Evan J. Pineda and David E. Myers

Glenn Research Center, Cleveland, Ohio

Daniel N. Kosareo

Vantage Partners, LLC, Brook Park, Ohio 

Bart F. Zalewski

ZIN Technologies, Middleburg Heights, Ohio 

Genevieve D. Dixon

Langley Research Center, Hampton, Virginia 

Buckling Testing and Analysis of Honeycomb 

Sandwich Panel Arc Segments of a 

Full-Scale Fairing Barrel

Part 2: 6-Ply In-Autoclave Facesheets

NASA/TM—2013-217822/PART2

August 2013
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Evan J. Pineda and David E. Myers

Glenn Research Center, Cleveland, Ohio

Daniel N. Kosareo

Vantage Partners, LLC, Brook Park, Ohio 

Bart F. Zalewski

ZIN Technologies, Middleburg Heights, Ohio 

Genevieve D. Dixon

Langley Research Center, Hampton, Virginia 

Buckling Testing and Analysis of Honeycomb 

Sandwich Panel Arc Segments of a 

Full-Scale Fairing Barrel

Part 2: 6-Ply In-Autoclave Facesheets

NASA/TM—2013-217822/PART2

August 2013

National Aeronautics and

Space Administration

Glenn Research Center

Cleveland, Ohio 44135
Available from

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7115 Standard Drive

Hanover, MD 21076–1320

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NASA/TM—2013-217822/PART2 1

Buckling Testing and Analysis of Honeycomb Sandwich 

Panel Arc Segments of a Full-Scale Fairing Barrel

Part 2: 6-Ply In-Autoclave Facesheets

Evan J. Pineda and David E. Myers

National Aeronautics and Space Administration

Glenn Research Center

Cleveland, Ohio 44135

Daniel N. Kosareo

Vantage Partners, LLC

Brook Park, Ohio 44142

Bart F. Zalewski

ZIN Technologies

Middleburg Heights, Ohio 44130

Genevieve D. Dixon

National Aeronautics and Space Administration

Langley Research Center

Hampton, Virginia 23681

Abstract

Four honeycomb sandwich panel types, representing 1/16th arc segments of a 10-m diameter barrel 

section of the Heavy Lift Launch Vehicle (HLLV), were manufactured and tested under the NASA 

Composites for Exploration program and the NASA Constellation Ares V program. Two configurations 

were chosen for the panels: 6-ply facesheets with 1.125 in. honeycomb core and 8-ply facesheets with 

1.000 in. honeycomb core. Additionally, two separate carbon fiber/epoxy material systems were chosen 

for the facesheets: in-autoclave IM7/977-3 and out-of-autoclave T40-800b/5320-1. Smaller 3- by 5-ft 

panels were cut from the 1/16th barrel sections. These panels were tested under compressive loading at the 

NASA Langley Research Center (LaRC). Furthermore, linear eigenvalue and geometrically nonlinear 

finite element analyses were performed to predict the compressive response of each 3- by 5-ft panel. This 

manuscript summarizes the experimental and analytical modeling efforts pertaining to the panels

composed of 6-ply, IM7/977-3 facesheets (referred to as Panels B-1 and B-2). To improve the robustness 

of the geometrically nonlinear finite element model, measured surface imperfections were included in the 

geometry of the model. Both the linear and nonlinear models yield good qualitative and quantitative 

predictions. Additionally, it was correctly predicted that the panel would fail in buckling prior to failing in 

strength. Furthermore, several imperfection studies were performed to investigate the influence of 

geometric imperfections, fiber angle misalignments, and three-dimensional (3-D) effects on the 

compressive response of the panel.

1.0 Introduction

Two manufacturing demonstration honeycomb sandwich panels (1/16th arc segments of the 10 m 

diameter cylinder) were fabricated under the NASA Composites for Exploration (CoEx) program and two 

under the NASA Constellation Ares V program. All four panels were manufactured by Hitco Carbon 

Composites. Two distinct configurations were chosen for the panels. The first configuration, fabricated 

under the CoEx program, was composed of 8-ply facesheets with a [45°/90°/-45°/0°]s lay-up and 1.000 in.

aluminum honeycomb core. The second configuration, fabricated under the Constellation Ares V 
NASA/TM—2013-217822/PART2 2

program, consisted of 6-ply facesheets with a [60°/–60°/0°]s stacking sequence and a 1.125 in. aluminum 

honeycomb core. In addition to the two configurations, two different carbon fiber/epoxy facesheet 

material systems were chosen for the panels: in-autoclave (IA) IM7/977-3 and out-of-autoclave (OOA) 

T40-800b/5320-1. It should also be noted that the honeycomb used in the 8-ply panels was machined to 

match the curvature of the panel while the honeycomb used in the 6-ply panels was flat. Additionally, in 

each panel, an adhesive splice joint was used to join discontinuous sections of the honeycomb core.

Following delivery to NASA Langley Research Center (LaRC), non-destructive evaluation (NDE) 

inspection (including ultrasonic testing and flash thermography) was performed on the full manufacturing 

demonstration panel. The results of the NDE guided the decision on where to cut 36-in. wide by 62-in. long 

sections for edgewise compression buckling tests. Following removal of the 36- by 62-in. panels from the 

manufacturing demo, the panels were re-inspected using infrared (IR) thermography to ensure that no 

damage had occurred. In preparation for testing, the load introduction ends of the panels were potted in 1.0 

in. thick aluminum end plates. The purpose of the end plates was to stabilize the facesheets and prevent local 

crushing, thus generating a predictable and repeatable end condition. As such, the panels are referred to as 3-

by 5-ft according to the acreage dimensions of the test panels. Preliminary finite element analysis (FEA)

indicated that no additional reinforcement was needed at the load introduction ends of the panels. A 

summary of the five 3- by 5-ft panels that were tested is given in Table I. 

TABLE I.—DETAILS OF FIVE 3-ft WIDE BY 5-ft TALL PANEL TYPES CUT FROM 1/16TH ARC 

SEGMENTS OF THE 10 m BARREL SECTION THAT WERE LOADED UNTIL BUCKLING

3- by 5-ft 

panel I.D.

1/16th arc segment 

panel I.D.

Facesheet material Facesheet 

lay-up

Core thickness,

in.

Panel A a8000-CMDP IM7/977-3 (IA) [45°/90°/-45°/0°]s 1.000 (curved)

Panel B-1 bMTP-6003 IM7/977-3 (IA) [60°/-60°/0°]S 1.125 (flat)

Panel B-2 MTP-6000 IM7/977-3 (IA) [60°/-60°/0°]S 1.125 (flat)

Panel C 8010-CMDP T40-800b/5320-1 (OOA) [45°/90°/-45°/0°]s 1.000 (curved)

Panel D MTP-6010 T40-800b/5320-1 (OOA) [60°/-60°/0°]S 1.125 (flat) a Composite Manufacturing Demonstration Panel (CMDP) b Manufacturing Test Panel (MTP) 

The current document provides details specifically pertaining to Panels B-1 and B-2, which consisted 

of 6-ply facesheets composed of in-autoclave IM7/977-3 and a 1.125 in. honeycomb core. Similar, 

separate documents have been prepared for Panels A, C, and D. The remaining subsections of Section 1.0

summarize the experimental and modeling objectives pertaining to all five panels. Section 2.0 provides 

details on Panels B-1 and B-2. Section 3.0 describes several approaches that were used to predict the 

buckling loads of Panel B-1 and B-2. The experimental and numerical results are presented in Section 4.0.

Finally, additional sensitivity studies are presented in Section 5.0. 

1.1 Test Objectives

The primary objective of the test is to measure the maximum compressive load carrying capability 

(buckling load) of each 3-ft wide by 5-ft long panel and to provide data for analysis correlation and 

validation. A secondary objective is to study the effect of geometric and manufacturing imperfections on 

the deformation and buckling load.

1.2 Test Success Criteria

The test will be considered successful if each of the following criteria are met:

1) All critical instrumentation is fully operational during the test

2) The loads are applied in a uniform and controlled manner.

3) Maximum attained load and all associated data are recorded and saved in the desired format.
NASA/TM—2013-217822/PART2 3

1.3 Modeling Objectives

The primary modeling objective is to predict the global buckling load and structural response of each 

3-ft wide by 5-ft long panel as accurately as possible using standard, commercially available, analysis 

tools. Linear eigenvalue baselines, obtained from a finite element method (FEM), will be compared to the 

experiment. More sophisticated, progressive collapse analyses, incorporating non-linear geometric effects 

and the measured geometric imperfections of the panel surfaces, will be executed in an attempt to 

improve the baseline numerical FEM prediction. Additionally, linear strength analyses will be performed 

to ensure that predicted buckling occurs before expected strength failure. Finally, parametric studies will 

be performed to determine the sensitivity of the buckling load of the panels to varying degrees of 

imperfections including as manufactured geometry, fiber angle misalignment, and loading eccentricity.

