NASA Technical Memorandum 4644

Shear Buckling Analysis of a Hat-Stiffened Panel

November 1994

William L. Ko and Raymond H. Jackson

NASA Technical Memorandum 4644

National Aeronautics and Space Administration

Office of Management

Scientific and Technical Information Program

1994

William L. Ko and Raymond H. Jackson

Dryden Flight Research CenterEdwards, California

Shear Buckling Analysis of a Hat-Stiffened Panel

ABSTRACT

A buckling analysis was performed on a hat-stiffened panel subjected to shear loading. Both localbuckling and global buckling were analyzed. The global shear buckling load was found to be several timeshigher than the local shear buckling load. The classical shear buckling theory for a flat plate was found tobe useful in predicting the local shear buckling load of the hat-stiffened panel, and the predicted local shearbuckling loads thus obtained compare favorably with the results of finite element analysis.

NOMENCLATURE

cross-sectional area of one corrugation leg,

cross-sectional area of global panel segment bounded by p,

Fourier coefficient of assumed trial function for w (x, y), in.

a length of global panel, in.

b horizontal distance between centers of corrugation and curved region, in.

width of rectangular flat plate segment, in.

c width of global panel, in.

D flexural rigidity of flat plate,

D* flexural stiffness parameter,

transverse shear stiffnesses in

effective bending stiffnesses of equivalent hat-stiffened panel, in-lb

one-half of diagonal region of corrugation leg, in.

modulus of elasticity of hat material,

modulus of elasticity of face sheet material,

lower flat region of hat stiffener, in.

upper flat region of hat stiffener, in.

shear modulus of hat material,

shear modulus of face sheet material,

distance between middle surfaces of hat top flat region and face sheet,

distance between middle surfaces of hat upper and lower flat regions, in.

A A ltc in2 ,=

AA A pts

12--- f 1 f 2–( )tc in

2,+ +=

Amn

b12--- p

12--- f 1 f 2+( )– ,=

bo

DEsts

3

12 1 νs2

–( )------------------------- in-lb,=

DxDy , in-lb

DQx DQy, xz-, yz-planes, lb/in

Dx Dy Dxy, ,

d

Ec lb/in2

Es lb/in2

f 1

f 2

Gc lb/in2

Gs lb/in2

hh hc

12--- tc ts+( ) in.,+=

hc

distance between middle surface of face sheet and centroid of global panel segment, in.

moment of inertia, per unit width, of corrugation leg,

moment of inertia, per unit width, of one-half of reinforcing hat taken with

respect to the neutral axis of the hat stiffened panel,

moment of inertia of corrugation leg of length l taken with respect to its neutralaxis

moment of inertia, per unit width, of corrugation flat region

moment of inertia, per unit width, of face sheet with respect to axis passing

through the centroid of the global panel segment,

moment of inertia, per unit width, of face sheet and corrugation flat region combined,

shear buckling load factor

l length of corrugation leg,

length of one-half of hat,

m number of buckle half-waves in x-direction

panel shear load, lb/in

n number of buckle half-waves in y-direction

p one half of reinforcing hat pitch, in.

shear buckling load, lb

shear flow in flat panel, lb/in

shear flow in hat, lb/in

radius of circular arc segments of corrugation leg, in.

thickness of reinforcing hat, in.

thickness of face sheet, in.

w panel out-of-plane displacement, in.

x, y rectangular Cartesian coordinates, in.

panel twist, 1/in

neutral axis of corrugation leg and face sheet combined

ho

Ic112------tc

3in

4/in,

Ic

ηo in4/in

Ic *

η in4,

I f112------tc

3in

4/in,

Is ηo

Is tsho2 1

12------ts

3in

4/in,+=

Is′112------ ts tc+( )3

in4/in,

kxy

l f 2 2d 2Rθ in.,+ +=

l l l12--- f 1 f 2–( ) in.,+=

Nxy

Qcr

q1

qc

R

tc

ts

∂2w

∂x∂y------------

ηo

2

corrugation angle (angle between the face sheet and the straight diagonal segment of corrugation leg), rad

Poisson ratio of hat material

Poisson ratio of face sheet material

shear stress,

critical value at buckling

INTRODUCTION

Recently, various hot-structural panel concepts were advanced for applications to hypersonic aircraftstructural panels. Among those panels investigated, the hat-stiffened panel (fig. 1) was found to be an ex-cellent candidate for potential application to hypersonic aircraft fuselage panels. This type of panel isequivalent to a corrugated core sandwich panel with one face sheet removed.

