NASA Technical Memorandum 110309

Evaluation of a Composite Sandwich 

Fuselage Side Panel With Damage and 

Subjected to Internal Pressure

Marshall Rouse and Damodar R. Ambur

Langley Research Center, Hampton, Virginia

Jerry Bodine and Bernhard Dopker

Boeing Commercial Aircraft Company, Seattle, Washington

February 1997

National Aeronautics and

Space Administration

Langley Research Center

Hampton, Virginia 23681-0001
1

Evaluation of a Composite Sandwich Fuselage Side Panel With Damage

and Subjected to Internal Pressure

Marshall Rouse and Damodar R. Ambur

NASA Langley Research Center

Hampton, VA 23681-2331

Jerry Bodine and Bernhard Dopker

Boeing Commercial Aircraft Company

Seattle, WA

Abstract

The results from an experimental and analytical study of a composite sandwich

fuselage side panel for a transport aircraft are presented. The panel has two window

cutouts and three frames, and has been evaluated with internal pressure loads that

generete biaxial tension loading conditions. Design limit load and design ultimate

load tests have been performed on the graphite-epoxy sandwich panel with the middle

frame removed to demonstrate the suitability of this two-frame design for supporting

the prescribed biaxial loading conditions with twice the initial frame spacing of 20

inches. The two-frame panel was damaged by cutting a notch that originates at the

edge of a cutout and extends in the panel hoop direction through the window-belt

area. This panel with a notch was tested in a combined-load condition to demonstrate

the structural damage tolerance at the design limit load condition. The two panel

configurations successfully satisfied all desired load requirements in the experimental

part of the study, and the three-frame and two-frame panel responses are fully

explained by the analysis results. The results of this study suggest that there is

potential for using sandwich structural concepts with greater than the usual 20-in.-wide

frame spacing to further reduce aircraft fuselage structural weight.

Introduction

The potential for cost and weight reduction offered by composite-facesheet

sandwich structures in aircraft fuselage side panels is currently being investigated in

the NASA Advanced Composite Technology Program. Structural trade studies for

sandwich concepts that use advanced material placement methods, such as tow

placement for skin and three-dimensional braiding for frames, have identified a 25

percent cost and weight reduction compared to conventional integrally-stiffened

metallic structures (Ref. 1). Sandwich structures offer additional potential for weight

reduction by decreasing the number of frames by increasing the fuselage frame

spacing. Sandwich structures are good candidates for implementing greater frame
2

spacing than the usual 20 to 22 in. frame spacing since skin panels for these

structures have much higher bending stiffnesses than the more conventional stringerframe stiffened skins with minimum gauge thicknesses. The sandwich panel

described in the present paper has been designed to generate preliminary

performance information for sandwich structures with twice the usual fuselage frame

spacing.

The design studies for the curved panel described in the present paper utilized

existing tension fracture data for flat sandwich panels which could result in

conservative structural designs. Understanding the response of undamaged and

damaged sandwich structures when they are subjected to combined loading

conditions that are representative of the actual operating flight environment is an

important aspect of designing aircraft structures. Very limited information currently

exists for curved composite sandwich panels with damage at critical locations and

subjected to combined loading conditions. To understand better the structural

behavior of a sandwich fuselage side panel with windows and with damage at a highly

stressed location, biaxial tension tests have been performed by subjecting the

damaged panel to internal-pressure loading conditions.

Finite element analyses have been performed on the sandwich panel in the test

machine and subjected to different test loading conditions. Inplane stress and strain

results for an infinite composite flat plate with an elliptical cutout are compared with

finite element analysis results to help explain the stress gradients along the cutout in

the panel. The finite element analysis results are compared with experimental results

for corresponding loading conditions. The present paper discusses the experimental

results and their correlation with the analysis results.

Test panel and test description

The sandwich fuselage panel considered in the present study has three frames

and has overall dimensions of a 122-in. radius, a 72-in. length, and a 63-in. arc width.

