September 2011 

NASA/TP–2011-217178 

Design, Optimization and Evaluation of 

Integrally Stiffened Al 7050 Panel with Curved 

Stiffeners 

Wesley C. H. Slemp 

Virginia Polytechnic Institute and State University, Blacksburg, Virginia 

R. Keith Bird 

Langley Research Center, Hampton, Virginia 

Rakesh K. Kapania 

Virginia Polytechnic Institute and State University, Blacksburg, Virginia 

David Havens, Ashley Norris, and Robert Olliffe 

Lockheed Martin Aeronautics Company, Marietta, Georgia 
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September 2011 

NASA/TP–2011-217178 

Design, Optimization and Evaluation of 

Integrally Stiffened Al 7050 Panel with Curved 

Stiffeners 

Wesley C. H. Slemp 

Virginia Polytechnic Institute and State University, Blacksburg, Virginia 

R. Keith Bird 

Langley Research Center, Hampton, Virginia 

Rakesh K. Kapania 

Virginia Polytechnic Institute and State University, Blacksburg, Virginia 

David Havens, Ashley Norris, and Robert Olliffe 

Lockheed Martin Aeronautics Company, Marietta, Georgia 
Available from: 

NASA Center for AeroSpace Information 

7115 Standard Drive 

Hanover, MD 21076-1320 

443-757-5802 

Acknowledgments 

The work presented here was funded under NASA Subsonic Fixed Wing Hybrid Body 

Technologies NRA (NASA NN L08AA02C) with Ms. Karen M. Brown Taminger as the API 

and Ms. Cynthia Lach as the COTR. We are thankful to both Ms. Taminger and Ms. Lach for 

their suggestions. The authors would like to thank Mr. John Barnes and Dr. Steve Englestad, 

both of Lockheed Martin Aeronautics Company of Marietta, GA, for technical discussions. The 

tests that were conducted at NASA Langley Research Center were sponsored by the Subsonic 

Fixed Wing project of the Aeronautics Research Mission Directorate. The bulk of this paper was 

previously published in the AIAA Journal of Aircraft. Appendix C was added to create the 

current publication to provide a complete archive of the load-strain curves and load-displacement 

curves for each strain gage and displacement measurement location. 

The use of trademarks or names of manufacturers in this report is for accurate reporting and does not 

constitute an official endorsement, either expressed or implied, of such products or manufacturers by the 

National Aeronautics and Space Administration. 
1 

Abstract 

A curvilinear stiffened panel was designed, manufactured, and tested at the NASA 

Langley Research Center in the Combined Load Test Fixture. The panel was optimized 

for minimum mass subjected to constraints on buckling load, yielding, and crippling or 

local stiffener failure using a new analysis tool named EBF3PanelOpt. The panel was 

designed for a combined compression-shear loading configuration that is a realistic load 

case for a typical aircraft wing panel. The panel was loaded beyond buckling and strains 

and out-of-plane displacements were extracted from a total of 32 strain gages and 5 

linear variable displacement transducers. The VIC-3D system was utilized to obtain full 

field displacements/strains in the lower half of the stiffened side of the panel. The 

experimental data were compared with the strains and out-of-plane deflections from a 

high fidelity nonlinear finite element analysis. The experimental data were also 

compared with linear elastic finite element results of the panel/test-fixture assembly. 

The numerical results indicated that the panel buckles at the linearly elastic buckling 

eigenvalue predicted for the panel/test-fixture assembly. The out-of-plane displacement 

measured by the VIC-3D system compared well both qualitatively and quantitatively with 

the nonlinear finite element solution in the post-buckling regime. Furthermore, the 

experimental strains prior to buckling compared well with both the linear and nonlinear 

finite element model. For the post-buckling regime, the nonlinear model compared well 

at some locations and poorly at others. 

1 Introduction 

Topology optimization methods for continuum structures have increased in popularity in recent 

years. With these approaches, both two and three dimensional optimal solid designs can be obtained 

without the traditional trial and error decision making process that design engineers have used for 

decades. Bendsoe and Kikuchi developed the theoretical foundation for the topology optimization 

methodology in 1988 (ref.1). The first commercial software was developed and released in 1994 and 

utilized the topology optimization approach (ref.2). 