Buckling behavior of the hat-stiffened panel under compressive loading in the hat-axial direction, wasinvestigated by Ko and Jackson recently (ref. 1). They calculated both the local and global (general panelinstability) compressive buckling loads for the panel. The calculated local compressive buckling load wasfound to be far lower than the global compressive buckling load, and compared fairly well with the exper-imental data. To fully understand buckling characteristics of the hat-stiffened panel, the shear buckling be-havior of this panel needs to be investigated.

This report presents the local and global buckling analyses of the hat-stiffened panel subjected to shearloading. The predicted shear buckling loads are compared with the finite element shear buckling solutions.

SHEAR BUCKLING ANALYSIS

To analyze the buckling behavior of the complex structure shown in figure 1, two approaches weretaken: (1) local buckling analysis, and (2) global buckling analysis (general panel instability). The follow-ing sections describe these approaches.

Local Buckling

The purpose of local buckling analysis was to study the buckling behavior of a local weak region ofthe panel. This weak region is identified as a rectangular flat plate region bounded by two legs of the re-inforcing hat located at the center of the global panel (left diagram of fig. 2). The analysis looked at thebuckling behavior of this rectangular flat plate (slender strip). Because the reinforcing hat has high flexuralrigidity, the four edges of the rectangular plate were assumed to be simply supported (right diagram offig. 2). From reference 2, the shear buckling stress in the rectangular flat plate may be written as

(1)

θ

νc

νs

τxy lb/in2

( )cr

τxy( )cr

τxy( )cr kxy π2

D

bo2ts

----------=

3

4

Figure 1. Hat-stiffened panel under shear loading.

Figure 2. Shear buckling of hat-stiffened panel analyzed using a simple model.

where is the shear buckling load factor, which is a function of panel aspect ratio . For (a

square panel), ; and for (an infinitely long panel), . For intermediate val-

ues of , may be found from a parabolic curve-fitting equation of the form (ref. 2)

(2)

The curve described by equation (2) is shown on the left in figure 3. The panel shear load for the hat-stiffened strip (left diagram of fig. 2) may be written in terms of shear flows (fig. 4) as (ref. 4)

kxy

bo

a-----

bo

a----- 1=

kxy 9.34=bo

a----- 0= kxy 5.35=

bo

a----- kxy

kxy 5.35 4 bo

a-----

2

+=

Nxy

5

Figure 3. Shear buckling load parameter as a function of panel aspect ratio.

Figure 4. Shear flows in the reinforcing hat and the flat region under the hat.

6

(3)

where and are, respectively, the shear flows in the flat panel and the hat, and are given by (ref. 4)

(4)

and

(5)

where is the panel twist.

From equations (4) and (5), the ratio may be calculated. Then, from equation (3), the panel shearbuckling load of the hat-stiffened strip may be calculated as a function of (eq. (1)).

Global Buckling

In the global buckling analysis (general instability analysis), the complex panel was represented by ahomogeneous anisotropic panel having effective elastic constants. These effective elastic constants mustbe calculated first (ref. 3). This analysis is similar to the conventional buckling analysis of a sandwichpanel with one face sheet removed.

By using the small-deflection theory developed for flat sandwich plates (ref. 5) and solving the shearbuckling problem of the hat-stiffened plate using the Rayleigh-Ritz method of minimizing the total poten-tial energy of a structural system (refs. 5 through 9), the following shear buckling equation is obtained:

(6)

where

(7)

classical thin transverse shear effect termsplate theory

(8)

Nxy q1 qc+=

q1 qc

q1 τxyts 2Gshots ∂2

w∂x∂y------------= =

qc

Gctc p

l-------------- h 2ho

hc

2 p------ f 1 f 2–( )––

∂2w

∂x∂y------------=

∂2w

∂x∂y------------

q1 /qcNxy( )cr τxy( )cr

Mmn

kxy-----------Amn δmnij Aij

j 1=

∞

∑i 1=

∞

∑+ 0=

Mmn132------ ab

D *-------- a

π---

2amn

11 amn12

amn23

amn31

amn21

amn33

–( ) amn13

amn21

amn32

amn22

amn31

–( )+

amn22

amn33

amn23

amn32

–------------------------------------------------------------------------------------------------------------------------+=