The panel has two window cutouts, one located midway between the center frame and

each of the outer frames. The elliptical window cutouts are 19.92-in.-long in the

fuselage circumferential direction and 15.30-in.-long in the fuselage longitudinal

direction. The sandwich panel facesheets were fabricated from Hercules, Inc.

AS4/8552 graphite-epoxy material and the core is made of a Hexcel Korex

honeycomb material. The facesheet utilizes tow-placed inner plies and fabric outer

layers. The fuselage frames and window frames were fabricated from fiber preforms

consisting of triaxially braided AS4 graphite fibers impregnated with 3M Company

PR500 epoxy resin and cured by using a Resin Transfer Molding (RTM) process. The

sandwich skin and the precured frames are cocured in a single stage. Typical material

properties for the tow placed, fabric, and triaxially braided AS4/8552 and AS4/PR500

graphite-epoxy material systems are presented in Table 1. Typical construction details

of the test panel are shown in Figure 1. The cross-sectional view illustrates details of

the panel in the window region. The sandwich core is contoured on both the concave

and convex sides of the panel to accommodate ±45° plies added to the 8-ply-thick
3

facesheet near the window region. When cured, the sandwich panel has a constant

inner and outer mold line radius resulting in a uniform total thickness throughout the

skin. Graphite-epoxy doublers fabricated from preimpregnated fabric were cocured

with the curved and flat edges of the panel to introduce the axial and hoop loads into

the panel skin. A photograph of the finished test panel is shown in Figure 2.

To evaluate the sandwich panel design, several tests were performed on the

undamaged panel prior to inflicting damage in the form of a notch and re-evaluating

the panel response using a pressure-box test machine described in Reference 1. In

the undamaged condition, the panel was subjected to an axial load of 2,450 lb/in. with

no internal pressure; a pressure only condition of 18.2 psi; and a combined load

condition with 13.65 psi of internal pressure and 2,450 lb/in. of axial tension. The

undamaged test conditions were also applied to the panel with its center frame

removed to gather preliminary structural performance information on a panel with

twice the initial frame spacing. A notch was then cut along the hoop direction starting

at the window and extending through the window frame and the skin, and the panel

was loaded to the design limit load condition of 8.85 psi of internal pressure and 1,630

lb/in. of axial tension. The panel was instrumented with electrical resistance strain

gages to record strains and with displacement transducers to monitor panel

displacements.

Finite element model

The finite element model of the panel in the pressure-box test machine is shown

in Figure 3. The sandwich panel is modeled using the ABAQUS finite element

analysis program (Ref. 2) with 4-node isoparametric elements for the facesheets and

three 8-node solid elements through-the-thickness to represent the honeycomb core. 

The ply drop-offs in the facesheets are discretely modeled to represent the thickness

changes appropriately. The circumferential frames and the window frames are also

modeled using the 4-node shell elements. The window glazing is also modeled using

shell elements. Only reaction forces along the edges perpendicular to the window

glazing are transmitted to the window frame. It is assumed that no inplane forces are

transmitted to the panel.

The hoop and axial load introduction plates of the test fixture are modeled with

shell elements. Since symmetry boundary conditions are assumed at the axial and

hoop centerlines, only a quarter of the structure is modeled and analyzed. Along the

sandwich panel hoop direction, the test fixture hoop-load-reaction turnbuckles for the

skin and frames are represented with the appropriate length and stiffnesses to model

the panel boundary conditions properly. Axial load is applied to the beams

representing the hydraulic actuators attached to the axial load introduction plate. The

quarter model of the test panel in the pressure box has a total of 5,343 elements and

approximately 26,650 degrees of freedom. Geometric nonlinear analyses have been

performed for all load cases considered in the present paper.
4

Results and Discussion

The sandwich panel was modeled with the pressure-box test machine and was

analyzed for critical loading conditions to determine the panel response both with and

without damage. Some of the analytical results are compared with the experimental

results in this section.

