknesses ts and t c , respectively. The cross-section of the microdent or microbulge of the face sheet is

circular arc in shape with d indicating the degree of microdent or microbulge.

For the MMC panels, three cases of face sheet layups are considered, each of which is combined with

various hat layups (fig. 3). Table 1 lists the MMC layup combinations studied.

3
Table1.MMC layupcombinations.

Face-sheet Hatlayup

layup

[90/0/0/90]

[0/90/90/0]

[45/-45/45/45]

[0/-0/-0/0]

[90/0/0/90]

[0/90/90/0]

In table 1, 0 is the fiber orientationanglemeasuredfrom the x-axis (fig. 3), ranging from 0 to

90 degrees.

The present study uses the finite-element method to analyze the unit strip of hat-stiffened panel:

1. To investigate the effect of microdent and microbulge on the thermal and mechanical buckling

strengths of the monolithic and the MMC hat-stiffened panels.

2. To investigate the effect of composite layups on the thermal and mechanical buckling strengths of

the MMC hat-stiffened panels.

3. To identify the type of MMC layup combination that would give the optimum panel buckling

strength for design of hypersonic vehicles.

FINITE-ELEMENT MODELING

The structural performance and resizing (SPAR) computer program (ref. 14) was used in the finiteelement analysis. For each type of hat-stiffened panel, only one unit strip of the panel was considered

(fig. 4). For axial, lateral, and thermal buckling, one-quarter of the unit strip was modeled, and symmetry

commands were used to generate the whole strip. If the lowest buckling mode was antisymmetrical, then

the antisymmetry command in the SPAR program was used instead of the symmetry command. For shear

buckling, the whole unit strip was modeled because the symmetry and antisymmetry commands could

not be used. Figure 5 shows a typical quarter-strip, finite-element model adjusted for the microbulged

face sheet panel. The model has 1596 joint locations (JLOCs) and 1500 E43 elements (quadrilateral

combined membrane and bending elements). Figure 6 shows a typical whole-strip, finite-element model

adjusted for the microbulged-face sheet panel for shear-buckling analysis. The model has 3040 JLOCs

and 3000 E43 elements.

BOUNDARY CONDITIONS

For all four loading conditions (described as follows), the rotation with respect to the z-axis at every

node of each model was constrained using the SPAR constraint command ZERO 6, where 6 denotes the

conventional 6th degree of freedom. When the commands SYMMETRY PLANE = 1 (yz-plane) and

SYMMETRY PLANE = 2 (xz-plane) were used for the quarter-strip model to generate the mirror images,

the SPAR program automatically imposes internally the constraints ZERO 1, 5 and ZERO 2, 4, respectively, for the yz- and xz-planes of symmetry.

4
Axial Buckling

Axial buckling is buckling in the hat axial direction (i.e., x-direction). Figure 7 shows all the constraint

conditions for the quarter-strip panel for axial buckling. Because the unit hat strip is part of the whole

panel, the closest boundary constraints were chosen to approximate the actual condition of the unit hat

strip, which is surrounded by the rest of the whole panel. Thus, at the ends of the unit strip, constraint

ZERO 3, 5 was imposed at the face sheet and hat flat regions. Along the long edges of the face sheet,

constraint ZERO 2, 4 was imposed to allow the unit strip to deform freely in the z-direction, like the

whole panel.

Lateral Buckling

Lateral buckling is buckling in the direction transverse to the hat axial direction (i.e., y-direction).

Figure 8 shows the constraint commands for lateral buckling. The two long edges of the face sheet are

simply supported (i.e., constraint ZERO 3). This edge condition could give the buckling mode shape

similar to the whole-panel case. At each end of the face sheet and hat flat regions, constraint ZERO 1, 3,

5 was imposed.

Shear Buckling

Figure 9 shows the constraint conditions for shear buckling of the whole unit strip. One long edge is

fixed with constraint ZERO 1, 2, 3, 4; the other with constraint ZERO 2, 3, 4. The ends of the face sheet

are constrained with ZERO 3, 5. The ends of the hat are unconstrained.

Thermal Buckling

Figure 10 shows the constraint conditions for thermal buckling. The long side of the face sheet is

constrained with ZERO 2, 3, 4; the ends of the face sheet and hat flat region with constraint ZERO 1, 3, 5.