δmnijmnij

m2

i2

–( ) n2

j2

–( )---------------------------------------------

m \ i n \ j,=,=

m i = odd,± n j± odd=;≡

7

and are the undetermined Fourier coefficients of the assumed out-of-plane displacement w (x, y) ofthe plate given by

(9)

Lastly, the shear buckling load factor appearing in equation (6) and the coefficients of characteristicequation = 1, 2, 3) appearing in equation (7) are defined, respectively, as (ref. 7)

(10)

(11)

(12)

(13)

(14)

(15)

(16)

where the flexural stiffness parameter D* and the flexural rigidities of the effective panel aredefined as

(17)

where

(18)

Amn

w x y,( ) Amnmπx

a----------- nπy

c---------sinsin

n=1

∞

∑m=1

∞

∑=

kxyamn

rsr s,(

kxy

Nxy( )cra2

π2D*

------------------------=

amn11

Dx mπa

------- 4

Dxνyx Dyνxy 2Dxy++( ) mπa

------- 2 nπ

c------

2Dy

nπc

------ 4

+ +=

amn12

amn21

Dx mπa

------- 3 1

2--- Dxνyx D+ yνxy 2Dxy+( )

mπa

-------

nπc

------ 2

+–= =

amn13

amn31

Dy nπc

------ 3 1

2--- Dxνyx D+ yνxy 2Dxy+( )

mπa

------- 2 nπ

c------

+–= =

amn22

Dx mπa

------- 2 Dxy

2---------

nπc

------ +

2DQx+=

amn23

amn32 1

2--- Dxνyx Dyνxy Dxy++( )

mπa

-------

nπc

------ = =

amn33

Dy nπc

------ 2 Dxy

2---------

mπa

------- +

2DQy+=

Dx Dy,

D*

DxDy Dx,Dx

1 νs2–

-------------- Dy,Dy

1 νs2–

--------------= = =

Dx EcI c EsIs Dy,+ EsIs

1EcI cEsIs------------+

1 1 νs2–( )

EcI cEsIs------------+

------------------------------------------= =

8

Figure 5. Segment of hat-stiffened flat panel.

where

(19)

and is the moment of inertia, per unit width, taken with respect to the panel neutral axis (fig. 5),and is given by

(20)

Is tsho2 1

12------ts

3+=

I c ηo

I cIc *

p------

Ap--- 1

2--- hc tc ts+ +( ) ho–

2 124 p--------- f 1 f 2–( )tc

3f 1 f 2–

2 p-----------------tc ho

tc ts+

2--------------–

2

+++=

9

where is the moment of inertia of a corrugation leg of length l, taken with respect to its neutral axis (fig. 5), and is given by

(21)

and appearing in equation (19) is the distance between the middle surface of the face sheet and the panelneutral axis given by

(22)

The twisting stiffness appearing in the expressions of (eqs. (11) through (16)) may be obtainedfrom reference 4 with slight modification to fit the present problem in the following form:

(23)

where is the torsional stiffness given by

(24)

where

(25)

and

(26)

(27)

The shear stiffnesses and appearing in equations (14) and (16) are given by

(28)

Ic * η

Ic * hc

3tc14---

f 2

hc----- 1

13---

tc2

hc2

-----+ 2

3---d3

hc3

----- sin2 θ 14---

tc2

d2----- cos2θ+

+

=

Rhc-----

θ2---

R2

hc2

------ θ 1 θcos–( ) Rhc----- 2 3

Rhc-----–

– θ θsin–( )sin–

+

hoηo

ho1

2A------- A hc tc ts+ +( ) 1

2---tc f 1 f 2–( ) tc ts+( )+=

Dxy amnrs

Dxy 2GJ=

GJ

GJ GstskGJ2

pGctc2

Ac--------------- k

GJkc–( )2+ h

2=

kGJ

kc

1AcGsts

pGctc----------------+

--------------------------=

kc12--- 1

f 1 f 2–( )hc

2 ph----------------------------–=

Ac l12--- f 1 f 2–( )+ tc l tc= =

DQx DQy

DQx

Gctch2

pl---------------- DQy, Sh

Ec

1 νc2–

-------------- tc

hc-----

3= =

10

where the nondimensional coefficient is defined as

(29)

where the nondimensional parameters and are defined as

(30)

(31)

(32)

where

(33)