1.4 Modeling Success Criteria

The modeling will be considered successful if each of the following criteria are met:

1) The buckling load is predicted within 20 percent

2) The buckling mode/direction and location is predicted accurately

3) Local strain fields correlate well qualitatively with visual imaging data measured during the 

experiment

2.0 1/16th Panel Description

The 1/16th fabrication demo panels were constructed on a concave composite tool (5.00-m radius of 

curvature) using an automated tape laying process. The pre-impregnated (pre-preg) tape was 6-in. wide

and was composed of IM7 unidirectional fibers and 977-3 epoxy resin. The stacking sequence of the 

facesheets was [60°/-60°/0°]s and these facesheets were bonded to the 1.125 in. thick aluminum core 

using FM 300 film adhesive with a density 0.08 lb/ft2

. The aluminum honeycomb core manufactured by 

Hexcel was flat, not machined to panel curve dimension, and composed of HexWeb 5052, 0.0007-in.

thick with 0.125-in. cell size, and a density of 3.1 pcf. A Hysol 9396.6 foaming adhesive was used to join 

(or splice) discontinuous sections of the honeycomb core because the 1/16th barrel section panel 

dimensions exceeded the size of the pre-manufactured core. Upon completion of the panel assembly the 

panel was installed in an autoclave and cured in a single cycle. The manufacturing demonstration 1/16th

arc segment (of a 5 m outside radius cylinder) panel is shown in Figure 1.

Figure 1.—Cured 1/16th arc segment panel and the tool it was molded on.
NASA/TM—2013-217822/PART2 4

2.1 Test Specimen Description

Two, 36-in. wide by 62-in. long test specimens were machined from the manufacturing demo panels 

(Panel B-1 and Panel B-2) following non-destructive examination. The end plates were 1.0-in. thick 

aluminum plates with a slot in the shape of the specimens cross section machined in the center. The slot 

width and length were such that, when centered, the specimen had a clearance of 0.5-in. around the 

perimeter. After the specimen-end was centered in the slot and squared, it was potted with “UNISORB” 

V-100 epoxy grout, see Figure 2. Following the potting and curing of each end plate the specimen ends 

were machined flat and parallel to within ± 0.0025 in. A photograph of a test specimen with potted ends is 

shown in Figure 3. The potted dimensions of the 977-3 panels are shown in Figure 4. In addition to the 

overall dimensions, Figure 4 shows the relative position of the core splices with respect to the panel ends.

For complete details on the CoEx experimental efforts, the reader is referred to Kellas, et al. (2012).

Figure 2.—The 3- by 5-ft arc segment test panel and test fixture end view.

Figure 3.—Test panel with potted aluminum end plates.
NASA/TM—2013-217822/PART2 5

Panel B-1 Panel B-2

Figure 4.—Potted specimen dimensions for Panels B-1 and B-2. Note that the outside surfaces of the aluminum end 

plates were machined flat and parallel. The position of the core splices are also shown relative to the inside surface 

of the aluminum end plates.

Upon completion of the installation of the end plates, the panels were painted using a speckle pattern 

for photogrammetric measurements. Visual image correlation (VIC) was utilized to obtain the pre-test 

panel geometry (i.e., geometric imperfection data). VIC was employed to obtain full-field strain 

measurements during the tests as well as video. NDE was performed using flash thermography to obtain a 

baseline for post-test comparison. In addition, strain gages were affixed to the inner diameter (I.D. or 

IML) and outer diameter (O.D. or OML) surfaces of the panels, as shown in Figure 5. The even numbered 

gages were located on the I.D. while the odd numbered gages were located on the O.D. These gages were 

monitored and the strains were recorded during loading of the panel. The panel was tested at the LaRC in 

a servo-hydraulic test frame. The panels were secured between two loading platens, with the bottom 

loading platen being fixed and the top platen allowed to move in the y-direction. The panels were loaded 

in compression until buckling occurred. Additional instrumentation included three direct-current 

displacement transducers (DCDTs), shown in Figure 6 used to measure the global, axial deformation of 

the panels, and a load cell attached to the load platen to measure the applied loads. Also, out-of-plane 

measurements were recorded at two points along the horizontal center line as is shown in Figure 7. 
NASA/TM—2013-217822/PART2 6

a.) Panel B-1

b.) Panel B-2

Figure 5.—Panel geometries and strain gage locations/nomenclature.
NASA/TM—2013-217822/PART2 7

Figure 6.—Location of DCDT’s on test machine platen.

Figure 7.—Location of DCDT’s on front (IML) surface of Panel B-1 and back 

(OML) surface of Panel B-2.

3.0 Finite Element Analysis Description

Pre-test predictions of the buckling loads for Panel B-1 and B-2 were determined using commercially 

available FEM software packages: MSC/NASTRAN, Abaqus, and ANSYS. Figure 8 shows the test panel 

geometry used in the FE models. The panels were modeled as 60.00-in. tall (section between the 

aluminum end plates) and 35.60-in. along the arc (35.55-in. along the chord) using two-dimensional (2-D) 

layered shell elements. The shell models were offset so that the geometry corresponded to the OML. The 

1.0 in. sections of the panels on the top and bottom that were supported in the potting material were not 

modeled. The element size was 1.00- by 0.97-in., and the models were comprised of 2257 nodes and 2160

DCDT on test machine platen

Top of load plate with potted test panel 

underneath

DCDTs on test machine platen

#1

#2 #3

Center Line

Center Line

DCDTs on front (IML) panel surface

#4

#5
NASA/TM—2013-217822/PART2 8

elements. All three displacements and all three rotations were fixed along the bottom edge of the panels.

The same boundary condition was applied to the top edges, except a displacement was applied in the 

negative y-direction.

The stacking sequence of the facesheets was [60°/–60°/0°]s with 0.0053 in. plies. The IM7/977-3 

elastic properties and allowables (used in strength analysis) were obtained from the Orion materials

database, and are not shown as they are ITAR restricted (Lockheed Martin, 2010). The aluminum 

honeycomb properties were obtained from the database included with the commercially available 

structural sizing software, HyperSizer, and are presented in Table II. The in-plane normal and shear 

stiffnesses were reduced from 75.0 ksi to 1.00×10–7 ksi since in-plane load carrying capability of the 

honeycomb is typically neglected in honeycomb sandwich panel analysis.

Figure 8.—Panel geometry with boundary conditions.

TABLE II.—ALUMINUM HONEYCOMB 

MATERIAL PROPERTIES, 3.1 pcf, 1/8 in.-5052-0.0007

E1, ksi ........................................................................... 1.00×10–7

E2, ksi ........................................................................... 1.00×10–7

ν12 ........................................................................................ 0.333

G12, ksi.......................................................................... 1.00×10–7

G1Z, ksi .................................................................................. 45.0

G2z, ksi................................................................................... 22.0

ρ, pcf ..................................................................................... 3.10

Ft1, ksi.................................................................................... 0.20

Fc1, ksi ................................................................................... 0.20

Ft2, ksi.................................................................................... 0.20

Fc2, ksi ................................................................................... 0.20

Fs12, ksi .................................................................................. 0.09
NASA/TM—2013-217822/PART2 9

To arrive at the baseline buckling failure predictions, linear eigenvalue buckling analyses (Sol 105) 

were performed in MSC/NASTRAN. These preliminary analyses were completed for two reasons. First, 

the analyses provided reasonable estimates of what the non-linear analyses should predict as the panel 

buckling loads with an efficient, quick turnaround. Second, this is the typical method of calculating 

buckling loads for flight structures, and it is informative to compare the results to the experimental 

buckling loads and the buckling loads obtained from higher-fidelity models.

In addition, to improve numerical predictions, it was also pertinent to predict which direction 

(towards the I.D. or O.D.) the panels would buckle as a DCDT was to be placed to measure the out-of 

plane displacement of the panels and severe displacement in the unexpected direction would damage the 

gage. The eigenvectors obtained from an eigenvalue analysis are in an arbitrary direction and do not 

indicate the direction the panels would buckle. Therefore, geometrically non-linear static analyses were 

performed in MSC/NASTRAN (Sol 106), Abaqus, and ANSYS to arrive at more accurate buckling loads

and determine the direction of buckling correctly.

Hause et al. (1998, 2000), Hilburger et al. (2001), Hilburger and Starnes, Jr. (2002), Lynch et al. 

(2004), Schultz and Nemeth (2010) have shown that FEM simulations of progressive collapse 

incorporating geometric non-linearities are extremely sensitive to the geometric imperfections in the 

panel. Thus, it was desired to use some measure of the actual imperfections of the panels and include 

them in the models. Preliminary photogrammetry data of the panel showed that the bag side (I.D.) 

surfaces contained some initial imperfections that were biased towards the I.D. On the O.D., or the tool 

side, the surface imperfections were sinusoidal in nature. Herein, these surface imperfections are referred 

to as the bow shapes of the panels. In the progressive collapse analyses, the bow data from the bag side of 

the panels was used to incorporate geometric imperfections into the model. Figure 9 shows the 

imperfection, or bow, data measured vertically from the top of the panels to the bottom of the panels at 

the horizontal center. The raw photogrammetry data was first rotated such that both the top and bottom 

had an out-of-plane bow displacement of 0.000 in. The data was then scaled (60 in./total height of 

photogrammetry data) so that it covered the full 60 in. of the panel. The approximated bow geometry was 

then swept along an arc of radius 198 in. and 10.272°, providing a uniform tangential panel cross section.