APPLIED LOADS

Axial Buckling

For axial buckling, an unit axial compressive load F x = 1 lb was applied. This axial load was distributed over the nodes of the cross-section of the unit strip (i.e., face sheet and hat cross-sections; fig. 11) to

generate an uniform axial compressive stress of

Fx 1

- (1) CYx- A A

where A is the cross-sectional area of the unit strip. The effective panel load N x

defined as

Fx 1

Nx- 2p - 2p

for the unit strip is

(2)

5
The input nodal force Pi at node i of a finite-element model is calculated from

1

Pi = 2 (ai-1 + Ai)(Yx (3)

where AiM and A i are the cross-sectional areas of the two adjacent elements at node i.

If the node i is at the juncture where the face sheet and hat meet, the nodal force Pi is calculated from

1

Pi = _ (Ai-1 + A.t + Ah)_x (4)

where A h is the cross-sectional area of the hat element adjacent to the juncture node i.

If the node i is at the comer of the face sheet, then Pi is calculated from

1

Pi = _ Ai_x (5)

Lateral Buckling

For lateral buckling, the panel lateral compressive load Ny = 1 lb/in, was applied only to the long

edges of the face sheet. The lateral compressive nodal force Qi at node i is then calculated from

1 (6)

Qi = 2 (Li-1 + Li)Ny

where Li_ 1 and L i are the widths of the two adjacent edge elements at node i.

When node i is at the comer of the face sheet, equation (6) becomes

1

Qi : _ LiNy (7)

Shear Buckling

For shear buckling, the panel shear load Nxy = 1 lb/in, was applied at the edges of the face sheet only.

The shear nodal force R i at node i was calculated from

1

R i = _ (Li-1 + Li)Nxy

or

if node i is at the comer of the face sheet.

(8)

1

R i = _ LiNxy (9)

Thermal Buckling

For thermal buckling, the panel was subjected to a uniform temperature field. The uniform nodal

temperature of AT = 1 °F was used as thermal load input to every node of the finite-element models.

6
In calculating buckling temperature ATcr, a problem is that the input material properties, which are

temperature dependent, must correspond to the unknown buckling temperature ATcr + T r, where T r is

room temperature (70 °F). For this reason, one has to assume a temperature T a, and use the material

properties corresponding to T a as inputs to calculate ATcr. This material property iteration process must

continue until the assumed temperature T a approaches the calculated buckling temperature ATcr + T r .

Thus, the thermal buckling solution process requires both eigenvalue and material property iterations.

BUCKLING LOADS AND TEMPERATURES

If _x' _'y' _'xy' and _'T are the lowest eigenvalues for the axial, lateral, shear, and thermal buckling

cases, respectively, then the buckling loads (Nx)cr, (Ny)cr, (Nxy)cr, and the buckling temperature

ATcr associated with the four buckling cases may be obtained by multiplying the respective applied

loads and temperature by the corresponding eigenvalues (i.e., scaling factors) as

)_x 1

( U x) cr = )_xU x = _p ; U x = _pp

(Ny)c r = )_yNy = )_y; Ny = 1

(10)

(11)

(Nxy)cr = _'xyNxy = _xy; Nxy = 1 (12)

ATcr = )_TAT = )_T; AT = 1 (13)

In the eigenvalue extractions that the SPAR program uses, the iterative process consists of a Stodola

matrix iteration procedure, followed by a Rayleigh-Ritz procedure, and finally a second Stodola procedure. This process results in successively refined approximations of m eigenvectors associated with the m

eigenvalues. Reference 14 describes the detail of this process.

NUMERICAL EXAMPLES

Tables 2 and 3 show geometrical dimensions and material properties, respectively, for the monolithic

and the metal-matrix composite hat-stiffened panels.

Table 2. Geometry of

the hat-stiffened panel.

a = 0.64 in.

b = 0.4 in.

d = 0.015 or 0.03 in.

h = 1.25 in.

p = 1.46in.

r = 0.33 in.

t c = 0.032 in.

ts = 0.032 in.
Notethattwo valuesof d were used for the microdented and microbulged face-sheet cases.

Table 3. Temperature-dependent material properties for monolithic titanium (Ti-6A1-4V, ref. 15).