The shear buckling equation (6) yields a set of homogeneous equations associated with different values ofm and n. This set of equations may be divided into two groups that are independent of each other: onegroup in which m ± n is odd (that is, antisymmetrical buckling), and the other in which m ± n is even (that

S

S

6hc

p-----Dz

Fts

tc---

phc-----

2+

12 hhc----- p

hc-----Dz

F 2phc-----

2Dz

H–hc

h----- 6

ts

tc--- Dz

FDyH Dz

H2–( ) phc-----

3Dy

H++

------------------------------------------------------------------------------------------------------------------------------------------------------------=

DzF, Dz

H, DyH

DzF 2

3--- d

hc-----

3 cos2 θ 2

3---

Ic

I f-----

18---

phc-----

3

bhc-----

3–+=

Rhc----- 2

bhc-----

2 θ 4

Rb

hc2

-------– 1 – cos θ( ) Rhc-----

2θ θsin θcos–( )++

Ic

hc2tc

--------- 2dhc-----sin2 θ R

hc----- θ θsin θcos–( )++

DzH 2

3---

dhc-----

3θ csin osθ 1

2---

Ic

I f-----

14---

phc-----

2 bhc-----

2–+=

Rhc-----

bhc-----

θ 2Rb

hc2

------- θ θsin–( )–Rhc----- 1 – cos θ( ) 1 R

hc----- 1 – cos θ( )––

+

Ic

hc2tc

--------- 2dhc----- sinθ θ R

hc-----+cos sin2 θ

–

DyH 2

3---

dhc-----

3 sin2θ 1

2---

Rhc-----θ 1

2--- f

hc-----

Ic

I f-----+

+=

Rhc-----

2 2 3

Rhc-----–

θ θsin–( ) Rhc----- θ 1 θcos–( )sin+–

Ic

hc2tc

--------- fhc-----

tc

t f---- 2

dhc-----cos2 θ R

hc----- θ θ cos sin θ+( )+ ++

f12--- f 1 f 2+( ) b, 1

2--- p

12--- f 1 f 2+( )– Ic, 1

12------tc

3 I f, 1

12------ts

3= = = =

11

is, symmetrical buckling) (refs. 7 and 9). Those equations may be written for as many half-wave numbersas required for convergence of eigenvalue solutions. For the deflection coefficients to have valuesother than zero, the determinant of the coefficients of the unknown of the simultaneous homogeneousequations must vanish. The largest eigenvalue thus obtained will give the lowest value of .

Representative 12 12 determinants in terms of the coefficients of homogeneous simultaneousequations written out from equation (6) for which m ± n is even and odd are given in the following(refs. 10 and 11):

For m ± n = even (symmetrical buckling):

(34)

where the nonzero off-diagonal terms satisfy the conditions m =\ i , n =\ j, m ± i = odd, and n ± j = odd.

m=1, n=1 0 0 0 0 0 0 0

m=1, n=3 0 0 0 0 0 0

m=2, n=2 0 0 0

m=3, n=1 0 0 0 0 0

m=1, n=5 0 0 0 0

m=2, n=4 0 0 = 0

m=3, n=3 Symmetry 0 0 0

m=4, n=2 0

m=5, n=1 0 0

m=3, n=5 0

m=4, n=4

m=5, n=3

Amn

Amn1kxy------- kxy

×

m n\, i j,A11 A13 A22 A31 A15 A24 A33 A42 A51 A35 A44 A53

M11

kxy---------- 4

9--- 8

45------ 8

45------ 16

225---------

M13

kxy----------

45---– 8

7---

825------–

1635------

M22

kxy----------

45---–

2063-------–

3625------

2063------–

47--- 4

7---

M31

kxy----------

825------–

87--- 16

35------

M15

kxy----------

4027------–

863------–

1627------–

M24

kxy----------

7235------–

863------–

83---

120147---------–

M33

kxy----------

7235------–

14449---------

M42

kxy----------

4027------–

120147---------–

83---

M51

kxy----------

1627------–

M35

kxy----------

8021------–

M44

kxy----------

8021------–

M53

kxy----------

12

For m ± n = odd (antisymmetrical buckling):

(35)

where the nonzero off-diagonal terms satisfy the conditions m =\ i , n =\ j, m ± i = odd, and n ± j = odd.