A critical limitation of the topology optimization approach is its computational intensity. The 

Density Method uses the density of each element as the design variable (ref. 3). Thus, the method can be 

impractical for everyday design. Furthermore, the manufacturability of the optimal design is not 

guaranteed. The design engineer must transfer the optimal design solution to a practical solution. In 

addition, difficulties arise when imposing constraints on buckling (ref. 4). The problem arises from 

numerical difficulties in the presence of low material density. To overcome this difficulty, a two step 

optimization was proposed using topology optimization to minimize compliance while placing a 

constraint on mass (ref. 4). In the second step, a size optimization was performed on the resulting 

topology. 

Stiffened plate or shell structures are widely used in the aerospace, automobile and ship 

industries. Optimization of isogrid-stiffened panels and shells has been performed for many years. A 

software tool (PANDA2) was developed to obtain minimum weight designs for metallic or composite 

panels with isogrid stiffeners subjected to buckling constraints (ref. 5). Optimization of the size and 

placement of isogrids of straight stiffeners for buckling load and natural frequency have been studied (ref. 

6). Because the geometry is mostly defined a priori, the number of design variables is small relative to 

topology optimization. Traditional aircraft structures have straight stiffening members like spars, ribs, 
2 

stringers, longerons and stiffeners of uniform thicknesses which are riveted to fuselage/wing panels using 

to traditional manufacturing process. However, recent new metallic manufacturing processes such as 

friction stir welding (FSW) (ref. 7) and electron beam freeform fabrication (EBF3

) (ref. 8) allow the 

design engineer to consider a more broad design space. Moreover, the topology optimization method 

often results in curved geometries (e.g., the fillet problem in ref. 1). Therefore, considering a design 

space in which stiffeners can take a curvilinear profile rather than linear may result in a reduction in mass 

for the same structural design requirements. 

The benefits of unitized structures can be summarized as (a) reduced part count, manufacturing 

cycle time, and fabrication cost; (b) added design flexibility, weight savings, inspectability, and resistance 

to fatigue and corrosion; (c) enhanced automation, improved ergonomics and reduced work; and (d) 

increased determinant assembly opportunities, improved fit and reduced rework (ref. 9). Experts also 

pointed out that the use of unitized structure is expected to grow exponentially by the year 2020 (ref. 10). 

An integrally stiffened fuselage concept was developed in which analyses and experimental tests 

demonstrated equal or better performance than conventional designs with regard to weight and structural 

integrity, while achieving a significant reduction in manufacturing cost (ref. 11). 

A new analysis tool, EBF3PanelOpt (ref. 12-15), is being developed for design and optimization 

of complex multifunctional aircraft structural concepts with application toward pressurized non-circular 

fuselage structures within hybrid wing/body vehicles where complex structural load cases are not well 

characterized using current design databases. EBF3PanelOpt is a tool for optimization of stiffened plate 

and shell structures in which stiffeners are not limited by traditional manufacturing techniques. Utilizing 

curved stiffeners broadens the design space without substantially adding to the computational cost of the 

optimization. While the tool is much more computationally efficient than topology optimization 

techniques in that there are very few design variables, the design space is much larger than traditional 

techniques that rely on linear stiffener grids. EBF3PanelOpt is being developed to exploit emerging 

additive manufacturing processes that offer the ability to efficiently fabricate complex structural 

configurations. The ultimate goal is to enhance aircraft performance and environmental responsibility 

through reductions in weight, emissions, and cabin noise, and to integrate functions such as acoustic 

damping, adaptive active aerodynamic controls, and aeroelastically tailored structures. 

The tool development is being conducted under a NASA Research Announcement (NRA) 

contract at Virginia Polytechnic Institute and State University with support and aircraft manufacturing 

expertise provided through a subcontract with Lockheed Martin Aeronautics Company. The work is 

complementary to electron beam freeform fabrication (EBF3

) additive manufacturing research activities at 

NASA Langley Research Center (LaRC). 