70 OF 200 OF 300 OF 400 OF 500 OF 600 OF 700°F 800 OF 900°F 1000°F

E, lb/in 2 x 106 16.0 15.28 14.80 14.40 14.02 13.63 13.15 12.64 11.84 10.56

G, lb/in 2 x 10 6 6.20 5.83 5.65 5.50 5.37 5.20 5.02 4.82 4.52 4.03

v 0.31 0.31 0.31 0.31 0.31 0.31 0.31 0.31 0.31 0.31

_,in/in-°Fx 10-6 4.85 5.00 5.10 5.19 5.27 5.36 5.44 5.52 5.59 5.62

The data in table 4 were plotted in figure 12 to show the nonlinearity of the temperature-dependent

material property curves.

Table 4. Temperature-dependent material properties

for metal-matrix composite.

70 °F 1200 °F

Ell , lb/in 2 27.72 x 106 23.22 x 106

E22, lb/in 2 18.08 x 106 8.69 x 106

G12, lb/in 2 8.15 x 106 3.5 x 106

V12 0.3 0.3

txll, in/in-°F 2.16x 10 .6 3.21 × 10 .6

o_22, in/in-°F 4.61 x 10.6 6.15 x 10.6

o_12, in/in-°F 0.0 0.0

MATERIAL PROPERTY ITERATIONS

Monolithic Panels

As mentioned earlier, calculations of buckling temperatures require material property iterations.

Figure 13 illustrates the iteration process for calculation of buckling temperatures ATcr for a panel with

a microdented face sheet. The calculated buckling temperature ATcr is plotted against the assumed

temperature T a for the material properties. The 45-degree line represents the solution line for the buckling temperature ATcr. For example, if the assumed material temperature T a agrees with the calculated

buckling temperature ATcr + T r , then the data point of ATcr falls right on the 45-degree line. In the first

iteration, the material properties at, for example, (Ta) 1 = T r = 70 °F was used to calculate the first buckling temperature (ATa)1" The second iteration then uses the material properties at any other temperature,

for example, (Ta) 2 = 300 °F, to update the input material properties to calculate the second buckling

temperature (ATcr)2. In the third iteration, the two data points (ATcr)l and (ATcr) 2 were connected

8
with astraightline to locatetheintersectionpoint with the45-degreeline, andthenthisintersection-point

temperaturewasusedto updatethematerialpropertiesfor calculationof the third bucklingtemperature

(ATcr)3. This iterationprocesscontinuesuntil the nth-calculated buckling temperature (ATcr)n data

point falls fight on the 45-degree solution line.

From the geometry of figure 9, (ATcr) 3 may be expressed as a function of (ATcr) 1 and (ATcr)2 as

(ATcr) l (14)

(ATcr) 3 = (Arcr) 2 - (ATcr)l

1-

(Ta) 2 - (Ta) 1

For the present monolithic material, the (ATcr)3 data point (less than 400 °F) falls practically on the

45-degree solution line, giving an acceptable solution for ATcr (less than 0.5 percent error). That is, the

value of (ATcr)3 calculated from the third material iteration practically agrees with that obtained from

equation (14), because the material property curves (fig. 12) are almost linear in the range 0 < T < 500 °F.

Metal-Matrix Composite Panels

Because of the lack of material data between room temperature and 1200 °F, linear interpolation was

used to find the material properties at any temperature. Figure 14 shows the material property iteration

process for a typical composite panel with [90/0/0/90] flat face sheet and [45/-45/45/45] hat. Similar

to the monolithic case, in the first iteration, the (ATcr)l data point was calculated using the roomtemperature material properties. In calculating (ATcr)2, a new temperature (Ta) 2 = (ATcr)l + (Ta) 1

{where (Ta) 1 = T r }, instead of any temperature on the right-hand side of the 45-degree line, was used to

update the input material properties. Because the coefficients of thermal expansion o_ij increase with

temperature, (ATcr)2 would fall below the 45-degree line. In the third iteration, similar to the monolithic

case, the two data points (ATcr)l and (ATcr)2 were connected with a straight line that intersects the

45-degree solution line. Then, the temperature at the intersection point was used to update the material

properties for the calculations of the third data point (ATcr)3. Because of the linear interpolation of the

material properties, the (ATcr)3 data point falls right on the 45-degree solution line, giving the desired

thermal buckling solution.