Realistically, the cross section of the panel varies in the circumferential direction, but it was assumed that 

the imperfect, but uniform, cross section used in the numerical model is sufficient to capture the primary 

effects of the geometric imperfections in the panel. The imperfection data used to sweep the Panel B-1 

model geometry is labeled “Avg IML Bow – MTP 6003” in Figure 9. The geometry of Panel B-2 was 

generated using the imperfection data labeled “Avg IML Bow – MTP 6000” in Figure 9. However, the 

response of the panel did not correlate with the expected panel buckling direction, and it was deemed that 

the data contained some erroneous scatter, especially near the bottom of the panel were the data show 

imperfection deflection towards the O.D. The Panel B-2 imperfection data was then approximated with a 

spline, shown in Figure 9 labeled as “Modified Spline Approximation – MTP 6000,” and data from this

spline was used to sweep the geometry of the Panel B-2 model. All numerical results presented herein for 

Panel B-2 (MTP 6000) utilize the imperfection data obtained from the spline approximation of the 

measurements.

Finally, linear static solution in MSC/NASTRAN (Sol 101) was executed to determine the strength 

margins of safety at the time of onset of buckling. A similar analysis was performed in HyperSizer. These 

results were used to determine whether the failure of the panel was stiffness critical (buckling) or strength 

critical (local facesheet or core failure).
NASA/TM—2013-217822/PART2 10

Figure 9.—Imperfection, or bow, data from the bag side (I.D.) of the panel. Data were taken 

vertically along the height of the panel, in the horizontal center of the panel.

Figure 10.—Method for determining 

buckling load (Singer et al.,1998).

4.0 Test and Analysis Comparison

To determine the panel buckling loads, a method from Singer, et al. (1998), shown in Figure 10, was 

used. This method utilizes global load versus local strain gage data (axial strain) to mark the onset of 

buckling. In Figure 10, a vertical tangent line intersects the load-strain curve at a local strain where the 

local strain increment reverses which is designated the local buckling strain. The load corresponding to

that local strain is designated the buckling load. It should be noted that the buckling strain, and hence

buckling load, can only be determined at monitored locations and therefore can actually be lower than the 

lowest measured value. Thus, the postulated buckling load is somewhat subjective and based upon the 

location where the strains are being monitored for reversal. Test data for Gages 9 and 10 exhibited strain 

reversal at the lowest applied edge loads. These loads, 70,315 lb for Panel B-1 and 67,863 lb for Panel B2, will be considered the buckling loads, and the numerical buckling loads will be determined from the 

global load versus local strain plots obtained from points on the models corresponding to these gage 

locations. It should be noted that for Panel B-1, the strain gages were monitored during the test, and the 

test was stopped upon apparent strain reversal in the gages to prevent and damage from arising in the 

panel.

-30

-20

-10

0

10

20

30

-0.01 0 0.01 0.02 0.03 0.04 0.05

Vertical Location, in.

Out-of-Plane Bow, in. 

Avg IML Bow - MTP 6000

Modified Spline Approximation - MTP 6000

Avg IML Bow- MTP 6003

O.D. I.D. 
NASA/TM—2013-217822/PART2 11

Panel B-1 Panel B-2 (Spline)

Figure 11.—Euler eigenvector buckling plot obtained from MSC/NASTRAN.

4.1 Linear Buckling Analysis

Linear buckling analyses were performed using Nastran Sol 105. Figure 11 shows the eigenvector plots 

when a 0.242 in. displacement was applied to the edges of Panel B-1 and Panel B-2. The corresponding 

reaction loads were 74,245 lb (Panel B-1) and 75,248 lb (Panel B-2). Thus, the linear eigenvalue solution 

predicted buckling loads 5.59 and 10.9 percent higher than the test results. It should be noted that there was 

relatively little difference between the eigenvalues computed for Panel B-2 using the two different bow 

approximation methods, shown in Figure 9. As mentioned before, the eigenvectors do not indicate the 

direction of buckling in a panel where there is a preferred direction, such as a curved panel.

4.2 Non-Linear Buckling Analysis 

To obtain more accurate pretest predictions of the buckling loads, geometrically non-linear analyses 

were executed using MSC/Nastran Sol 106. For verification, several additional analyses were completed, 

including static nonlinear ANSYS, and static nonlinear Abaqus. Note that the ANSYS models included

both the approximated imperfection geometries, presented in Figure 9, and were seeded using the mode 

shapes from a preliminary, linear eigenvalue buckling analysis. For complete details on the ANSYS 

analysis, please refer to Section 5.4. Table III summarizes details of the various analysis tools that were 

used to predict the buckling loads of the panels. Figure 12 shows the load-deflection curves for all Panel 

B-1 analyses as well as the experimental results, while Figure 13 and Figure 14 show the same data in a 

less cluttered format. The figures show that all numerical predictions were more compliant than the test 

results, with the Abaqus and Nastran Sol 106 solutions closely matched. Note, the buckling loads and 

stiffnesses predicted by Abaqus, ANSYS, and Nastran were similar. Very little globally nonlinear 

behavior was exhibited in the test results prior to catastrophic failure.

TABLE III.—SUMMARY OF ANALYSIS TOOLS USED TO PREDICT BUCKLING RESPONSE OF SANDWICH PANELS

Software Solution Description Imperfection Seeding

MSC/NASTRAN 105 Linear eigenvalue solution Approximated bow

MSC/NASTRAN 106 Static solution with nonlinear geometry Approximated bow

Abaqus Static, NLGEOM Static solution with nonlinear geometry Approximated bow

ANSYS Static, NLGEOM Static solution with load increments and nonlinear 

geometry

Scaled mode shapes and

approximated bow
NASA/TM—2013-217822/PART2 12

Figure 12.—Total Panel B-1 reaction load versus end shortening for all analyses.

Figure 13.—Total Panel B-1 reaction load versus end shortening for Sols 105, 

106 and test.
NASA/TM—2013-217822/PART2 13

Figure 14.—Total Panel B-1 reaction load versus end shortening for Sols 105, 

ANSYS, Abaqus, and test.

Figure 15.—DCDT end shortening versus total reaction load (Panel B-1).

In all the Panel B-1 (MTP-6003) analyses the linear pre-buckling panel stiffness was nearly the same. 

However, the stiffness obtained from test results was higher than the analysis stiffness. Figure 15 shows 

the measurements of all three DCDTs that were affixed to the panel during loading. All three DCDTs 

showed higher stiffnesses, yielding an average measurement that produces a higher stiffness than the 

analytical predictions. Additionally, there is some initial non-linearity in the DCDT results due to initial 

settling, as expected. This indicates that there is some factor contributing to the stiffness of the panel that 

is not captured in the analyses. The slopes of the “NASTRAN SOL 106,” DCDT#1,” “DCDT#2,” 

“DCDT#3,” and “DCDT Specified Average” curves are presented in Table IV at an end shortening of 0.1 

in. (to eliminate settling). Thus, additional sources of discrepancy between the stiffness of the FEM model 

and the experiment may be due to machine compliance, slight misalignments of the fibers within the plies 
NASA/TM—2013-217822/PART2 14

to the intended ply angle, or variation in the fiber volume fraction/actual thickness of the plies resulting 

from the curing process. Results from a sensitivity study on fiber misalignment are presented in Section 

5.2. In addition, results from a sensitivity study on 3-D effects using ANSYS are presented in Section 5.4.

Figure 16 shows the experimental data obtained from the three DCDTs and the analytical predictions 

from Sol 105 and 106 using the average I.D. bow data, and the spline approximation of that data, for 

Panel B-2 (MTP-6000). Table V shows the slopes of the curves presented in Figure 16. There is relatively 

no difference in the slopes of the curves from Sol 106 analysis of Panel B-2 utilizing the two different 

bow approximation methods and Panel B-1, indicating the stiffness of the panel is relatively insensitive to 

geometric imperfections. The slopes from DCDT#1, DCDT#2 of Panel B-2 are closest to the analytical 

results, but the slope calculated using DCDT#3 is significantly higher. There was some slight 

misalignment of the test fixtures, as a maximum 5 percent difference in back-to-back strain gage 

measurements was permitted.

TABLE IV.—TANGENT SLOPES OF CURVES IN FIGURE 15

AT AN END SHORTENING OF 0.1 in. (PANEL B-1).

Curve Slope

“NASTRAN SOL 106” .......................................... 306.2 kips/in.

“DCDT#1” ............................................................. 338.0 kips/in.

“DCDT#2” ............................................................. 333.0 kips/in.

“DCDT#3” ............................................................. 334.6 kips/in.

“DCDT Specified Average” ................................... 335.2 kips/in.

Figure 16.—DCDT end shortening versus total reaction load (Panel B-2).
NASA/TM—2013-217822/PART2 15

TABLE V.—TANGENT SLOPES OF CURVES IN FIGURE 16

AT AN END SHORTENING OF 0.1 in. (PANEL B-2)

Curve Slope

“NASTRAN SOL 106” Avg IML Bow............................ 310.0 kips/in.

“NASTRAN SOL 106” Modified Spline Approx. ........... 311.1 kips/in.

“DCDT#1” ....................................................................... 326.2 kips/in.

“DCDT#2” ....................................................................... 323.0 kips/in.

“DCDT#3” ....................................................................... 341.7 kips/in.

“DCDT Specified Average” ............................................. 330.3 kips/in.

Figure 17.—DCDT end shortening versus total reaction load comparison of Panel B-1 

with Panel B-2.

The MSC/NASTRAN Sol 106 and average DCDT results are plotted for both panels in Figure 17.

Both models consistently underpredicted the stiffness of the panels; however, the Panel B-2 stiffness was 

closer to the experimental stiffness than Panel B-1. The load deflection prediciton for Panel B-2 deviated 

from linearity at a higher load than Panel B-1 and also plateaued at a higher load, indicating that the

buckling load for Panel B-2 was higher than Panel B-1. Since everything in the models of the two panels 

was identical, except for the geometric imperfections, it indicates that the different imperfection profiles 

were driving the discrepancy in the buckling loads.