This paper describes the initial phases of development of the EBF3PanelOpt tool. The tool was 

used to design and optimize a baseline structural panel with curved stiffeners. In the case of this baseline 

panel, the optimization was based on minimum mass subjected to constraints on buckling load, yielding, 

and crippling or local stiffener failure under a combination of compression and shear loads to evaluate the 

capability of the tool to handle complex loading conditions. The optimized panel design was used to 

fabricate an integrally-machined test panel using aluminum alloy 7075-T851. The panel was tested in the 

NASA LaRC Combined Loads Test Fixture (CLTF) (ref. 16) under a combined compression-shear 

loading case. The test results were compared against a linear finite element analysis (FEA) of the test 

fixture/panel assembly through which EBF3PanelOpt obtains the optimization constraints and a 

conventional high fidelity nonlinear FEA. The test results and analyses were used to assess the strengths 
3 

and weaknesses of the EBF3PanelOpt tool for the next iteration of its development as a tool for structural 

panel design and optimization. 

2 EBF3PanelOpt Framework 

A framework has been developed by researchers at Virginia Polytechnic Institute and State 

University (Virginia Tech) for design optimization of curvilinear stiffened panels under in-plane and 

transverse loading (ref.12-15). The framework named EBF3PanelOpt is an object-oriented script written 

in PYTHON that interfaces with MSC.Patran, and MSC.Nastran to perform finite element analysis on a 

panel with curvilinear, blade-type stiffeners and returns the mass of the panel and constraints on yielding, 

buckling, and crippling or local failure of the panel. 

The EBF3PanelOpt script obtains design data from an optimizer software such as VisualDoc, 

DAKOTA, or MAMOP and translates the design data into an MSC.Patran session (.ses) file which 

generates the appropriate parameterized geometry, the FE mesh (.bdf file), and an input file (.dat) to 

MSC.Nastran. A schematic of the EBF3PanelOpt Framework may be seen in figure 1. The script calls 

Nastran to perform the FEA and waits for the analysis to complete. After completion of the FEA, the 

script reads the results from the .f06 file and calculates the responses. The responses include the mass, 

the buckling constraint, Von Mises stress constraint, and the local crippling constraint. The buckling 

constraint is calculated by: 

1 1

0



 (1) 

where λ0 is the buckling eigenvalue. The Von Mises stress constraint is calculated by: 

1

y

vm





(2) 

where σvm is the Von Mises stress and σy is the material yield strength. The Von Mises stress constraint is 

imposed using the Kreisselmeir-Steinhauser criteria for constraint aggregation as described in (ref. 2). 

The crippling constraint was calculated by: 

1

cc

stiff

F



(3) 

where σstiff was taken as the minimum principal stress in the stiffener and where Fcc is the maximum 

allowable stress in the stiffener given by: 



















	

	















	

	















 	

	















  



 1

/ , 0.61525/

0.61525

 1

/ , 0.61525

0.78387 0.78387

0.78387

t

b E

t

b E

t

b E

F

y y

y

y

y

cc

 







(4) 

where E is the Young’s modulus of the stiffener material, b is the stiffener height, t is the stiffener 

thickness. The maximum allowable stress formula, Eq. (4), was obtained from the plot given on page 444 

of reference 17. 
4 

Figure 1. Schematic of EBF3PanelOpt Framework. 

2.1 Parametric Modeling of the Panel 

A key ingredient to EBF3PanelOpt is the ability to specify the geometry in a parametric fashion 

such that the optimizer fully specifies the panel shape and size by a discrete number of design variables. 

Size quantities such as panel thickness, stiffener thickness, and stiffener height are used as design 

variables to define the geometry. The parameterization of the stiffener shape and position merits some 

clarification. In figure 2, the design variables identifying the shape and position of the stiffener are 

indicated. Note that the beginning and end points of each stiffener are indicated by design variables x1 to 

x4, while the shapes of the stiffeners are determined by the angle to the center point (x5 and x6). Because 

rational B-splines are used to determine the stiffener curves, the stiffeners always remain within the panel 

interior as long as the center point remains in the panel interior. 

A total of 11 design variables fully define the panel geometry: variables x1 – x6 are shown in 

figure 2 and define the stiffener location and shape, variables x7 and x8 are the heights of the two 

stiffeners, variables x9 and x10 are the thicknesses of the stiffeners, and x11 is the panel thickness. 