The value of (ATcr)3 obtained from the material iteration process may be compared with the value

of (ATcr) 3 calculated from

(ATcr) 1

- (15)

(Arcr)3 (ATcr)2

2

(ATcr) 1

which was established using figure 14.
RESULTS

In the finite-element buckling analysis, the eigenvalue iterations were terminated if the convergence

control criterion [(L j-_j_l)/_j] < 10 -5 was reached. The following subsections present numerical

results of the buckling analysis for the different types of hat-stiffened panels.

Monolithic Panels

Figures 15 through 18, respectively, show the buckled shapes of the three types of monolithic hatstiffened panels under axial compressive, lateral compressive, shear, and thermal loadings. For axial

buckling (fig. 15) and thermal buckling (fig. 18), microbulging of the face sheet increased the number of

buckles more than microdenting of the face sheet. For lateral and shear buckling (figs, 16 and 17), the

buckle number is not affected by microdenting or microbulging.

Table 5 summarizes the mechanical buckling loads and thermal buckling temperatures calculated for

different types of monolithic hat-stiffened panels.

Table 5. Buckling loads and buckling temperatures of monolithic hat-stiffened panels.

Buckling load or

buckling temperature

Face-sheet type

Flat Microdented Microbulged

d 2d d 2d

( Nx)cr, lb/in. 1979.69 2451.33 3563.42 2471.87 3583.46

(Nx)cr/(Nx)cr fiat 1.0 1.2382 1.7999 1.2486 1.8101

(Ny)c r , lb/in. 270.04 269.76 270.50 272.03 275.00

(Ny)cr/(Ny)cr flat 1.0 0.9990 1.0017 1.0074 1.0184

(Nxy)cr, lb/in. 912.43

(Nxy) cr/(Nxy) cr flat 1.0

1208.60 2023.15 1218.87 2073.01

1.3246 2.2173 1.3359 2.2720

ATcr,°F 116.56 188.15 350.48 188.17 352.75

ATcr/ATcr fiat 1.0 1.6142 3.0069 1.6144 3.0263

The data given in table 4 are plotted in figures 19 and 20 for better visualization of the effect of

microdenting or microbulging on the panel buckling strengths. Notice that by microdenting or microbulging the face sheet by an amount slightly less than the face-sheet thickness, the axial and shear buckling

loads {(Nx)cr, (Nxy)cr} and the buckling temperature ATcr could be increased considerably. However,

10
the lateralbuckling load (Ny)c r is practically unaffected by microdenting or microbulging of the face

sheet. The microbulged face-sheet case appears to be slightly more buckling efficient than the microdented

face-sheet case, which may be attributed to the increase in the moment of inertia about the neutral axis. In

actual applications, either the axis of the face-sheet microdent (or microbulge) is parallel to the free stream

(fuselage-panel case) or normal to the freestream direction (wing-panel case), and the degree of aerodynamic heating disturbance that the microdenting (or microbulging) causes remains to be investigated.

Metal-Matrix Composite Panels

The buckled shapes of the MMC hat-stiffened panels are very similar to those of the monolithic cases

and, therefore, are not shown. Table 6 summarizes the mechanical and thermal buckling data for the composite panels with different degrees of face-sheet microdent or microbulge. The composite panels chosen

for this study have [90/0/0/90] face-sheet and [45/-45/-45/45] hat layups.

Table 6. Buckling loads and buckling temperatures of MMC hat-stiffened panels with [90/0/0/90] face

sheet and [45/-45/-45/45] hat.

Buckling load or

buckling temperature

Face-sheet type

Flat Microdented Microbulged

d 2d d 2d

(Nx)cr, 1b/in. 2944.39 3344.24 4337.56 3366.47 4399.88

(Nx)cr/(Nx)cr flat 1.0 1.1358 1.4732 1.1434 1.4943

(Ny)cr, 1b/in. 715.63 738.31 750.73 724.42 726.12

(Ny)cr/(Ny)cr flat 1.0 1.0317 1.0490 1.0123 1.0147

(Nxy)cr, lb/in. 1401.33 1709.09 2702.55 1899.04 3075.62

(Nxy)cr/(Nxy)cr flat 1.0 1.2196 1.9286 1.3552 2.1948

A Tcr, °F 195.18 252.37 413.53 275.96 439.43

ATcr/ATcr flat 1.0 1.2930 2.1187 1.4139 2.2514

The mechanical and thermal buckling data of table 6 are plotted, respectively, in figures 21 and 22 as

functions of the degree of microdent or microbulge d. It is seen that for the composite cases, the benefit of

the microdenting or microbulging of the face sheets in increasing the axial and shear buckling loads

{(Nx)cr , (Nxy)cr}, and the buckling temperatures ATcr, is similar to the case for monolithic panels.