Undamaged panel results

 2,450 lb/in. axial loading condition 

The test panel was first analyzed for the 2,450 lb/in. ultimate loading condition

for the axial loading condition. The inner and outer surface hoop strain contours

obtained from the finite element analysis for this loading condition are presented in

Figure 4. The influence of boundary conditions on the induced strain state in the panel

can be seen in this figure. The abrupt variation in the strain state away from the edge

of the elliptical cutout along its major axis is representative of the reduced hoop

stiffness in the outer region of the panel. The maximum hoop strain corresponding to

this loading condition is 1,580 μin./in. and occurs on the panel inner surface at two

locations along the edge of the window cutout at approximately 50° and 130° from the

longitudinal axis of symmetry for the panel. The axial strain contours on the inner and

outer surfaces of the panel are presented in Figure 5. A maximum axial strain of

approximately 3,840 μin./in. occurs at the 90° location along the window cutout on the

panel outer surface. The analytically determined hoop and axial strain profiles around

the elliptical cutout for an infinite flat plate made with the same ply stacking sequence

are presented in Figure 6. These results are from a closed-form analysis method that

utilizes a linear elastic solution and the method of superposition (Ref. 3) to determine

the stresses and strains around the cutout. The hoop and axial strain results from this

closed-from analysis are presented in Figure 6. These strain profiles compare very

well with the panel outer surface strains along the window cutout obtained from the

finite element analysis. The corresponding hoop and axial stress concentration

factors, which are ratios of the stress magnitude at a given location along the cutout

normalized by the far field stress, are plotted in Figure 6(b). The maximum value for the

axial stress concentration factor is 3.57. The strain results from the test are presented

in Figure 7(a) and 7(b). These strain values are measured at the locations along the

edge of the window cutout indicated in Figure 7(c). The maximum experimental hoop

and axial strains are 1,600 μin/in. and 4,000 μin./in., respectively, and compare very

well with the finite element analysis results. Local bending of the inner facesheet at

the edge of the hole at the 90° location seems to have influenced the hoop and axial

strain distribution as indicated in both the analytical and experimental results. For this

reason, discussions of strain results for the other loading conditions are limited only to

the panel outer facesheet.
5

 Combined 18.2 psi internal pressure and 1,110 lb/in. axial loading condition 

This loading condition corresponds to twice the design limit pressure condition

of 9 psi of internal pressure and a 1,110 lb/in. load in the panel axial direction. The

outer surface hoop and axial strain variations along the elliptical hole edge obtained

from the finite element analysis for this loading condition are presented in Figure 8.

These results are compared with the analysis results presented in Figure 9 for a flat

plate with an elliptical cutout. The hoop strain has a small negative value at the edge

of the elliptical cutout near the major axis and the largest positive value along a radial

line which is inclined at approximately 45° to the major axis. The axial strain results in

Figure 9(a) indicate a large positive strain value at the edge of the elliptical cutout at

the ellipse major axis and a small negative value at the boundary of the cutout at its

minor axis. The finite element analysis results in Figure 8(b) are consistent with these

results. The analytical stress concentration factor results presented in Figure 9(b) for

an infinite flat plate suggest that the axial stress concentration factor is 3.01 for this

loading condition.

The experimental strain results for this loading condition are presented in

Figure 10. For the outer surface, the measured axial strain values at the minor axis is

-1,000 μin/in. and the value at the major axis is 2,200 μin./in. The finite element

analysis results at the corresponding locations are -662 μin./in. and 1,420 μin./in.,

respectively.

 Combined 13.65 psi internal pressure and 2,450 lb/in. axial loading condition 

This test condition corresponds to the design ultimate loading condition with

13.65 psi of internal pressure and 2,450 lb/in. of axial loading. The outer surface hoop

and axial strain results from the finite element analysis are presented in Figure 11.