3 Combined Loads Test Fixture 

The Combined Loads Test Fixture (CLTF) was developed by researchers at NASA LaRC to 

perform combined compression-shear load tests on 24-inch x 28-inch panels. A detailed description of 

the design, assembly, and operation of the test fixture can be found in reference 16. Figure 3 shows the 

test system without the panel installed. Upper and lower L-shaped shear frames are bolted to the upper 

and lower compression platens of a 300-kip capacity screw-driven compression test system The lower 

shear frame is attached to a hydraulic ram to apply the shear loads. The bottom of the lower shear frame 

rests on roller guides to allow lateral motion. A steel picture frame-type support is attached to the test 

specimen via a double row of fasteners (see figure 4). The picture frame edges are pinned together at the 

corners to allow in-plane rotation. This support provides the clamped boundary condition to the 
5 

aluminum tabs while allowing the panel to deform to a quadrilateral. After installation of the test panel 

the CLTF, shear load bars (not shown in figure 3) are attached across the upper and lower shear frames to 

produce a self-reacting shear load.

Figure 2. Design variables identifying the stiffener shape and position. 

Upper 

shear 

fixture

Compression drive column

Lower 

shear 

fixture

Upper 

platen

Lower 

platen

Roller 

guide

Shear 

load 

hydraulic 

ram

Figure 3. Compression-shear test system without test panel installed. 
6 

Figure 4. Picture frame support mounted on a generic test panel. 

4 Panel Design and Optimization 

A 24-inch x 28-inch curvilinear stiffened panel was designed using the EBF3PanelOpt software 

and VisualDoc Optimization software. The particle swarm optimization (PSO) was used to estimate the 

global minimum mass while satisfying constraints on buckling, crippling, and yielding. The VisualDoc 

optimization parameters for the PSO algorithm used for the analysis are provided in table 1. For the 

details regarding the definition of the parameters, please see (ref. 18). 

Table 1. VisualDoc Optimization parameters for PSO optimization (ref. 18). 

Inertia weight parameter 1.40 

Local optimum trust parameter, C1 1.50 

Global optimum trust parameter, C2 2.50 

Number of particles 20 

Maximum number of iterations 70 

Minimum number of iterations 5 

Absolute objective convergence 10-6 

Relative objective convergence 10-3

Absolute design variable convergence 10-6

Relative design variable convergence 10-3

To assess the ability of the tool to design panels for complex loading conditions, a combined 

compression-shear loading condition was selected. The overall panel size was selected based on the 

capability of the CLTF test system. The panel was designed for a limit load of 42 kips in compression 

and 9.7 kips in shear (4.35 lb compression per 1 lb shear) against buckling, crippling, and yielding. The 

material properties of the aluminum alloy used in the panel optimization are shown in table 2. Table 3 

lists the optimal design variables along with the lower and upper bounds placed on each variable during 

the optimization. 
7 

Table 2. Material properties for Al 7050-T851 used for the panel optimization with EBF3PanelOpt. 

Young’s modulus, [Msi] 10.6 

Poisson’s ratio 0.33 

Yield stress, [ksi] 68 

Table 3. Design variable bounds and optimal values. 

Lower 

bound 

Upper 

bound 

Optimized 

design 

Stiffener 1 starting point, [inch] 28.4 51.6 43.9 

Stiffener 1 ending point, [inch] 80.4 103.6 89.5 

Stiffener 2 starting point, [inch] 28.4 51.6 37.0 

Stiffener 2 ending point, [inch] 80.4 103.6 95.7 

Stiffener 1 angle to midpoint, [degree] -10.0 10.0 1.92 

Stiffener 2 angle to midpoint, [degree] -10.0 10.0 1.95 

Height of stiffener 1, [inch] 0.394 1.969 0.769 

Height of stiffener 2, [inch] 0.394 1.969 0.826 

Thickness of stiffener 1, [inch] 0.039 0.315 0.123 

Thickness of stiffener 2, [inch] 0.039 0.315 0.129 

Thickness of the panel, [inch] 0.039 0.158 0.104 

4.1 Test Fixture Interface 

Early study of the CLTF indicated that it only transmitted about 35% of the compression load into 

the panel while 100% of the shear load was transmitted to the panel (ref. 12). Therefore, to facilitate the 

loading and boundary conditions as closely as possible to those imposed by the CLTF, a reduced gridpoint interaction model of the test fixture/panel interface was utilized within the EBF3PanelOpt

framework to apply the loading and boundary conditions during optimization. The reduced model via a 

superelement was developed from a detailed nonlinear finite element model of the fixture developed by 

Lockheed Martin which may be seen in figure 5. 