However, the degree of buckling load improvement is slightly lower for the composite panels (cf.,

tables 5 and 6). Again, the microbulging of the face sheet is slightly more effective in improving the

11
panel axial, shear,and thermal buckling strengthsthan microdenting of the face sheet.Like the

monolithic case,the lateral buckling load (Ny)cr is practically unaffectedby either microdentingor

microbulgingof thefacesheet.

Table 7 summarizesthe mechanicaland thermalbuckling solutionsfor the flat-face-sheet,metalmatrixcomposite,hat-stiffenedpanelswith differentlayups.

Table7.Bucklingloadsandbucklingtemperaturesof MMC hat-stiffenedpanelswith flat facesheets.

Face-sheet Hat (Nx)cr, (Ny)cr, (Nxy)cr, ATcr,

layup layups lb/in, lb/in, lb/in. °F

90/0/0/90

0/90/90/0

45/-45/45/45

0/0/0/0 3387.65 722.83 1406.97 189.95

15/- 15/-15/15 3316.96 723.16 1406.41 190.42

30/-30/-30/30 3140.69 723.66 1404.43 192.45

45/-45/-45/45 2944.39 715.63 1401.33 194.97

60/-60/-60/60 2806.54 703.86 1398.01 197.34

75/-75/-75/75 2740.19 696.19 1395.22 198.75

90/-90/-90/90 2721.67 693.88 1394.02 200.00

90/0/0/90 3095.51 728.89 1402.88 195.26

0/90/90/0 3061.76 718.91 1400.85 194.47

0/0/0/0 3462.72 557.09 1072.94 149.71

15/-15/-15/15 3389.76 557.39 1072.64 150.50

30/-30/-30/30 3200.16 558.34 1071.39 152.78

45/-45/-45/45 2991.69 559.90 1069.18 155.70

60/-60/-60/60 2850.15 561.74 1066.61 158.86

75/-75/-75/75 2782.44 563.25 1064.27 161.48

90/-90/-90/90 2764.38 563.83 1063.25 162.57

90/0/0/90 3149.51 566.31 1069.73 155.92

0/90/90/0 3114.00 557.41 1068.56 156.23

0/0/0/0 3662.30 619.45 1256.47 168.36

15/-15/-15/15 3594.30 619.86 1255.68 169.21

30/-30/-30/30 3386.48 621.19 1253.19 171.59

45/-45/-45/45 3169.40 623.37 1249.61 175.11

60/-60/-60/60 3017.60 625.99 1246.06 177.82

75/-75/-75/75 2945.04 628.14 1243.24 179.78

90/-90/-90/90 2938.29 628.97 1242.07 181.06

90/0/0/90 3341.18 632.31 1251.30 175.04

0/90/90/0 3300.32 619.66 1249.77 175.14

12
Figure23showstheaxial,lateral,andshearbucklingloads {(Nx)cr, (Ny)cr, (Nxy)cr}, respectively,

plotted against the hat-fiber orientation angle 0 for the metal-matrix composite, hat-stiffened panels with

flat face sheets having three types of layups. In the figure, two types of hat layups, [90/0/0/90] and [0/90/

90/0] (indicated by 90/0 and 0/90 on the 0 axis, respectively), are added for comparison.

The axial buckling load (Nx)cr decreases with the increase of 0; however, both the lateral and shear

buckling loads {(Nx)cr, (Nxy)cr} are insensitive to the change of 0. Notice that for any hat fiber orientation 0, the panels with [45/-45/-45/45] face sheet have the highest axial buckling strength compared with

the panels having [90/0/0/90] and [0/90/90/0] face sheets. This phenomenon was also observed in the

case of buckling of composite sandwich panels studied by Ko and Jackson earlier (ref. 4).

The buckling strength of the panel depends not only on the longitudinal stiffness but also on the lateral

and shear stiffnesses (ref. 5). For this reason, the [45/-45/-45/45] face sheet turned out to provide higher

axial buckling strength than the other two types of face sheets. For both lateral and shear buckling, panels

with [90/0/0/90] face sheet combined with any hat layup (i.e., 0) ranks at the top among the three facesheet cases studied.