Notice that the diagonal terms in equations (34) and (35) came from the first term of equation (6), andthe series term of equation (6) gives the off-diagonal terms of the matrices. The 12 12 determinant wasfound to give sufficiently accurate eigenvalue solutions.

m=1, n=2 0 0 0 0 0

m=2, n=1 0 0 0 0 0

m=1, n=4 0 0 0 0

m=2, n=3 0 0 0 0

m=3, n=2 0 0 0

m=4, n=1 0 0 0 = 0

m=1, n=6 Symmetry 0 0

m=2, n=5 0 0

m=3, n=4 0

m=4, n=3 0

m=5, n=2

m=6, n=1

m n\, i j,A12 A21 A14 A23 A32 A41 A16 A25 A34 A43 A52 A61

M12

kxy----------

49---– 4

5---

845------–

2063------ 8

25------

435------–

M21

kxy----------

845------– 4

5---

435------–

825------ 20

63------

M14

kxy----------

87---–

16225---------–

4027------

1635------–

8175---------–

M23

kxy----------

3625------–

49---–

7235------

47---–

M32

kxy----------

87---–

47---–

7235------

49---–

M41

kxy----------

8175---------–

1635------–

4027------

M16

kxy----------

2011------–

845------–

361225------------–

M25

kxy----------

83---–

100441---------–

M34

kxy----------

14449---------–

845------–

M43

kxy----------

83---–

M52

kxy----------

2011------–

M61

kxy----------

×

13

NUMERICAL RESULTS

The titanium hat-stiffened panel has the following material properties and geometries:

Local Buckling

For and equation (2) gives The shear buckling stress may then be calculated from equation (1) as

(36)

From equations (4) and (5) the ratio of / has the value

(37)

Thus, from equation (3), the panel shear buckling load may be calculated as

(38)

(39)

(40)

which gives the shear buckling load of

=

=

=

=

=

=

=

=

=

=

=

=

=

=

=

Es Ec 6.2 106 lb/in

2×=

Gs Gc 6.2 106 lb/in

2×=

νs νc 0.31=

a 24 in.

bo 1.77 in. (width of rectangular flat strip)

c 24 in.

d 0.3505 in.

f 1 1.12 in.

f 2 0.26 in.

h hc12--- tc ts+( )+ 1.2180 in.=

hc 1.1860 in.

p 1.49 in.

R 0.346 in.

ts tc 0.032 in.=

θ 79.13° 1.3811 rad=

a 24 in.= bo 1.77 in.,= kxy 5.37 .=τxy( )cr

τxy( )cr 25 553 lb/in2,=

q1 qc

q1

qc----- 3.4727=

Nxy( )cr

Nxy( )cr q1 1qc

q1-----+

=

τxy( )cr ts 1 13.4727----------------+

=

1 054 lb/in,=

Qcr 25 296 lb.,=

14

Figure 6. Buckling shape of hat-stiffened panel under shear loading (finite element analysis byW. Percy, Mc-Donnell-Douglas; full-panel model).

This local shear buckling load prediction is slightly higher than the value calcu-lated from finite element buckling analysis carried out by W. Percy of McDonnell-Douglas.* Figure 6shows the shear buckling shape of the hat-stiffened panel based on Percy’s full-panel finite element model.Clearly, the panel is under local buckling rather than general instability. The local buckling analysis pre-dicts a slightly higher value of because the four edges of the rectangular plate strip analyzed wereassumed to be simply supported. In reality, those four edges are elastically supported.

Global Buckling

To find the order of the determinant (review eqs. (34) and (35)) for converged eigenvalue solutions,several different orders of the determinants were used for the calculations of . The eigenvalues werefound to have sufficiently converged beyond order 10. In the actual calculations of , the orders of thedeterminants were taken to be 12, which were shown in equations (34) and (35). The eigenvalue solutionsthus obtained give the following lowest values of

m ± n = even: (41)

m ± n = odd: (42)

Thus, the square panel will buckle symmetrically. Using = 1.89, the panel shear buckling load may be calculated from equation (10) as

*Personal communication with author.

Nxy( )cr 900 lb/in=

Nxy( )cr

kxykxy

kxy :

kxy 1.89=

kxy 1.93=

kxy Nxy( )cr

15

(43)

which gives the shear buckling load of this is about four times higher than the localshear buckling load of Thus, the panel is unlikely to fail under global buckling.

Summary of Data

The results of the shear buckling analysis of the hat-stiffened panel are summarized in the followingtable.