The strain contours along the edge of the cutout agree well with the analytical results

presented in Figure 12(a). These analytical results suggest that the hoop strain has a

small negative value along the cutout boundary at the ellipse major axis and changes

to a positive value at the ellipse minor axis. The axial strains are positive at the major

axis and negative at the minor axis. The stress concentration factors from the infinite

flat plate analysis are presented in Figure 12(b). For this loading condition, which has

high tensile forces in both the panel axial and hoop directions, the stress concentration

factors are 2.88 and 2.05 for the hoop and axial stresses, respectively, at the edge of

the cutout. The hoop and axial strain distributions from the experiment are presented

in Figure 13. The trends of the experimental results agree extremely well with the finite

element analysis results. The experimentally measured strains on the panel outer

surface in the hoop direction vary from 1,150 μin./in. to -900 μin./in. compared to the

finite element analysis results which vary from 937 μin./in. to -949 μin./in. In the axial

direction, the measured strains vary from 4,000 μin./in. to -775 μin./in. The

corresponding results from the finite element analysis vary from 3,540 μin./in. to -815

μin./in.
6

Neither of the above loading conditions resulted in strain magnitudes that

exceed the strain allowables for the material systems used for manufacturing the test

panel. There were no other indications from the experiment that suggested test panel

failure. Further testing was conducted and it was assumed that the panel was in the

pristine condition at the end of all the previous tests. 

Results for the panel with the center frame removed

The next set of loading conditions was imposed on the panel with the center

frame removed. The objective of these tests was to gather preliminary information on

the sandwich panel response with an increased frame spacing of 40.0 inches. The

frame was removed by severing the frame web above the frame attachment flange at

the skin. The finite element analysis and experimental results corresponding to two

load conditions for this panel configuration are presented below.

 Combined 18.2 psi internal pressure and 1,110 lb/in. axial loading condition 

The finite element analysis results for this loading condition are presented in

Figure 14. The hoop and axial surface strains are presented in the figure for the outer

facesheet. The test was conducted by redistributing the loads in the severed frame to

the remaining two frames to ensure that the panel is evaluated for the same load ratio

of 80 and 20 percent of the load in the skin and the frames, respectively, for a given

loading condition. The frame load for the panel with two-frame configuration is greater

than that for the frame load for the panel with the three-frame configuration. This

increase in frame load is indicated by comparing of results for the two-frame panel

presented in Figure 14 with the results for the three-frame panel in Figure 4. The hoop

strain in the remaining two frames increases by approximately 25 percent and the

hoop strain in the skin between the two cutouts increases by approximately 12 percent

due to the severing of the center frame. This increase in skin hoop strain is due to

bending of the unsupported skin between the cutouts. The axial strain results from the

finite element analysis for the inner facesheet are presented in Figure 15(a). Bending

of the skin between the frames is also present for the inner and outer facesheet hoop

strain contours. The experimental axial strain results for this panel are presented in

Figure 15(b). The outer facesheet hoop strains from the experiment vary from

approximately -400 μin./in. to 2,200 μin./in. compared to the finite element results

which vary from -770 μin./in. to 2,100 μin./in. Bending of the skin between the two

cutouts can be noticed in Figure 15(b) and is indicated by the differences in the

experimental hoop strains for the inner and outer panel surfaces at θ =0. The axial

strain results for this panel configuration corresponding to this loading condition are

very similar to those for the panel with a three-frame configuration.

 Combined 13.65 psi internal pressure and 2,450 lb/in. axial loading condition 

The panel outer surface hoop and axial strain results from finite element

analysis are presented in Figure 16 for this loading condition. The overall

observations for the axial and hoop strains for this loading condition are very similar to
7

the previous loading condition for the two-frame panel. The experimental strain results

for the two-frame panel are compared with the three-frame panel results in Figure 17.

The maximum experimental axial strain along the cutout for the two-frame panel varies

from -850 μ in./in. to 4,000 μ in./in. compared to the analytical results which vary from

-540 μ in./in. to 3,860 μ in./in. These strain magnitudes are comparable to the axial

strains for the three-frame panel for the same load condition. Bending of the skin

between the frames is also observed for this loading condition and is similar to that

observed for the previous loading condition for the two-frame panel.