Based on figure 23, the panel with optimum axial-buckling strength is the one with [45/-45/-45/45]

face sheet and [0/0/0/0] hat. However, the [0/0/0/0] unidirectional composite lacks sufficient transverse

tensile strength. For practical purposes, the hat layups in the range of 10 deg < 0 < 30 deg and the [90/0/

0/90] and [0/90/90/0] hats could provide quasi-optimum axial-buckling strength for the panels.

Figure 24 shows the buckling temperature ATcr plotted against the hat fiber orientation angle 0 for

the metal-matrix composite, hat-stiffened panels with flat face sheets having three types of layups. The

panels with [90/0/0/90] face sheet give the highest thermal buckling strength among the three face-sheet

cases. As shown in the figure, ATcr increases slightly with the increase of 0 for any face-sheet layup

(except for 90/0 and 0/90 hat layup cases).

CONCLUDING REMARKS

Thermal and mechanical buckling characteristics of monolithic and metal-matrix composite hatstiffened panels were investigated. The study focused on the effect of face-sheet microdenting and

microbulging on the panel buckling strengths. Also, for the metal-matrix composite panels, the effect of

fiber orientation on the panel buckling strengths was investigated. The key findings of the study are

as follows:

1. Microdenting and microbulging of the face sheet could greatly enhance the axial, shear, and

thermal buckling strengths of the hat-stiffened panels. However, the lateral buckling strength is

not affected by either microdenting or microbulging of the face sheet.

2. Microbulging of the face sheet is slightly more efficient than microdenting of the face sheet in

increasing the panel axial, shear, and thermal buckling strengths.

3. For any hat layup, the composite hat-stiffened panels using [45/-45/-45/45] face sheet have

higher axial-buckling strengths than those using [90/0/0/90] or [0/90/90/0] face sheet.

13
4. For the compositepanelswith any face-sheetlayup, the axial buckling strengthdecreaseswith

theincreaseof the hatfiber orientationangle.However,the lateral,shear,andthermalbuckling

loadsareinsensitiveto thechangeof hatfiberorientation.Thecompositehat-stiffenedpanelswith

[45/-45/-45/45] face sheetcombinedwith [90/0/0/90]hat, [0/90/90/0]hat, or [0/-0/-0/0] hat

(10deg< 0 < 30deg),offer optimumaxial-bucklingstrength.

5. The effectof microdentingor microbulgingon the improvementof buckling strengthsis more

conspicuousfor themonolithichat-stiffenedpanelsthanfor theMMC hat-stiffenedpanels.

Dryden Flight Research Center

National Aeronautics and Space Administration

Edwards, California, April 22, 1996

14
REFERENCES

o

1

°

.

°

o

°

°

°

10.

11.

12.

13.

14.

Siegel, William H., Experimental and Finite Element Investigation of the Buckling Characteristics

of a Beaded Skin Panel for a Hypersonic Aircraft, NASA CR-144863, April 1978.

Ko, William L., John L. Shideler, and Roger A. Fields, Buckling Characteristics of Hypersonic

Aircraft Wing Tubular Panels, NASA TM-87756, December 1986.

Ko, William L. and Raymond H. Jackson, Thermal Behavior of a Titanium Honeycomb-Core

Sandwich Panel, NASA TM-101732, January 1991.

Ko, William L. and Raymond H. Jackson, Compressive and Shear Buckling Analysis of Metal

Matrix Composite Sandwich Panels Under Different Thermal Environments, NASA TM-4492,

June 1993.

Ko, William L., Mechanical and Thermal Buckling Analysis of Rectangular Sandwich Panels Under

Different Edge Conditions, NASA TM-4585, April 1994.

Ko, William L., Predictions of Thermal Buckling Strengths of Hypersonic Aircraft Sandwich Panels

Using Minimum Potential Energy and Finite Element Methods, NASA TM-4643, May 1995.

Percy, Wendy C. and Roger A. Fields, "Buckling of Hot Structures," Eighth National Aero-Space

Plane Symposium, Naval Postgraduate School, Monterey, California, Mar. 26-30, 1990.