For simplification, only analytical results obtained from MSC/NASTRAN will be presented in the 

remainder of this section (Section 4.2). Figure 18 shows the out-of-plane displacement contour plots and 

deformed shapes obtained from analysis, at an applied end displacement of –0.300 in., well into the postbuckled regime. This plot displays that panel buckling was predicted towards the I.D, for the Panel B-1 

and Panel B-2 utilizing the spline approximation of the geometry, which is consistent with the buckling 

direction observed in the experiment. The Panel B-2 results that utilized the average I.D. bow predicted 

buckling towards the O.D. It is suspected that some noise in the data (see Figure 9), which showed 

imperfection deflections towards the O.D., was responsible for the erroneous prediction of the buckling 

direction. As such, the results from this analysis will no longer be presented in this document, in lieu of 

results for Panel B-2 only using the spline approximation of the imperfection data.
NASA/TM—2013-217822/PART2 16

Panel B-1

Panel B-2 (Spline)

Panel B-2 (Average I.D. Bow)

Figure 18.—Panel displacement plot.
NASA/TM—2013-217822/PART2 17

Table VI shows that the first strain reversal occurred at the location of gages 9 and 10, located at the 

center of the left edge of the panel (see Figure 5), at a load of 70,315 lb for Panel B-1 and 67,863 lb for 

Panel B-2. Loads corresponding to all strain gage locations are tabulated with the experimental values in

Table VI. Figure 19 to Figure 21 show that, in the corner, the axial O.D. panel strains went into 

compression up to the onset of buckling, after which the strain increment reverses and the axial strain is 

alleviated as the load increases during post-buckling. This local behavior (observed both experimentally 

and numerically) is consistent as the panel buckled towards the I.D. Note that, since the major curvature 

of the panel is biased towards the O.D., the analysis would predict buckling towards the O.D. if no 

geometric imperfections (bow) were introduced into the model. Figure 22 shows the strain gage

measurements at a panel inflection point at the 3⁄4 panel length location. Figure 23 to Figure 25 shows that 

at the horizontal center of the panel, the I.D. panel strain goes into compression up to buckling and then 

starts reversing as the load increases during post-buckling. The results from Figure 26 the lower inflection 

or 1⁄4 length location, match the results from Figure 22 while the results from Figure 27 and Figure 29

match the results from Figure 20 and Figure 21, respectively. The error in the nonlinear analyses ranges 

from 0.42 to 9.16 percent for Panel B-1 and 5.65 to 9.60 percent for Panel B-2 (Table VI), which was not

much of an improvement over the linear analyses.

TABLE VI.—APPROXIMATE TEST AND ANALYSIS PREDICTION BUCKLING LOADS

[See Figure 5 for gage locations on panel]

Gage Test, lb

(Panel B-1/Panel B-2)

Analysis, lb

(Panel B-1/Panel B-2)

Percent error

(Panel B-1/Panel B-2)

1,2 70,397/70,171 70,097/74,134 0.42/5.65

3,4 71,283/69,470 68,321/74,314 4.16/6.97

5,6 71,057/69,100 68,321/74,314 3.85/7.55

9,10 70,315/67,863 64,118/74,375 8.81/9.60

11,12 71,448/68,543 66,283/74,375 7.23/8.51

13,14 70,583/69,100 64,118/74,544 9.16/7.88

17,18 71,036/69,285 68,321/74,314 3.82/7.26

19,20 71,139/69,841 68,321/74,314 3.96/6.40

Figure 19.—Load/strain plot for MTP-6003 and MTP-6000 Approximated Spline Gages 1 and 2 upper, left side, even 

numbers on I.D. Analysis obtained from MSC/NASTRAN, Sol 106.
NASA/TM—2013-217822/PART2 18

Figure 20.—Load/strain plot for MTP-6003 and MTP-6000 Approximated Spline Gages 3 and 4, upper, left side, even 

numbers on I.D. Analysis obtained from MSC/NASTRAN, Sol 106.

Figure 21.—Load/strain plot for MTP-6003 and MTP-6000 Approximated Spline Gages 5 and 6,upper, right side, 

even numbers on I.D. Analysis obtained from MSC/NASTRAN, Sol 106.

Figure 22.—Load/strain plot for MTP-6003 and MTP-6000 Approximated Spline Gages 7 and 8, upper 1⁄4 length, 

center, even numbers on I.D. Analysis obtained from MSC/NASTRAN, Sol 106.
NASA/TM—2013-217822/PART2 19

Figure 23.—Load/strain plot for MTP-6003 and MTP-6000 Approximated Spline Gages 9 and 10,center, left side, 

even numbers on I.D.. Analysis obtained from MSC/NASTRAN, Sol 106.

Figure 24.—Load/strain plot for MTP-6003 and MTP-6000 Approximated Spline Gages 11 and 12,center of panel,

even numbers on I.D. Analysis obtained from MSC/NASTRAN, Sol 106.

Figure 25.—Load/strain plot for MTP-6003 and MTP-6000 Approximated Spline Gages 13 and 14 center, left side, 

even numbers on I.D. Analysis obtained from MSC/NASTRAN, Sol 106.
NASA/TM—2013-217822/PART2 20

Figure 26.—Load/strain plot for MTP-6003 and MTP-6000 Approximated Spline Gages 15 and 16,lower 1⁄4 length, 

center, even numbers on I.D. Analysis obtained from MSC/NASTRAN, Sol 106.

Figure 27.—Load/strain plot for MTP-6003 and MTP-6000 Approximated Spline Gages 17 and 18 lower, left side, 

even numbers on I.D. Analysis obtained from MSC/NASTRAN, Sol 106.

Figure 28.—Load/strain plot for MTP-6003 and MTP-6000 Approximated Spline Gages 19 and 20 lower, right side, 

even numbers on I.D. Analysis obtained from MSC/NASTRAN, Sol 106.
NASA/TM—2013-217822/PART2 21

The non-linear MSC Nastran Sol 106 analysis full field results are compared qualitatively with the 

test results. Since both panels exhibited the same qualitative response, strain contours are only presented 

here for Panel B-1. Figure 29 shows that the post-buckled, in-plane displacement photogrammetry results 

qualitatively compared well with the analytical predictions. Since shell elements were used in the 

analysis, the nodal displacements do not vary on the O.D. and I.D. surfaces, whereas, the test results 

showed some slight variation in displacement for the I.D. and O.D. surfaces due to the finite width of the 

panel. Figure 30 shows the evolution of the in-plane displacement, obtained from the numerical analysis, 

as the applied compressive load is increased. Figure 31 shows that the post-buckled, out-of plane,

displacement also compared well qualitatively with the analytical predictions. Figure 32 shows that the 

out-of-plane displacement was negligible up to the load of 74,358 lb.

Figure 29.—Post-buckling Y (in-plane) displacement comparison.

Figure 30.—Analytical Y (in-plane) displacement.
NASA/TM—2013-217822/PART2 22

For the O.D. surface, Figure 33 and Figure 34 show the minimum principal strain test results did not 

compare well with the analytical predictions. This may indicate that the test panel was not loaded high 

enough for the minimum principle strains to fully develop in the post-buckled regime. Like the out-ofplane displacement, the minimum principal strains, from the analysis, were negligible up until postbuckling. For the I.D. surface, Figure 35 and Figure 36 show that the minimum principal strain also did 

not compare well. Figure 37 to Figure 40 show the maximum principal strain comparisons. Again, it 

appears that the photogrammetric strains do not fully develop in the post-buckled state, and that the 

applied loading during the experiment may have needed to be taken to a slightly higher value. 

Figure 31. Post-buckling X (out-of-plane) displacement comparison.

Figure 32.—Analytical X (out-of-plane) displacement.
NASA/TM—2013-217822/PART2 23

Figure 33.—Post-buckling O.D. minimum principal (Y) strain comparison.

Figure 34.—Analytical minimum principal strain (Y) strain O.D.
NASA/TM—2013-217822/PART2 24

Figure 35.—Post-buckling I.D. minimum principal (Y) strain comparison

Figure 36.—Analytical minimum principal strain (Y) strain I.D.
NASA/TM—2013-217822/PART2 25

Figure 37.—Post-buckling O.D. maximum principal (Z) strain comparison.

Figure 38.—Analytical maximum principal strain (Z) strain O.D.
NASA/TM—2013-217822/PART2 26

Figure 39.—Post-buckling I.D. maximum principal (Z) strain comparison.

Figure 40.—Analytical maximum principal strain (Z) strain I.D.
NASA/TM—2013-217822/PART2 27

4.3 Strength Analysis at Buckling Load

In a separate linear static analysis, Panel B-1 was loaded up to the buckling load (determined from the 

non-linear static analysis) using MSC/Nastran Sol 101. This analysis was performed to confirm that panel 

failure was stiffness driven (i.e., the panel would be expected to buckle before it failed in strength). Figure 

41 shows the strength ratio plot for the panel at the buckling load. The strength ratio is the local stress 

versus the allowable, and it incorporates one of three multiaxial failure criteria: Tsai-Wu, Tsai-Hill,

Hoffman (Jones, 1999). Figure 41 shows the lowest strength ratio among the three criteria across all 

facesheet plies for each element. The analysis showed that a load 2.15 times greater than the buckling 

load would be required to fail the panel in strength, indicating the panel is indeed stiffness driven. It 

should also be noted that the regimes exhibiting the lowest strength ratios are limited to the corners of the 

panel, while the majority of the panel exhibits strength ratios above 3.0. The magnitude of the stresses 

near the corners is likely to be dependent on the size of the elements used in those areas, due to the 

presence of perfectly sharp corners in the model.