CONCLUSION

The shear buckling behavior of a hat-stiffened panel was analyzed in light of local buckling and globalbuckling. The predicted local buckling loads were slightly higher than those predicted using finite elementbuckling analysis. The global buckling theory predicted a buckling load about four times higher than waspredicted from local buckling theory. Therefore, the hat-stiffened panel will buckle locally instead ofglobally.

REFERENCES

1. Ko, William L. and Raymond H. Jackson, Compressive Buckling Analysis of Hat-Stiffened Panel,NASA TM-4310, Aug. 1991.

2. Timoshenko, Stephen P. and James M. Gere, Theory of Elastic Stability, McGraw-Hill Book Co., NewYork, 1961.

3. Ko, W. L., “Elastic Stability of Superplastically Formed/Diffusion Bonded Orthogonally CorrugatedCore Sandwich Plates,” AIAA 80-0683, presented at the AIAA/ASME/ASCE/AHS/AHC 21st Struc-tures, Structural Dynamics, and Materials Conference, Seattle, WA, May 12–14, 1980.

4. Libove, Charles and Ralph E. Hubka, Elastic Constants for Corrugated-Core Sandwich Plates,NACA TN-2289, 1951.

5. Libove, C. and S. B. Batdorf, A General Small-Deflection Theory for Flat Sandwich Plates, NACATN-1526, 1948.

6. Bert, Charles W. and K. N. Cho, “Uniaxial Compressive and Shear Buckling in Orthotropic SandwichPlates by Improved Theory,” AIAA 86-0977, presented at the AIAA/ASME/ASCE/AHC 27th Struc-tures, Structural Dynamics, and Materials Conference, San Antonio, TX, May 19–21, 1986.

7. Ko, William L. and Raymond H. Jackson, Combined Compressive and Shear Buckling Analysis of Hy-personic Aircraft Structural Sandwich Panels, NASA TM-4290. Also AIAA 92-2487-CP, presented

Comparison of shear buckling loads.

,

Case lb/in lb

Local buckling 1,054 25,296

Global buckling 4,296 103,107

W. Percy’s finite element (footnote, p. 15)

900 21,600

Nxy( )cr 4 296 lb/in,=

Qcr 103 107 lb;,=Qcr 25 296 lb.,=

τxy( )cr, Qcr

16

at the AIAA/ASME/ASCE/AHS/ASC 33rd Structures, Structural Dynamics, and Materials Confer-ence, Dallas, TX, Apr. 13–15, 1992.

8. Ko, William L. and Raymond H. Jackson, Combined Load Buckling Behavior of Metal-Matrix Com-posite Sandwich Panels Under Different Thermal Environments, NASA TM-4321, Sept. 1991.

9. Ko, William L. and Raymond H. Jackson, Compressive and Shear Buckling Analysis of Metal-MatrixComposite Sandwich Panels Under Different Thermal Environments, NASA TM-4492, June 1993.Originally prepared for the 7th International Conference on Composite Structures, University of Pais-ley, Paisley, Scotland, July 1993.

10. Stein, Manuel and John Neff, Buckling Stresses of Simply Supported Rectangular Flat Plates in Shear,NACA TN-1222, 1947.

11. Batdorf, S. B. and Manuel Stein, Critical Combinations of Shear and Direct Stress for Simply Sup-ported Rectangular Flat Plates, NACA TN-1223, 1947.

17

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Shear Buckling Analysis of a Hat-Stiffened Panel

WU 505-63-40

William L. Ko and Raymond H. Jackson

NASA Dryden Flight Research CenterP.O. Box 273Edwards, CA 93523-0273

H-2019

National Aeronautics and Space AdministrationWashington, DC 20546-0001 NASA TM-4644

A buckling analysis was performed on a hat-stiffened panel subjected to shear loading. Both localbuckling and global buckling were analyzed. The global shear buckling load was found to be severaltimes higher than the local shear buckling load. The classical shear buckling theory for a flat plate wasfound to be useful in predicting the local shear buckling load of the hat-stiffened panel, and the predict-ed local shear buckling loads thus obtained compare favorably with the results of finite elementanalysis.

Hat-stiffened panel; Global buckling; Local buckling; Minimum energy method; Shear buckling

A03

20

Unclassified Unclassified Unclassified Unlimited

November 1994 Technical Memorandum

Available from the NASA Center for AeroSpace Information, 800 Elkridge Landing Road, Linthicum Heights, MD 21090; (301)621-0390