Figure 5. Detailed finite element model of test fixture/curvilinear stiffened panel assembly. 
8 

4.2 Nonlinear finite element model 

A nonlinear finite element model (FEM) of the CLTF was developed by Lockheed Martin 

Aeronautics Company (see figure 5). The FEM includes both elastic-plastic (for the aluminum) and 

geometric nonlinearity and thus is suitable for the post-buckling analysis. The test fixture FE model was 

developed to interface to a panel model generated by the EBF3PanelOpt. The test fixture was modeled 

using a total of 44,186 shell, beam, and gap elements. Shell elements were used to model the steel test 

fixture upper and lower L-arms of the CLTF as well as the picture frame support secured to the panel (see 

figure 6). The test fixture is constructed predominately from 15-5 (or 17-4) H1025 stainless steel (ref. 

16). The material properties used for the test fixture FEM are given in table 4 (ref. 19). A linear stressstrain relation was used for the test fixture as the fixture's thickness precludes significant nonlinearity 

therein. 

The compressive load is introduced into a single node above the upper L-arm and applied to the 

upper L-arm using a multipoint constraint (see figure 5). The shear load is introduced in a similar manner 

to lower L-arm. In each case, two concentric nodes attached by zero length spring elements were used to 

provide the appropriate stiffness to the load introduction location. The stiffnesses of these springs were 

chosen by correlating data from previous Lockheed Martin tests in the CLTF. 

Gap elements were used in the FEM to numerically model the “rollers” on which the lower L-arm 

sits. The gap elements allow the test fixture to pull off the rollers while providing a very large stiffness to 

prevent penetration. The bottom of the test fixture was constrained to prevent out-of-plane deflection 

using two parallel rows of single point constraints applied to the exterior nodes on both sides of the lower 

L-arm. The shear load was reacted using single point constraints applied to the bolt locations on the top 

L-arm (see figure 6). 

The aluminum test panel was modeled using shell elements. The test panel FEM model was 

provided by the EBF3PanelOpt analysis software and modified to include the elastic-plastic material 

model (see figure 7). Initial eccentricity of the panel was provided by moving the nodes in the direction 

of the first buckling mode shape (positive towards the stiffeners) by 0.000104 inch, thus producing a 

slightly imperfect panel to help guide the geometric nonlinear analysis off the trivial solution path. The 

adhesively bonded steel tabs were modeled using shell elements with an elastic-plastic material law. The 

stress-strain curve used for the adhesively bonded steel tabs is shown in figure 7. Zero-length spring 

elements with stiffness of 41,250 lb/inch were used to model the adhesive bond. The FEM of the test 

panel assembly can be seen in figure 8. 

The double row of fasteners, the four corner fasteners, and the bolts though which the shear load 

was introduced were modeled using beam elements with appropriate material and geometric properties 

assigned. The fasteners are shown in figure 6. 
9 

Figure 6. Steel shell elements in the nonlinear test fixture model and the single point constraints 

applied to the test fixture model. 

Table 4. Material properties (ref. 19) used in the nonlinear finite element model. 

15-5 (or 17-4) H1025 Stainless Steel Al 7050 

Young’s Modulus, E [ksi] 29,200 10,600 

Poisson’s ratio, ν 0.32 0.33 

Yield Stress, [ksi] 152.9 59.4 

Figure 7. Elastic-plastic material model for the steel test fixture and the aluminum panel. (Strain 

is presented in units of inch/inch.) 
10 

Figure 8. Model of Al 7050 panel with bonded steel tabs modeled using linear spring elements. 

Initial numerical experiments with the nonlinear test fixture model indicated that the FEM of the 

test fixture interface used by EBF3PanelOpt incorrectly predicted the buckling load by a substantial 

amount. The correlated test fixture model was used to extract a grid point interaction model superelement 

which would better facilitate the load introduction to the panel in EBF3PanelOpt. Furthermore, the 

adhesively bonded steel tabs were modeled in the version of EBF3PanelOpt used to design the panel 

using concentric elements sharing nodes. While the test fixture had geometric spaces between the tabs 

along the vertical edges, the model in EBF3PanelOpt had no spaces. Therefore, the steel tabs carried 

much of the load and resulted in a substantially higher predicted buckling load. When the modeling 

discrepancy was noticed, the panel model/test fixture interface in EBF3PanelOpt was modified to 

completely remove the steel tabs. The design limit loads of 42 kips compression and 9.7 kips in shear 

(4.35 lb compression per 1 lb shear) were modified, noticing that the new model predicted the onset of 

buckling at a load of 25 kips in compression and 5.2 kips in shear (4.8 lb compression per 1 lb shear). 