In addition to performing the strength analysis using MSC/Nastran Sol 101, a strength analysis was 

performed in HyperSizer, a commercially available structural sizing and design software (HyperSizer, 

2012). The honeycomb properties used in this analysis are shown in Figure 42. The element forces and 

moments were obtained using finite element analysis where the facesheets of the honeycomb sandwich 

composite were constructed using explicit ply lay-ups. An element-based comparison was used to ensure 

that worst case behavior was captured. The following modes of failure were of most interest: core 

crimping, core crushing, facesheet wrinkling, and facesheet dimpling, as these modes are difficult to 

assess using finite element analysis alone.

Figure 41.—Strength ratio plot at buckling load.
NASA/TM—2013-217822/PART2 28

Figure 42.—Honeycomb Hexcel core properties.

Figure 43 shows that all the margins are positive for core crimping, core crushing, facesheet

wrinkling, and facesheet dimpling. It should be noted that the minimum strength ratios (margin of safety 

plus one) from Nastran and HyperSizer matched very well, both indicated a strength ratio of 2.15. It was 

determined that the wrinkling equations used to produce the margin of safety contour plot (with a 

minimum margin of safety of 0.149) in Figure 44 were not appropriate for a honeycomb sandwich panel

with laminated composite facesheets (Zalewski et al., 2012). Therefore, wrinkling stress (sw) was 

assessed using the wrinkling Equation (1) (where tf is the facesheet thickness, tc is the core thickness, Ef is 

the facesheet modulus, Ec is the core modulus, and υf is the facesheet Poisson’s ratio) for anisotropic

facesheets and cellular core (Vinson, 1999), as is more appropriate for this panel. To improve the 

accuracy the wrinkling margin of safety, a combined loading condition was used, Equation (2), with two 

compressive principal stresses (Ley et al., 1999). Using this more appropriate method, the minimum 

margin of safety further increased from 0.149 to 0.963. Thus, it was predicted that facesheet wrinkling in 

the corners of the panel would not be an issue, and the experimental data presented in Figure 19 supports 

this assumption.

( ) 2 3 1

2 =

c f

f c f

t υ

t E E

sw − (1)

1

σ σ

1 MOS =

2

3

1

−

 + 

 





sw sw

(2)
NASA/TM—2013-217822/PART2 29

Figure 43.—HyperSizer results.

Figure 44.—HyperSizer margin of safety plot for core 

crimping, core crushing, facesheet wrinkling, and 

facesheet dimpling.
NASA/TM—2013-217822/PART2 30

5.0 Sensitivity Studies

5.1 Sensitivity to Panel Geometry

The analyses presented in Section 4.2 utilized geometric imperfection data from the panel measured 

vertically along a single horizontal coordinate. It is very likely, that if a different location was chosen to 

measure this data, the bow shape, and maximum imperfection would have been different. The results 

presented in Section 4.2 indicate that the buckling load and direction of these curved panels are very 

sensitive to the geometric imperfections contained in the panel. To investigate the imperfection sensitivity 

further, a parametric study was conducted incorporating various levels of bow imperfection. A regular arc 

shape was assumed with the maximum deflection towards the I.D. being located at the vertical center of 

the panel. This bow shape was then swept horizontally to arrive at the full geometry of the panel. The 

maximum bow deflection was varied from 0.01 to 0.04 in.

Previous studies showed that the geometric imperfections had a negligible effect on the stiffness of 

the panel (Myers et al., 2013). The buckling loads obtained using the various levels of imperfection are 

plotted in Figure 45, along with the test results and the numerical predictions utilizing approximations of 

the actual imperfection data. As the maximum bow deflection (towards the I.D.) increased from 0.010 to 

0.017 in., the buckling load increased 72,340 to 76,220 lb. As the maximum bow deflection is increased 

Figure 45.—Impact of initial panel bow geometry on panel buckling loads.
NASA/TM—2013-217822/PART2 31

beyond 0.017 in., the buckling load started to decrease. It should also be noted that when the bow was 

0.017 in. or less, the panel buckled towards O.D., but when the bow was greater than 0.017 in., the panel 

buckled towards the I.D. Thus, a geometric imperfection (in the shape of a swept arc) with a maximum 

deflection of 0.017 in. represents a transition point beyond which the direction of buckling switches. This 

is consistent with a similar study performed by Myers et al. (2013) for a similar panel with 8-ply 

facesheets composed of the same material. As the bow gets closer to this transition point, an increase in 

the bow deflection helps to resist buckling because the bow direction is opposite the buckling direction. 

Beyond this transition point, an increase in the bow deflection acts to aid the buckling because the 

buckling direction and bow deflection are the same.

The Panel B-1 and Panel B-2 simulations presented in Section 4.2 utilized bow shapes that contained 

maximum deflections beyond the 0.017 in. threshold. The predictions from these models followed a 

similar trend to that observed in the bow study. The buckling load prediction from the Panel B-2 model, 

for which the bow was modeled using a spline approximation, matched very closely with the 

corresponding buckling load from the bow study. However, the Panel B-1 prediction was significantly 

lower than the bow study prediction that incorporated the same maximum bow deflection. The 

imperfection geometry utilized in the Panel B-1 model was composed of the averaged imperfection data 

measured from the panel and did not conform to a regular shape (such as the spline approximation). This 

signifies that both maximum bow deflection and shape may influence the prediction results.

The experimental buckling loads did not follow the same trend as the bow study. This may imply that 

the full field imperfections are needed to predict the response of the panel accurately. However, there is a 

discrepancy in the stiffness of the panels (see Figure 17) which cannot be reproduced by incorporating 

imperfections (Myers et al., 2013). Moreover, it is other imperfections that are contributing to the 

discrepancies observed in the buckling loads and stiffnesses between the experimental data and analytical 

predictions.

5.2 60° Ply Fiber Misalignment Sensitivity Study

For this study, the Panel B-1 model as described in Section 3.0 was used; however, the orientation of 

the 60° plies was varied from 55° to 65° in increments of 1°. The 0° plies were not altered as it was 

assumed that their orientation does not vary during the ply lay-up process. Nastran Sol 106 was used to 

analyze the panel. Figure 46 shows the force-displacement results from the orientation variation study, 

and Figure 47 shows a magnified view of the plot near the region where the load plateaus. These figures 

show that the plateau load, and by extension the buckling load, predicted by the model can be 

significantly affected by plus/minus 5° of misalignment in the plies. Although, there is some change in 

the stiffness as a function of misalignment, the effect is minimal, and most likely, not the reason for the 

large discrepancy in stiffness observed between the experiment and the analytical results. An input from 

FiberSim would better model the true fiber alignment.
NASA/TM—2013-217822/PART2 32

Figure 46.—Nonlinear static analysis results for altered 60° ply angle.
NASA/TM—2013-217822/PART2 33

Figure 47.—Nonlinear static analysis results for altered 60° ply angle (magnified view).

5.3 Study of Eccentricity in Applied Displacement

To determine if eccentric application of the edge displacement would yield a change in the direction 

of buckling, a simulation was performed, accounting for some degree of eccentricity. Figure 48 shows the 

effect of eccentric loading on the through-thickness displacement of the edge of the sandwich panel.

Assuming the difference between the displacements applied to the front face of the panel and the 

centerline of the panel is equal but opposite to the difference in the displacement applied to the back face 

of the panel, the centerline of the panel yields a rotation Φ given by





 



 ∆ φ = −

t

sin 0.05128 1 (3),
NASA/TM—2013-217822/PART2 34

where Δ is the centerline displacement and t is the total thickness of the panel. The angle Φ is applied to the 

edge of the panel in the shell model as a rotation to simulate a through-thickness eccentricity in the applied 

edge displacement in the experiment. The angle used in the simulation is 20 percent of the buckling 

displacement from the linear eigenvalue solution and is calculated to be 0.12° using Equation (3). It is 

assumed that this level of eccentricity is present from the beginning of the analysis and is constant 

throughout the duration of the simulation.

Figure 49 shows the post-buckled shapes predict using a non-linear analysis with a uniform edge 

displacement an edge displacement with eccentricity corresponding to a rotation of 0.12°. Figure 50 shows a 

comparison in the load-deflection behavior from the two simulations. These two figures show that the 

buckling direction and the quantitative response of the panel is largely unaffected by the assumed 

misalignment. 

Figure 48.—Diagram showing eccentric 

loading applied through the thickness 

of the panel leading to rotation of the 

panel edge.

Figure 49.—Post-buckled shape with uniform applied displacement and 

simulated eccentric applied displacement.
NASA/TM—2013-217822/PART2 35

Figure 50.—Reaction load versus applied displacement with uniform applied displacement and simulated eccentric 

applied displacement. (Fix legend/scale lines on left side of plot.)