Percy, W. and R. Fields, "Buckling Analysis and Test Correlation of Hat Stiffened Panels for

Hypersonic Vehicles," AIAA-90-5219, presented at AIAA 2nd International Aerospace Planes

Conference, Orlando, Florida, Oct. 29-31, 1990.

Teare, Wendy P. and Roger A. Fields, "Buckling Analysis and Test Correlation of High Temperature

Structural Panels," Thermal Structures and Materials for High-Speed Flight, Earl A. Thornton, ed.,

vol. 140, Progress in Astronautics and Aeronautics, AIAA, Washington, DC, 1992, pp. 337-352.

Ko, William L. and Raymond H. Jackson, Compressive Buckling Analysis of Hat-Stiffened Panel,

NASA TM-4310, August 1991.

Hudson, Larry D. and Randolph C. Thompson, Single-Strain-Gage ForceStiffness Buckling Prediction Techniques on a Hat-Stiffened Panel, NASA TM-101733, February 1991.

Thompson, Randolph C. and W. Lance Richards, Thermal-Structural Panel Buckling Tests, NASA

TM- 104243, December 1991.

Ko, William L. and Raymond H. Jackson, Shear Buckling Analysis of a Hat-Stiffened Panel, NASA

TM-4644, November 1994.

Whetstone, W.D., SPAR Structural Analysis System Reference Manual, System Level 13A, vol. 1,

Program Execution, NASA CR- 158970-1, December 1978.

15. MIL-Handbook-5B, Aug. 31, 1973.

15
Figure 1.Hat-stiffenedpanelwith flat,microdented,or microbulgedfacesheet.

16
..dr

I

P

_ a-_

I

t C t s

960420

,_d

960421

Figure 2. Three types of hat-stiffened panels.

960422

17
[e/-el-ele],

[901010190], or

[o/9o/9o/o]_ __

Face sheet

[9o/o/o/9o], / -------_v

[0/90/90/0], or Y

[45/-45/-45/45]

' Z 960221

Figure 3. Composite layups for hat-stiffened panels.

Quarter region modeled for

axial, lateral, thermal buckling

Full region modeled

for shear bucklin(

Figure 4. Unit strip of a hat-stiffened panel.

960423

18
E43 1500

960424

Figure 5. Quarter-unit strip finite-element model; microbulged face sheet.

JLOC 3040

E43 3000

960425

Figure 6. Full-unit strip finite-element model; microbulged face sheet.

19
ZERO 3, 5 F x

ZERO 2, 4

F ZERO 3, 5

Z

Y

ZERO 2, 4

ZERO 1,5

ZERO 6 for all JLOC

Figure 7. Constraint conditions for axial buckling.

960426

ZERO 1,3, 5

ZERO 2, 4

ZERO 1,5

ZERO 6 for all JLOC

Figure 8. Constraint conditions for lateral buckling.

960427

2O
ZERO3,5

ZERO2,3,4

Y

ZERO1,2,3,4

SZERO3,5

ZERO6forallJLOC

Figure 9. Constraint conditions for shear buckling.

960428

AT ZERO 1,3, 5 7

/

ZERO 2,

Z

ZERO 2, 4

ZERO 1,5-

ZERO 6 for all JLOC

Figure 10. Constraint conditions for thermal buckling.

960429

21
Figure 11. Distributions of applied compressive forces.

17 x 106

16

15

14

E,

Ib/in2 13 . E--/ _ _

12

11

10 I I I I I I I I I

0 100 200 300 400 600 700 800

7x 10 -6

500

T,°F

6

5

4

3

2

1

0

900 1000

960431

Figure 12. Temperature-dependent material properties; Ti-6A1-4V titanium alloy.

22
ATcr,

oF

300 O First iteration _ d = 0.015 in.

z_ Second iteration

• Third iteration--_solution LU

(ATcr) 1 Solution

(ATor)3 = (ATor)2. (ATcr)1 line -_

1-

(ma)2- (Ta)l

(Amcr)3

200 (Amcr) 1

100

I

I

' (ATcr)2

IS(Ta)2

I I

0 100 200 300 400

(Ta)l=Tr = 70 Ta, °F 96o432

Figure 13. Iterations of buckling temperatures; monolithic hat-stiffened panel; microdented face sheet.