The test plan was modified to load at the corrected load ratio of 4.8 lb compression per 1 lb shear. 

5 Panel Manufacturing 

Prior to manufacturing the baseline optimized panel, a smaller scale risk-reduction panel was 

constructed which featured variable height curvilinear T-stiffeners (see figure 9). This panel was 

produced to validate the manufacturing process for integrally machined, thin-skinned, stiffened panels. 

The size of this panel was approximately 16-inch by 16-inch with 1.5-inch tall stiffeners at their peak 

height. Several manufacturability design features were reexamined after coordinating with the machine 

shop and receiving quotes including fillet radii and manufacturability stiffness to height ratio. The alloy 

chosen for the initial manufacturability and test panel was Al 7050 heat treated to a T-7451 condition. 

The material was received as 2-inch thick plate stock and high speed machined to the specified geometry. 

The completed panel was inspected to insure that the required tolerances were satisfied and that the panel 

remained flat on the non-stiffened side. All tolerances were met. 
11 

Figure 9. Illustration of risk reduction coupon manufactured by Lockheed Martin to verify the 

integral machining process. 

Once the risk reduction panel was completed, the solid model of the baseline curvilinear stiffened 

panel was converted to a detailed CAD file in CATIA V5 by Lockheed Martin. The geometry was 

modified to include fillets at the panel/stiffener intersections. The 24-inch x 28-inch panel was extended 

to include 2.94 inch x 24 inch tabs along the top and bottom edges with the bolt pattern specified by the 

CLTF (see figure 10). 2.25 inch x 28 inch tabs were also included along the left and right edge of the 

panel. While the panel had thickness of 0.104 inch, the tabs were required to be 0.25 inch to facilitate the 

interface between the CLTF and panel. A thickness taper was included to reduce the thickness from 0.25 

inch to 0.104 inch. The geometry was also modified to include stiffener run-outs at the ends. 

The baseline optimized test article was then machined. The test panel used blade stiffeners as 

opposed to the T-stiffeners used in the risk reduction panel. This panel was also machined from 2-inch 

thick plate stock and all required tolerances were met.

After the panel was machined and inspected, 4340 steel tabs conforming to the NASA combined 

loading fixture drawings (ref. 16) were adhesively bonded using Hysol EA9394 with 0.005-inch diameter 

glass micro-balloons added for bond-line thickness control. These bonds were cured at room temperature 

to prevent any residual thermal expansion stresses at the bond-line. The panel was then crated and 

shipped to NASA LaRC for testing. The completed panel is shown in figure 10. 
12 

Figure 10. Picture of the Al 7050 test panel with bonded steel tabs. 

6 Combined Load Compression-Shear Test 

A combined load compression-shear test was conducted at NASA LaRC on the panel using the 

CLTF. Linear variable displacement transducers (LVDTs) were attached to three corners of the top 

compression platen to measure panel end shortening and one LVDT was attached to the shear fixture to 

measure shear displacement. 

A total of 32 strain gages were attached to the panel. Six of the gages were 0°/45°/90° rosettes 

and 26 of the gages were uniaxial gages aligned parallel to the compression load direction. A description 

of the strain gage locations is provided in appendix A. The stiffened side of the panel was spray-painted 

with a speckled pattern to facilitate strain and displacement measurements using a VIC-3D automated 

stereophotogrammetic technique. The panel was installed into the CLTF. The lateral shear load 

hydraulic ram was attached to the CLTF's lower shear frame. The LVDT support brackets and 5 LVDTs 
13 

were installed into the test system and attached to the smooth side of the panel to measure out-of-plane 

displacement. A description of these LVDT locations is provided in appendix B. 

The data acquisition system was configured to scan and record all of the instrumentation at a rate 

of 1 scan per second. The load, displacements, and select strain gages were monitored on a real-time 

display during the test. The VIC-3D system was configured to obtain full-field stereophotogrammetic 

displacement/strain measurements on the lower half of stiffened side of panel. In addition to the VIC-3D 

cameras, a video camera was set up to record panel behavior during the test. 