5.4 ANSYS 3-D Finite Element Model

The 3- by 5-ft arc segment sandwich panels were investigated using two different ANSYS finite 

element models. The first models utilized 2-D layered structural shell element from which the results have 

been presented earlier. Additional models incorporated 3-D layered structural solid-shell element model 

in which the test fixtures were also included. In ANSYS, the 2-D layered shell element is called a 

SHELL281 finite element, and the 3-D solid-shell is called a SOLSH190 finite element. These finite 

element types are shown in Figure 51. A shell element is similar to a NASTRAN quad element, while the 

solid-shell is similar to a brick element. The SOLSH190 element can be used to model shell structures 

with a wide range of thickness from thin to moderately thick. Furthermore, the SOLSH190 element 

formulation permits small thickness to length ratios without producing errors due to large aspect ratios.

The thickness between the nodes must equal the sum of the individual layer thicknesses. Otherwise, 

ANSYS will scale the individual layer thicknesses to fit the actual element thickness. Since the results of 

the 2-D shell model were included with the Abaqus and MSC-NASTRAN results in previous sections, 

these results will only be used as a basis of comparison with the 3-D finite element model.

Figure 52 shows the model of the test panel geometries with the end plates. For clarity, the finite 

element edges are suppressed. The panels were modeled as 62-in. tall including the 1.0-in. Al end plates 

and 36.0-in. wide along the chord. The top and bottom 1 in. portions of the panels were supported in the 

potting material and end plates. Figure 53 shows the slot in the end plate shaped like the arc segment test 

specimen models. The end of the specimen models are centered in the slot, and the 0.5-in. space around 

the specimen was filled with solid elements modeling the UNISORB V-100 potting compound with the 

elastic properties given in Table VII. Each color represents a different material assignment: cyan for the 

IM7/977-3 facesheets, purple for the honeycomb core, red for the potting compound, and orange for the 

aluminum end plates.
NASA/TM—2013-217822/PART2 36

Figure 51.—ANSYS 2-D shell versus 3-D solid-shell (brick) finite elements.

Figure 52.—The 3- by 5-ft arc segment test panel configuration.

TABLE VII.—ELASTIC PROPERTIES FOR

UNISORB V-100 POTTING COMPOUND

Property Value

E .............................................................436 ksi

ν.................................................................. 0.35
NASA/TM—2013-217822/PART2 37

Figure 53.—The 3- by 5-ft arc segment test panel and test fixture end view.

The solid models were generated using a script file containing ANSYS preprocessing, finite element 

solution, and post-processing commands in the ANSYS Parametric Design Language (APDL) (ANSYS, 

2011). The basic geometry, ply stacking sequence, material properties, and geometric imperfections were 

defined using parameters. The script file can generate the finite element model, perform each analysis in 

sequence, and process the results in tabular or graphic format.

As shown in Figure 54, the stacking sequence of the facesheets was [60°/–60°/0°]S with 0.0053-in.

thick plies. Again, the IM7/977-3 elastic properties and allowables were obtained from Orion materials 

database, and they are not listed due to ITAR restrictions (Lockheed Martin, 2010). Referring to Table 

VIII, the aluminum (5052-T6 alloy) honeycomb properties were obtained from commercially available 

literature (Hexcel). Unlike the HyperSizer properties, the honeycomb in-plane longitudinal and transverse 

moduli (E1 and E2) were kept at 21.28 psi, and the in-plane shear modulus (G12) was kept at 5.32 psi in the 

ANSYS models. The honeycomb normal (out-of-plane) modulus (E3) was also kept at 75 ksi.

The actual panels were secured between two loading platens, with the bottom end plates fixed on the 

loading platen. The top end plates moved with the top platen in the axial direction. Referring to Figure 55, 

all three displacements in the solid-shell finite element models were fixed along the bottom edge of the 

panel and end plate. The same boundary conditions were applied to the top panel edges and top end 

plates, except displacements were applied in the negative z-direction.

It has been shown in this paper that the initial geometric imperfections have an impact on the 

buckling load and direction. Intuitively, a curved panel is expected to buckle towards the O.D. However, 

this 3- by 5-ft arc segment test panel buckled toward the I.D., which was primarily due to its bowed 

shape. Therefore, the initial imperfect geometry is important in a nonlinear buckling analysis (Hong and 

Jun, 1989). If the 3- by 5-ft panel is modeled as perfectly symmetric (i.e., in geometry and loading), 

nonlinear progressive collapse does not occur numerically in ANSYS.
NASA/TM—2013-217822/PART2 38

Figure 54.—Facesheet 6-Ply stacking sequence.

TABLE VIII.—ANSYS MODEL, Al HONEYCOMB MATERIAL

PROPERTIES, 3.1 pcf, 1/8 in.-5052-0.0007-in. THICKNESS

Property/units Value Property/units Value

E1, psi ............................................................................... 21.28

E2, psi ............................................................................... 21.28

E3, ksi .................................................................................... 75

υ12 ..................................................................................... 0.333

υ23 ................................................................................ 1.0×10–5

υ13 ................................................................................ 1.0×10–5

G12, psi................................................................................ 5.32

G13, ksi................................................................................... 45

G23, ksi................................................................................... 22

γ, lb/cu-in...................................................................... 0.00179

ρ, pcf..................................................................................... 3.1

Ft1, psi.................................................................................. 215

Fc1, psi.................................................................................. 215

Ft2, psi.................................................................................. 215

Fc2, psi.................................................................................. 215

Ft3, psi.................................................................................. 130

Fc3, psi.................................................................................. 300

Fs12, psi .................................................................................. 90

Fs23, psi .................................................................................. 90

Fs13, psi .................................................................................. 90

Figure 55.—ANSYS solid model boundary conditions.
NASA/TM—2013-217822/PART2 39

One way to introduce anti-symmetry to the model is to apply small perturbations to the applied loads 

or enforced displacements. This method is not ideal, because it is difficult to determine how to 

redistribute the loads. Furthermore, varying the load across the top of the panel too drastically could 

change the problem completely. Another way to introduce anti-symmetry is to superimpose small 

geometric imperfections (similar to those caused by manufacturing) on the model to trigger the buckling 

responses. One way to generate these imperfections is with pseudo-random shapes, where the coordinates 

of the nodes are slightly modified with random amplitudes. The disadvantage in using random 

imperfections is that they cannot be repeated, and the results would differ for each analysis of the same 

panel. An easier way to impose geometric imperfections on the finite element model is to employ the 

linear (Eigen) buckling mode shapes.

The buckling analysis of the 3- by 5-ft arc-segment panel requires several steps. First, the initial bow 

shape is imposed across the width of the panel model. The imperfections are obtained by running a 

preliminary linear buckling analysis, then updating the geometry of the finite element model to the 

deformed configuration. This technique is done by adding the displacements from the mode shapes 

multiplied by a scaling factor. The scaling factor is on the order of the manufacturing tolerances and 

initial bowed shape. A factor of –0.020 in. was chosen for the 3- by 5-ft panel. Furthermore, the scaling 

factor was negative to correspond to the direction of the initial bow shape. Applying a positive value 

could bring the panel model back to a near perfect condition. The imperfections are also added as a sum 

of the first 10 modes shapes extracted in the preliminary linear buckling analysis as shown in Figure 56.

The first 10 mode shapes were used to avoid any bias in the imperfections. Figure 57 shows the resulting 

geometry for Panel B-1. The same procedure was used to generate the geometry for Panel B-2 using the 

measured imperfections and mode shapes.

Figure 56.—The first 10 linear buckling mode shapes for the 3 by 5 panel with 6-ply facesheets.
NASA/TM—2013-217822/PART2 40

Figure 57.—Panel B-1 model with the applied initial bowed 

shape and geometric imperfections (exaggerated).

After the geometric imperfections are added to the finite element model, the nonlinear buckling 

analysis is performed. In ANSYS, a nonlinear buckling analysis is a static analysis with large deflections 

active. The magnitude of the applied axial compression is extended beyond the first linear (Eigen) 

buckling mode. In this analysis the compression was increased gradually using 50 small time increments 

to predict the critical buckling load.

Figure 58 shows the reaction load versus end compression for the linear and nonlinear shell and solid 

ANSYS models and the actual test data of Panel B-1. The two linear buckling analyses over-predicted the 

buckling load, but the two nonlinear analyses under-predicted the buckling load. The nonlinear shell FEM 

is closest to the test result buckling load. In both nonlinear ANSYS analyses, the panel stiffness was 

nearly the same. However, the predicted stiffnesses were lower than the test stiffness. Reasons for the 

difference in stiffness were discussed earlier.

Figure 61 shows the reaction load versus end compression for the linear and nonlinear shell and solid 

ANSYS models and the actual test data of Panel B-2. Note that, the maximum test value does not 

necessarily correspond to the experimental buckling load, rather local strain gage data must be used to 

assess the buckling load. The two linear buckling analyses over-predicted the buckling load, but the two 

nonlinear analyses just slightly over-predict the buckling load. The nonlinear solid FEM is closest to the 

test result buckling load. In both nonlinear ANSYS analyses, the panel stiffness was nearly the same.

However, the predicted stiffnesses were only lower than test stiffness as recorded by one DCDT. The 

predicted stiffnesses were in closer agreement with the other two DCDT's. 

Figure 59 and Figure 62 show the panel radial displacement plot (radial component of the total 

displacement field) when –0.21888 in. was applied to the top edge. As explained earlier, Figure 59 shows 

the panel buckles in towards the I.D. due to the initial bow and not in the direction of the panel’s outer 

surface. The plot also shows asymmetry in the radial displacements which is also evident in the buckling 

predictions shown in Table IX. The asymmetry in the radial displacements of Figure 59 and Figure 62 is 

due to the asymmetry in some of the linear buckling mode shapes (as shown in Figure 56) which were 

superimposed on the original geometry. The difference in the radial displacement contours is due to the 
NASA/TM—2013-217822/PART2 41

difference in the initial bow shapes of Panel B-1 and B-2 (see Figure 9). The differences in these radial 

displacements demonstrate the sensitivity of the buckling analysis and resulting loads to the initial 

geometric imperfections. Thus, imperfections must be accounted for accurately in the modeling if they are 

significant compared to the overall dimension of the panel.