The panel with the two-frame configuration responds in a predictable manner

and the strain magnitudes for this loading condition are well within the strain

allowables for failure initiation.

Results for the panel with a removed center frame and a notch at one

cutout

This test case is the final test case considered in the present study. A maximum

value for the undamaged test panel axial strain occurs at the edge of the elliptical

cutout at its major axis. The magnitude of the maximum strain is 3,860 μ in./in. for the

combined 13.65 psi internal pressure and 2,450 lb/in. axial loading condition.

Damage in the form of a 1-in.-long saw-cut notch was inflicted at this critical location to

study the damage tolerance of this sandwich panel concept with a combined loading

condition with 8.85 psi of internal pressure and 1,630 lb/in. of axial load. This loading

condition corresponds to 2/3 of the design ultimate load condition. The notch was

machined into the panel to extend in the panel hoop direction slightly beyond the

window frame edge. The panel outer surface hoop and axial strain results from the

finite element analysis are presented in Figure 18 for this combined loading condition.

The hoop strain for this loading condition varies from -1,100 μ in./in. at θ =90° to 1,900

μ in./in. at θ =0° . The strain magnitudes are significantly higher for this loading

condition than for the hoop strain results presented in Figure 16 for the combined

loading condition with 13.65 psi of internal pressure and 2,450 lb/in. of axial loading

which are 66 percent lower. This increased strain state in the panel for this test case is

due to the notch causing more panel bending in the skin between the two cutouts. The

axial strain results from the finite element analysis for the outer surface indicate that a

maximum strain of approximately 5,200 μ in./in. occurs at the tip of the machined notch.

The experimental strain results for this load case are presented in Figure 19. The axial

strain results vary from -500 μ in./in. to 5,800 μ in./in. and compare very well with the

analysis results. No growth in the notch length was observed during the test.

The experimental hoop strain results along Line CC in Figure 1 for the threeframe panel, for the two-frame panel, and for the two-frame panel with a notch at the

window cutout are compared in Figure 20. These results suggest that the far field

strains in the hoop direction are influenced more by the removal of the frame than by

the introduction of the notch. The increase in the panel strain state due to introducing

the notch is local and does not result in any significant load redistribution.
8

Concluding Remarks

The response of a sandwich fuselage side panel with two window cutouts has

been evaluated for internal pressure and axial tension. The panel has been tested in

a three-frame configuration with combined loading conditions that are representative

of the design limit load and design ultimate load conditions. The strain magnitudes

around the cutouts on the inner and outer surfaces of the test panel for these loading

conditions are within the design ultimate strain allowable value of 4,000 μ in./in. for the

material, suggesting that the structure satisfies the design requirements. The inner

facesheet exhibits more local bending in the cutout region than does the outer

facesheet. The strain states corresponding to the applied load conditions in an infinite

composite flat plate were used to identify the differences in strain distributions

between the inner and outer facesheets of the sandwich panel. The magnitude of the

axial stress concentration factor is higher (3.57) for the axial loading condition, and the

hoop stress concentration factor is higher (2.88) for the combined loading condition

with 13.65 psi of internal pressure and 2,450 lb/in. of axial loading. Although the

absolute values for the stress concentration factors determined from the flat plate

analyses are not directly applicable to the curved panel studies in the present

investigation, the locations for the maxima and the relative magnitudes of stress

concentrations for different loading conditions are comparable. The finite element

analysis results compare very well with the experimental results.

The finite element analysis results correlate very well with the experimental

strain values for the panel with a two-frame configuration, and the strain results are

less than the ultimate strain allowables for the material. The damage tolerance of the

two-frame configuration is also demonstrated by testing the panel at design limit load

conditions with a notch at a window cutout region that is in the location of the highest

value of axial stress. For this case, the maximum value for the axial strain obtained

from the test and from the analysis is approximately 5,200 μ in./in. with no growth in the

notch length. This result suggests that the panel with twice the original frame spacing

is capable of sustaining the design ultimate load conditions without damage and of

sustaining the design limit load conditions with a 1-in.-long notch. This finding from

the experiments is significant considering that reducing the number of frames results in

a lighter weight structure.