Figure 11 shows the test system with the panel installed and ready for testing. Figure 12 shows 

the stiffened side and flat side of the panel in the test system. The test system was configured to apply 

compression load and shear load simultaneously at a compression-shear load ratio of 4.8. The 

compression load rate of 4,000 lbs/min was used. Two preliminary tests were conducted up to a 

maximum compression load of 5,000 lbs to insure that all of the instrumentation was operational and that 

the compression-shear load ratio was correct. The data acquisition and VIC-3D systems were started and 

compression/shear load application was initiated. The panel was loaded to approximately 60,000 lbs in 

compression at which point there was a sharp reduction in load and a loud noise. It was assumed that this 

was a panel structural failure event. The test was stopped and the load was removed from the panel. 

Following the load removal, it was discovered that the panel had not been permanently deformed and that 

the load drop-off and noise events were associated with several of the steel tabs debonding from the panel 

(see figure 13). 

Self-reacting

shear 

load 

bar

Shear 

load 

hydraulic 

ram

Test

panel 

Combined

Load

test

fixture

Figure 11. Compression-shear test system with test panel installed. 
14 

Figure 12. Stiffened side and flat side of test panel in compression-shear test system. 

Figure 13. Post-test photograph of test panel with debonded steel tabs. 

7 Comparison of Experimental and Analytical Results 

The test results (LVDT, strain gages, and out-of-plane displacement from the VIC-3D image 

correlation system) were compared with results from a nonlinear finite element model and the predicted 

linear response from the finite element model generated by the EBF3PanelOpt script with the revised test 

fixture/interface model. For all the results, the non-dimensional load factor was used to indicate the load 
15 

level during the proportionally loaded FEM and experiment. The load factor was defined as the ratio of 

applied load to linear buckling eigenvalue for the test fixture/panel model. The response of the complete 

set of 32 strain gages and the 5 LVDT out-of-plane displacement measurements are plotted against the 

load factor from the nonlinear finite element model, linear test fixture/panel assembly model and the 

experimental results in appendix C. 

Results obtained by the VIC-3D system were processed and plotted using TecPlot. The contours 

of measured out-of-plane deflections obtained by the VIC-3D system are compared against those 

predicted by the nonlinear FEA at load factors of 1.0 and 2.4 in figures 14 and 15, respectively. The 

results from the VIC-3D system provided contours over a limited panel surface with much of the data 

being removed because it was compromised by the presence of the stiffeners, the stiffener shadows, and 

strain gage wires. However, the figures indicate that at a load factor of 1.0, the panel experienced far less 

out-of-plane deflection than was predicted by the nonlinear finite element analysis. Nonetheless, the 

contours of deformation appear qualitatively similar in shape to the FEM predictions. The discrepancy 

between the measured and predicted deflection magnitude could be a product of less eccentricity in the 

panel than was artificially imposed in the analysis. 

(a) Contours of out-of-plane deflection from VIC-3D 

image correlation system 

(b) Contours of out-of-plane deflection from the 

nonlinear finite element model. 

Figure 14. Comparison of out-of-plane deflection from VIC-3D image correlation system at a load 

factor of 1.0. (Units for deflection contours are presented in inches.) 

At a load factor of 2.4 (figure 15), the contours of out-of-plane deflection obtained by the VIC-3D 

system compare well qualitatively and quantitatively with the results from the nonlinear FEA. The shape 

of the contours indicates that the global features of the post-buckled shape compare very well with the 

analysis. The center deflection of the panel is quantitatively more accurate than at a load factor of 1.0. 

0 .025 .05 .075 .1 .125 .15 .175 .2 .225 .25
16 

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5

(a) Contours of out-of-plane deflection from VIC-3D 

image correlation system 

(b) Contours of out-of-plane deflection from the 

nonlinear finite element model. 

Figure 15. Comparison of out-of-plane deflection from VIC-3D image correlation system at a load 

factor of 2.4. (Units for deflection contours are presented in inches.) 

The measured out-of-plane deflection was plotted against the normalized load factor in figure 16 

for LVDT 7 and in figure 17 for LVDT 9. The LVDT locations are summarized in appendix B. The 

results from the nonlinear finite element analysis and the results from the linear test fixture/panel 

assembly model are included for comparison. Note that the test results clearly indicate the panel initially 

buckled at a load factor near 1, indicated by a dramatic increase in deflection over a small range of load 

factor. In general, the deflection predicted by FEA is higher than the measured deflection. The deflection 

predicted by the linear test fixture/panel assembly model compares fairly well within the linear region. 