Figure 60 and Figure 63 show load versus strain plots for gages located in the center of the panel. On 

the I.D. side of the panel, the strain goes into compression up to buckling and then starts relieving itself as 

the load increases during post-buckling. On the O.D. side, the strain remains compressive (negative) and 

suddenly increases in magnitude during post-buckling. The analysis results for the ANSYS shell and solid 

FEM's show the same trends in strain at that gage location.

Figure 58.—Total reaction load versus end shortening for ANSYS solid and shell FEMs of panel B-1.

TABLE IX.—APPROXIMATE TEST AND ANALYSIS PREDICTION BUCKLING LOADS

Gage Test, lb

(Panel B-1/Panel B-2)

Analysis, lb

(Panel B-1/Panel B-2)

Percent error

(Panel B-1/Panel B-2)

1,2 70,398 / 69,821 67,465 / 68,853 4.17 / 1.39

3,4 71,222 / 69,326 63,226 / 66,466 11.23 / 4.13

5,6 71,057 / 69,161 63,226 / 66,466 11.02 / 3.90

9,10 70,315 / 67,863 60,714 / 63,835 13.65 / 5.94

11,12 71,243 / 68,543 63,226 / 66,466 11.25 / 3.03

13,14 70,233 / 68,543 58,086 / 63,835 17.30 / 6.87

17,18 71,057 / 69,264 65,524 / 66,466 7.79 / 4.04

19,20 71,140 / 69,388 63,226 / 66,466 11.12 / 4.21
NASA/TM—2013-217822/PART2 42

Figure 59.—ANSYS solid FEM, radial displacement contour plot for Panel B1 at 0.219-in. end shortening.

Figure 60.—Load versus minimum principal strain plots for Panel B-1 at gages 11 and 12.

ANSYS 14.0

FEB 19 2013

16:43:33

PLOT NO. 2

NODAL SOLUTION

STEP=1

SUB =24

TIME=.48

UX

MIDDLE

LAYR=6

RSYS=1

DMX =.355216

SMN =-.33274

SMX =.701E-03

1

MN

MX

Global Radial Displacement Contours

Geometric Imperfections

Scale Factor = -.02

X Y

Z

-.33274

-.295691

-.258642

-.221593

-.184544

-.147495

-.110446

-.073397

-.036348

.701E-03

3x5 Coupon, 6-ply, IM7/977-3, Face Sheets, Bowed, -0.21888" Disp
NASA/TM—2013-217822/PART2 43

Figure 61.—Total reaction load versus end shortening for ANSYS solid and shell FEM's of Panel B-2.

Figure 62.—ANSYS solid FEM, radial displacement contour plot for Panel B-2 at 0.219-in. end shortening.

ANSYS 14.0

DEC 31 2012

11:28:28

PLOT NO. 2

NODAL SOLUTION

STEP=1

SUB =24

TIME=.48

UX

MIDDLE

LAYR=6

RSYS=1

DMX =.221086

SMN =-.187266

SMX =.001174

1

MN

MX

Global Radial Displacement Contours

Geometric Imperfections

Scale Factor = -.02

X Y

Z

-.187266

-.166328

-.14539

-.124453

-.103515

-.082577

-.061639

-.040702

-.019764

.001174

3x5 Coupon, 6-ply, IM7/977-3, Face Sheets, Bowed, -0.21888" Disp
NASA/TM—2013-217822/PART2 44

Figure 63.—Load versus minimum principal strain plot for Panel B-2 at gages 11 and 12.

Table IX shows that the first strain reversal occurred at the location of gages 13 and 14, located at the 

center of the right edge of the panel, at a load of 70,233 lb for Panel B-1 and at gages 9 and 10 at 

67,863 lb for Panel B-2. Loads corresponding to all strain gage locations are tabulated with the 

experimental values in Table IX. Note that the experimental values differ slightly from those in Table VI.

This is attributed to minor variations in the methodologies used to reduce the data. Figure 64 to Figure 66

show that, in the corners, the axial O.D. (OML) panel strains went into compression up to the onset 

buckling, after which the strain increment reverses and the axial strain is alleviated as the load increases 

during post-buckling. As pointed out earlier in this paper, this local behavior (observed both 

experimentally and numerically) is consistent as the panel buckled towards the I.D. Note that, since the 

major curvature of the panel is biased towards the O.D., the analysis would predict buckling towards the 

O.D. if no geometric imperfections (or bow) were introduced into the model. Figure 67 shows the strain 

gage measurements at a panel inflection point at the 3⁄4 panel length location. Figure 68 to Figure 70 show 

that at the horizontal center of the panel, the I.D. (IML) panel strain goes into compression up to buckling 

and then reverses as the load increases during post-buckling. The results from Figure 71 the lower 

inflection or 1⁄4 length location, match the results from Figure 67. The results in the lower corners from 

Figure 72 and Figure 73 match the results from the upper corners in Figure 65 and Figure 66, 

respectively. The error in the nonlinear analyses ranges from 4.17 to 17.3 percent for Panel B-1 and 1.39

to 6.87 percent for Panel B-2 (Table IX), which was not much of an improvement over the linear 

analyses.
NASA/TM—2013-217822/PART2 45

Figure 64.—Load versus minimum principal strain plot for gages 1 and 2, Panels B-1and B-2.
NASA/TM—2013-217822/PART2 46

Figure 65.—Load versus minimum principal strain plot for gages 3 and 4, Panels B-1and B-2.
NASA/TM—2013-217822/PART2 47

Figure 66.—Load versus minimum principal strain plot for gages 5 and 6, Panels B-1and B-2.
NASA/TM—2013-217822/PART2 48

Figure 67.—Load versus minimum principal strain plot for gages 7 and 8, Panels B-1and B-2.
NASA/TM—2013-217822/PART2 49

Figure 68.—Load versus minimum principal strain plot for gages 9 and 10, Panels B-1and B-2.
NASA/TM—2013-217822/PART2 50

Figure 69.—Load versus minimum principal strain plot for gages 11 and 12, Panels B-1and B-2.
NASA/TM—2013-217822/PART2 51

Figure 70.—Load versus minimum principal strain plot for gages 13 and 14, Panels B-1and B-2.
NASA/TM—2013-217822/PART2 52

Figure 71.—Load versus minimum principal strain plot for gages 15 and 16, Panels B-1and B-2.
NASA/TM—2013-217822/PART2 53

Figure 72.—Load versus minimum principal strain plot for gages 17 and 18, Panels B-1and B-2.
NASA/TM—2013-217822/PART2 54

Figure 73.—Load versus minimum principal strain plot for gages 19 and 20, Panels B-1and B-2.
NASA/TM—2013-217822/PART2 55

Since both panels exhibited the same qualitative response, displacement and strain contours are only 

presented here for Panel B-1. Figure 74 shows that the post-buckled, in-plane or longitudinal displacement 

photogrammetry results qualitatively compared well with the analytical predictions. In the ANSYS solid 

element model, the nodal displacements do not vary on the O.D. and I.D. surfaces, whereas, the test results 

showed some slight variation in displacement for the I.D. and O.D. surfaces due to the finite width of the 

panel. Figure 75 shows the evolution of the in-plane or longitudinal displacement, obtained from the 

numerical analysis, as the applied compressive load is increased. Figure 76 shows that the post-buckled, outof plane or radial, displacement also compared well qualitatively with the analytical predictions. Figure 77

shows that the out-of-plane displacement was negligible up to the load of 70,001 lb.

Figure 74.—Post-buckling Z (in-plane or longitudinal) displacement comparison

for Panel B-1.

Figure 75.—ANSYS solid FEM axial (Z-axis or longitudinal) displacement contour plots versus load for Panel B-1.
NASA/TM—2013-217822/PART2 56

Figure 76.—Post-buckling X (out-of-plane or radial) displacement 

comparison for Panel B-1.

Figure 77.—ANSYS solid FEM out-of-plane (X-axis or radial) displacement contour plots versus load for Panel B-1.

For the O.D. surface, Figure 78 shows that the post-buckled, minimum principal strain test results did 

not compare well with the analytical; however, both show most of the strain developing in the center of 

the panel. Like the out-of-plane displacement, the minimum principal strain (compressive) was uniform

up until the point of buckling, as shown in Figure 79. For the I.D. surface, Figure 80 shows that the 

minimum principal strain also did not compare perfectly, and shows the predicted progression of the 

minimum principal strain from the analysis. Figure 81 shows the minimum principal strain (compressive) 

on the I.D. surface was uniform up until the point of buckling. The minimum principal strain was the 
NASA/TM—2013-217822/PART2 57

primary strain in the buckling test. The magnitudes of the maximum principal strains were very low, thus 

slight discrepancies between the analysis and experiment are exacerbated. The I.D. minimum principal

strains in Figure 81 show the asymmetry in the ANSYS solid FEM. Again this was due to the scaled 

geometric imperfections superimposed from the linear buckling modes.

Figure 78.—Post-buckling O.D. minimum principal

(Z-axis or longitudinal) strain comparison for Panel 

B-1.