References

1. Rouse, M.; and Ambur, D. R.: Evaluation of Damaged and Undamaged Fuselage 

 Panel Responses Subjected to Internal Pressure and Axial Load. Sixth NASA/

 DoD/ARPA ACT Conference, Anaheim, CA, August 7-11, 1995.

2. Anon.: ABAQUS Finite Element Code. Hibbitt, Carlson and Sorenson, Inc., Vol. 

1-2, 1995.

3. Savin, G. N.: Stress Concentrations Around Holes. Pergamon Press, London, 

 1961.
9

Table 1. Typical material properties for the graphite-epoxy materials used to 

manufacture the sandwich panel.

Property Tow Fabric Triaxial Korex

 braid core

 AS4/8552 AS4/8552 AS4/PR500

____________________________________________________________________________________________

Longitudinal modulus, E1 (Msi) 18.30 9.20 7.50 0.00001

Transverse modulus, E2 (Msi) 1.36 9.20 7.50 0.00001

Lateral modulus, E3 (Msi) 1.36 1.30 ---- 0.0340

In-plane shear modulus, G12 (Msi) 0.76 0.72 0.57 0.00001

Transverse shear modulus, G23 (Msi) 0.52 0.50 0.40 0.0136

Transverse shear modulus, G13 (Msi) 0.76 0.50 0.57 0.0326

Major Poisson's ratio, ν 12 0.32 0.04 0.29 0.30

11

Figure 2. Photogaph of the sandwich panel.

Figure 3. Finite element model of the sandwich panel.

hoop load

plate

window

cutouts

axial load

plate

frames

window

frame

symmetry

planes

axial load

actuator

hoop load

plate

outer frame

turnbuckle

axial load

plate skin

turnbuckle

center frame

turnbuckle
12

Figure 4. Hoop strain from the finite element analysis results for 2,450 lb/in. axial loading condition.

Figure 5. Axial strain results from the finite element analysis for the 2,450 lb/in. axial loading

condition.

a. Test panel inner surface

εθmin

εθmax

εx

εθ

b. Test panel outer surface

εθmin

εθmax

εθmin

εθmax

εx

εθ

εxmin

εxmax

εx

εθ

εxmin

εxmax

εx

εθ

c. Test panel inner surface b. Test panel outer surface
13

Figure 6. Analytical results for a flat plate with an elliptical hole and subjected to 2,450 lb/in. of

axial load.

Figure 7. Experimental strain results for the 2,450 lb/in. axial load condition.

Figure 7. Concluded.

a. Strains b. Stresses

σmax

σmin

σx

σθ εθ εx

εmax

εmin

0.0010

0.0005

0.0020

-0.0005

-0.0015

0

0 50 100 150 200

θ, degrees

εθ

inner surface

outer surface

0 50 100 150 200

θ, degrees

0.003

0.002

0.001

0.004

εx

a. Hoop Strain b. Axial strain

strain gage

c. Strain gage locations

θ(degrees)

εx

εθ

rosettes
14

Figure 8. Finite element analysis results for strains on the panel outer surface for a combined

18.2 psi internal pressure and 1,110 lb/in. axial loading condition.

Figure 9. Analytical results for a flat plate with an elliptical hole and subjected to combined 18.2

psi internal pressure and 1,110 lb/in. axial loading codition.

εθ

εx

a. Hoop Strain b. Axial strain

εxmin

εxmax

εθmin

εθmax

σmax

σmin

a. Strain profiles along hole

boundary

b. Stress profiles along hole

boundary

εy εx

εmin

εmax

σy σx
15

Figure 10. Experimental strain results for a combined 18.2 psi and 1,110 lb/in. axial loading condition.