300 - O First iteration /-- d = 0

Z_ Second iteration

• Third iteration--_solution _ .... /

tAT _ k_J ;5OlUiion /

(ATor) 3 = !_' cr!l line _,

2-_ (ATcr)2 //_Ji '

200 O'"---=----------- _ ......

- (ATor)I ......

ATcr,

oF

100

I_1 /-- (Ta)2 = (ATcr)l + Tr I I I

_100 200 300 400

0(Ta) l=T r = 70" Ta, °F 960433

Figure 14. Iterations of buckling temperatures; metal-matrix composite hat-stiffened panel; [90/0/0/90]

flat face sheet, [45/-45/45/45] hat.

23
Flat --7

j.-Fx

Fx Fx

FS 960434

Figure 15. Buckled shapes of three types of hat-stiffened panels under axial compression; monolithic

panels.

24
s Flat

Ny

nted

Ny C Microbulged

Ny

5

Figure 16. Buckled shapes of three types of hat-stiffened panels under lateral loading; monolithic panels.

25
F Flat

Nxy

F Microdented

Nxy

Microbulged

N

Nxy

960436

Figure 17. Buckled shapes of three types of hat-stiffened panels under shear loading; monolithic panels.

26
Flat

S Microdented

Microbulged /--

60437

Figure 18. Buckled shapes of three types of hat-stiffened panels under uniform temperature loading; four

edges clamped; monolithic panels.

27
Buckling

load,

Ib/in.

4OOO

3500

3000

2500

2000

1500

1000

5OO

+ Dented

--o-- Bulged

- _-_ z- /. J/'/"

_ __CF

/--(Ny)cr

I I I I

0 .01 .02 .03 .04

d, in.

960438

Figure 19. Buckling loads as functions of dent or bulge; monolithic hat-stiffened panels.

ATcr,

oF

400

35O

3OO

250

200

150

100

Dented

--o-- Bulged

{d

5( I I I I

0 .01 .02 .03 .04

d, in.

960439

Figure 20. Increase of buckling temperatures with increase of dent or bulge; monolithic hat-stiffened

panels.

28
4500

4000

3500

3000_

Buckling 2500

load,

Ib/in. 2000

1500

1000 .[

500 l

0

Dented ,_2

- --o- - Bulged 1/7

_--(Nx)cr

/

jf_O

_--(Nxy)cr

.... .._F- (Ny)cr

I I I I

.01 .02 .03 .04

d, in.

960222

Figure 21. Buckling loads as functions of dent or bulge; metal-matrix composite hat-stiffened panels; [90/

0/0/90] face sheet, [45/-45/-45/45] hat.

ATcr,

oF

450 -

400

350

30O

250

2OO

150

Dented p

--o-- Bulged /

d //,,e

I I I I

0 .01 .02 .03 .04

d, in.

960223

Figure 22. Increase of buckling temperatures with increase of dent or bulge; metal-matrix composite hatstiffened panel; [90/0/0/90] face sheet; [45/-45/45/45] hat.

29
4OOO

3OOO

Buckling

load, 2000

Ib/in.

1000

_..._ _z= /- (Nx)cr

....

Face sheet _ .....

_ layup

_ [90/0/0/901

---_-- [0/90/90/0]

-.--_-. - [45/-45/-45/45]

/'-(Nxy)cr

/

....... _.- ....... _,--.-- t--..-_ ........ Z_- ........

/

0 (_ .... -0---- _--0-- 0

_-.--. _ .... __.... _.__-__.__ ..... __.

(Ny)cr

I I I I I

15 30 45 60 75

6, deg

A Z_

o o

o_

I

0 90 90/0

Figure 23. Buckling loads as functions of hat fiber orientation angle; metal-matrix

stiffened panels with three types of face-sheet layups; flat face sheet (d = 0).

I

0/90

960224

composite hat30O

200

ATcr,

oF

100

Face sheet

layup

[90/0/0/90]

---o-- [0190190/0]

-- _.- [45/-45/-45/45]

........ .._ ....... ZX- ....... "_ ....... -¢_ ....... _" ....... "_

..... O- .... -0-- .... O_ .... -0 ..... 0

I I I I I

0 15 30 45 60 75

e, deg

Figure 24. Buckling temperatures as functions of hat fiber orientation;

stiffened panels; flat face sheet (d = 0).

A A

o o

I I

90 90/0 0/90

960225

metal-matrix composite hat30