Figure 79.—ANSYS solid FEM, O.D. minimum principal strain (z-axis or longitudinal) for Panel B-1.
NASA/TM—2013-217822/PART2 58

Figure 80.—Post-buckling I.D. minimum principal (Z-axis 

or longitudinal) strain comparison for Panel B-1.

Figure 81.—ANSYS solid FEM, I.D. minimum principal strain (z-axis or longitudinal) for Panel B-1.
NASA/TM—2013-217822/PART2 59

6.0 Conclusion

Experimental and analytical results have been presented pertaining to the buckling of 3- by 5-ft, 

curved, sandwich panels: Panel B-1 and Panel B-2 (see Table I). The panel was composed of a 1.125-in. 

thick aluminum honeycomb core and 6-ply, quasi-isotropic, in-autoclave cured, IM7/977-3, laminated 

composite facesheets cut from a 1/16th arc segment of a 10 m barrel. Experimental and modeling success 

was evaluated using specifically defined criteria. Additionally, various parametric studies were performed 

to determine the impact of manufacturing defects, and modeling techniques.

In Section 1.2, the experimental success criteria were described, all of which were met. Namely, all 

critical instrumentation was fully operational during the test, loads were applied as described in this 

document, and the maximum attained load and all associated data were recorded and saved. Additionally, 

the modeling success criteria, described in Section 1.4 were also achieved: the buckling loads were

predicted within 10 percent (success required predictions within 20 percent), the buckling mode/direction

and location was predicted correctly, and the local strain fields correlated well with visual imaging data 

measured during the experiment.

Both linear eigenvalue and geometrically nonlinear analyses were performed using a variety of 

commercially available FEM software tools to predict the buckling load of the honeycomb sandwich 

panel. The linear eigenvalue predictions fell within ~11 percent of the experimental buckling loads.

Surface imperfection measurements were introduced into the FE model through swept bows, and 

geometrically non-linear analyses were utilized to predict the buckling loads via progressive collapse 

simulations. The simulations yielded buckling load predictions within ~9 percent of the experimental 

load. Furthermore, the direction of buckling (towards the I.D.) was predicted correctly, which was a direct 

consequence of including the measured geometric imperfections in the model. Full field displacement and 

strain measurements predicted with the nonlinear analysis also corresponded well qualitatively with 

experimental VIC data. Finally, linear strength analyses were completed at the buckling load, and they 

ensured that the predicted panel failure was driven by stiffness (i.e., buckling), not strength, as was

observed in test.

A sensitivity study was enacted to determine the influence of geometric imperfections on the overall 

buckling behavior of the panel. Generic, arc-shaped bows were introduced into the models and used to 

represent the geometric imperfections. The magnitude of the largest deflection point was varied from 

0.010 to 0.040 in. towards the I.D. It was discovered that the magnitude of the bow did not alter the 

stiffness of the panel but moderately influenced the buckling load and buckling direction. Applying a bow 

with a magnitude less than 0.017 in. resulted in buckling towards the O.D., or the direction of major 

curvature, whereas, including a bow with a magnitude 0.017 in. and higher led to buckling towards the 

I.D. (as observed in the experiment). The maximum buckling load was achieved at the transition point 

when the magnitude of the bow was 0.017 in. The buckling load would increase as the magnitude of the 

bow was increased up to this point; however, increasing the bow beyond 0.01700 in. yielded a decreasing 

buckling load.

An additional sensitivity study was carried out to investigate the effects of fiber misalignment on the 

panel response. Both panel stiffness and buckling load were found to be sensitive to small changes (5°) in 

the orientation of the 60° plies. Moreover, if manufacturing tolerances are defined, a fiber misalignment 

study can be used to bound the numerical predictions. The effects of load eccentricity was also 

investigated and determined to have a negligible effect on the overall buckling of the panel. Additional 

studies could be performed to look at the sensitivity of the analysis to facesheet and honeycomb core 

properties, as well as the panel dimensions because there is inherently some variation in the 

measurements.

It can be concluded that, a good buckling load prediction was achieved utilizing shell-based linear 

eigenvalue analysis in conjunction with nominal (perfect) panel geometry. This prediction was improved 

by utilizing a more sophisticated, geometrically nonlinear, progressive collapse analysis that incorporated 

measured geometric imperfections from the panel. Furthermore, sensitivity studies were used to quantify 

the effects of possible manufacturing defects on the performance of the panel. Although the results of 
NASA/TM—2013-217822/PART2 60

these studies cannot be directly applied to obtain better estimates of the buckling loads (beyond 

eigenvalue analysis) of full cylinders or larger cylinder segments (as the buckling modes and imperfection 

sensitivities are different for these different geometries), the practices presented here can be used to 

determine the same sensitivities of these other structures to similar imperfections. In the future, such 

studies may lead to more comprehensive linear bucking knockdown factors for cylindrical shells that 

consider the impact and degree of different imperfections or defects separately (Haynie et al., 2012; 

Hilburger, 2012; Kriegesmann et al., 2012). Furthermore, these sensitivity studies can be utilized to arrive 

at critical manufacturing tolerances.

References

ANSYS Mechanical Application User's Guide, Release 14.0, 2011 SAS IP, Inc.

Hause, T., Johnson, T. E., Librescu, L., Effect of face-sheet anisotropy on buckling and postbuckling of 

sandwich plates, Journal of Spacecraft and Rockets, 37(3), pp. 331-341, 2000.

Hause, T., Librescu, L., Johnson, T. F., Non-linear response of geometrically imperfect sandwich curved 

panels under thermomechanical loading, International Journal of Non-Linear Mechanics, 33(6), pp. 

1039-1059, 1998.

Haynie, W.T., Hilburger, M.W., Bogge, M., Maspoli, M. Benedikt, K., Validation of lower-bound 

estimates for compression-loaded cylindrical shells, 53rd AIAA/ASME/ASCE/AHS/ASC Structures, 

Structural Dynamics, and Materials Conference, 23-26 Apr., Honolulu, HI, 2012.

Hilburger, M.W., Developing the next generation shell buckling design factors and technologies, 53rd 

AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, 23-26 

Apr., Honolulu, HI, 2012.

Hilburger, M.W., Nemeth, M.P., Starnes, J.H., Jr., Nonlinear and buckling behavior of curved panels 

subjected to combined loads, 42nd AIAA/ASME/ASCE/AHS Structures, Structural Dynamics and 

Materials Conference and Exhibit, 16-19 Apr., Seattle, WA, 2001.

Hilburger, M.W., Starnes, J.H., Jr., Effects of imperfections on the buckling response of compressionloaded composite shells, International Journal of Non-Linear Mechanics, 37, pp. 623-643, 2002.

Hong, C.S., Jun S.M., Buckling behavior of laminated composite cylindrical panel with initial 

imperfections, Winter Annual Meeting of the American Society of Mechanical Engineers, cosponsored by Pressure Vessels and Piping Division & Aerospace Division, ASME, San Francisco, 

CA, Dec. 10-15, 1989, PVP-Vol. 183, AD-Vol. 18.

HyperSizer Structural Sizing Software, Collier Research Corp., Newport News, VA, 

www.HyperSizer.com, 2012.

Jones, R.M., Mechanics of Composite Materials, 2nd Edition, Taylor & Francis, Inc., Philadelphia, PA, 

1999.

Kellas, S., Lerch, B., Wilmoth, N., Mechanical characterization of in- and out-of-autoclave cured 

composite panels for large launch vehicles, SAMPE 2012, Baltimore, Maryland, May 21-24, 2012.

Kriegesmann, B., Hilburger, M. W., Rolfes, R., The effects of geometric and loading imperfections on the 

response and lower-bound buckling load of a compression-loaded cylindrical shell, 53rd 

AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, 23-26 

Apr., Honolulu, HI, 2012.

Ley, R.P., Lin, W., Mbanefo, U., Facesheet wrinkling in sandwich structures, NASA/CR—1999-208994, 

1999.

Lockheed Martin, Orion Materials and Design Allowables, Rev. D, 22 Sept, 2010.

Lynch, C., Murphy, A., Price, M., Gibson, A., The computational post buckling analysis of fuselage 

stiffened panels loaded in compression, Thin-Walled Structures, 42, pp. 1445-1464, 2004.

Myers, D.E., Pineda, E.J., Zalewski, B.F., Kosareo D.N., Kellas, S., Buckling testing and analysis of 

honeycomb sandwich panel arc segments of a full-scale fairing barrel – Part 1: 8-ply in-autoclave 

facesheets, NASA/TM—2013-217822, 2013
NASA/TM—2013-217822/PART2 61

Schultz, M.R., Nemeth, M.P., Buckling imperfection sensitivity of axially compressed orthotropic 

cylinders, 51st AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials 

Conference, 12-15 Apr., Orlando, FL, 2010.

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NASA/TM—2013-217822/PART2 63

Appendix.—Acronyms

CDMP Composite Manufacturing Demonstration Panel

CoEx Composites for Exploration

DCDT direct-current displacement transducer

FEA finite element analysis

FEM finite element method

IA in-autoclave

I.D. inner diameter

IML inside mold line

IR infrared

ITAR International Traffic in Arms Regulations

LaRC NASA Langley Research Center

MTP Manufacturing Test Panel

NDE non-destructive evaluation

O.D. outer diameter

OML outside mold line

OOA out-of-autoclave

VIC visual image correlation

3-D three-dimensional