Figure 11. Finite element analysis results for strain contours on the panel outer surface for a combined 13.65 psi internal pressure and 2,450 lb/in. axial loading condition.

Figure 12. Analytical results for a flat plate with an elliptical hole and subjected to a combined

13.65 psi internal pressure and 2,450 lb/in. axial loading condition.

0.0020

0.0015

0.0010

0.0005

-0.0010

-0.0015

εθ

0 50 100 150 200

θ, degrees

Outer surface

εx

0.0020

0.0015

0.0010

0.0005

0

-0.0005

-0.001

0 50 100 150 200

θ, degrees

outer surface

a. Hoop strain b. Axial strain

0.0025

εθmin

εθmax

εxmin

εxmax

εθ

a. Hoop strain b. Axial strain

εx

εθ

εx

a. Strain profiles along the hole

boundary

a. Stress profiles along the hole

boundary

εy εx

σy σx

εmax

εmin

σmax

σmin
16

Figure 13. Experimental strain results for a combined 13.65 and 2,450 lb/in. axial loading condition.

Figure 14. Finte element analysis results for strains on the two-frame panel outer surface for a

combined 18.2 psi internal pressure and 1,110 lb/in. axial loading condition.

Figure 15. Experimental strain results on the two-frame panel outer surface for a combined 18.2

psi and 1,110 lb/in. axial loading condition.

εθ

0.0015

0.0010

0.0005

0

−0.0005

−0.0010 0 150 200 50 100

θ, degrees θ, degrees

0 150 200 50 100

0.005

0.004

0.003

0.002

0.001

0

−0.001

εx

outer surface outer surface

a. Hoop strain b. Axial strain

εxmin

εxmax

a. Hoop strain

εθ

εx

εθmin

εθmax

b. Axial strain

0.0025

0.0020

0.0015

0.0010

0.0005

0

-0.0005

εθ

0 150 200 50 100

θ, degrees

three frames

two frames

0.0025

εx

0.0020

0.0015

0.0010

0.0005

0

-0.0005

0.00100 150 200 50 100

θ, degrees

a. Hoop strain b. Axial strain

three frames

two frames
17

Figure 16. Finite element analysis results for strains on the two-frame panel outer surface for a

combined 13.65 psi internal pressure and 2,450 lb/in. axial loading condition.

Figure 17. Experimental strain results on the two-frame panel outer surface for a combined 13.65

psi internal pressure and 2,450 lb/in. axial loading condition.

εxmin

εxmax

εθ

εx

a. Hoop strain b. Axial strain

εθmin

εθmax

a. Hoop strain b. Axial strain

0.002

0.015

0.010

0.005

0

-0.005

-0.010

εθ

0 150 200 50 100

θ, degrees

3-frames

2-frames

0.005

0.004

0.003

0.002

0.001

0

-0.001

εx

3-frames

2-frames

100

θ, degrees

0 150 200 50

three frames

two frames

three frames

two frames
18

Figure 18. Finite element analysis results for strains on the notched two-frame panel outer surface

for a combined 8.85 psi internal pressure and 1,630 lb/in. axial loading condition.

FIgure 19. Experimental axial strain results on the notched two-frame panel outer surface for a

combined 8.85 internal pressure and 1,630 lb/in. axial loading condition.

Figure 20. Comparision of experimental far-field outer service hoop strain results for the threeframe, two-frame, and notched two-frame panels.

εxmax

εxmin

a. Hoop strain b. Axial strain

εθ

εx

εθmax

εθmin

0.006

0.005

0.004

0.003

0.002

0.001

0

-0.001

εx

0 150 200 50 100

θ, degrees

three frames

two frames

two frames with

1-inch notch

0.0012

0.0008

0.0004

0

εθ

10 20 30 40 50 60 70

x, in.

three frames

two frames

two frames with 1-inch long notch

x, in.

εθ

Notch