Results from the remaining three LVDTs are compared against the nonlinear finite element 

analysis results and the linear test fixture/panel assembly model results in appendix C. The trends are 

comparable to those presented in figures 16 and 17. 

The results from each of the 32 strain gages were plotted against the load factor in appendix C. 

The results from 0° strain gages 5A and 6A are compared in figure 18 and from 90° strain gages 5B and 

6B are compared in figure 19. Note that gages 5 and 6 are located just below the center of the panel on 

the stiffened and flat side of the panel, respectively (see table A1 and figure A1 in appendix A). Within 

the linear region, the predicted strain compares very well with that measured by the gages for the 0° 

gages. The response predicted by the linear test fixture/panel assembly model is indistinguishable from 

the measured strain; however, the post-buckled response of the nonlinear analysis is substantially 

different from the measured response. The strain on the flat side (gage 6A) of the panel compares very 

well; however, the finite element analysis predicts substantially greater bending than seen by the 

experiment. 
17 

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.0 0.5 1.0 1.5 2.0 2.5

Load Factor

Displacement (in)

Figure 16. Comparison of the test, nonlinear FEM, and the linear test fixture/panel assembly 

model responses for LVDT 7 (positive deflection is measured towards the stiffeners). 

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.0 0.5 1.0 1.5 2.0 2.5

Load Factor

Displacement (in)

Figure 17. Comparison of the test, nonlinear FEM, and the linear test fixture/panel assembly 

model responses for LVDT 9 (positive deflection is measured towards the stiffeners). 
18 

-0.0024

-0.0020

-0.0016

-0.0012

-0.0008

-0.0004

0.0000

0.0 0.5 1.0 1.5 2.0 2.5

Load Factor

Strain

Figure 18. Comparison of the test, nonlinear FEM, and the linear test fixture/panel assembly 

responses for axial strain gages 5A and 6A (εyy). (Strain is presented in units of 

inch/inch.) 

0.0000

0.0004

0.0008

0.0012

0.0016

0.0 0.5 1.0 1.5 2.0 2.5

Load Factor

Strain

Figure 19. Comparison of the test, nonlinear FEM, and the linear test fixture/panel assembly 

responses for strain gages 5B and 6B oriented perpendicular to the direction of the 

dominate compressive loading (εxx). (Strain is presented in units of inch/inch.) 
19 

For the strain gages 5B and 6B, the response is accurately predicted by both the nonlinear FEA 

and the linear test fixture/panel assembly model within the linear region. The measured response clearly 

indicates a buckle occurring at a load factor of 1. However, there is substantial discrepancy between the 

post-buckled response predicted by the FEA and measured by the strain gages. 

Data from the strain gage rosettes (5 and 6; A, B, and C) were used to obtain the shear strain at 

gages 5 and 6 by: 

  A B 2 C ( + ) - 2

1

     xy (5) 

The experimental shear strain was compared with the predicted responses from the nonlinear and 

linear FEAs in figure 20. Note that there is substantial discrepancy between the predicted and measured 

response. The predicted strain is almost twice that obtained from the strain gage rosette. 

-0.0012

-0.0010

-0.0008

-0.0006

-0.0004

-0.0002

0.0000

0 0.5 1 1.5 2 2.5

Load Factor

Strain

Figure 20. Comparison of the test, nonlinear FEM, and the linear test fixture/panel assembly 

responses for shear strain extracted from strain gages rosettes 5 and 6 (εxy). (Strain is 

presented in units of inch/inch.) 

Similar analyses were conducted for strain gage rosettes 21 and 22 located in the bottom right 

corner of the panel. In figure 21, the axial strain was plotted against the normalized load factor from the 

measured strain gage data, the nonlinear FEA, and the linear test fixture/panel assembly FEA. The figure 

indicates the response is accurately predicted by the FEA, even in the post-buckling region. 

The shear strain was obtained using the three components of strain from the strain gage rosettes 

with Eq. (5). The results were compared against the nonlinear FEA and linear test fixture/panel assembly 

model that is utilized by EBF3PanelOpt (see figure 22). The figure indicates a much closer correlation 

between the measured and predicted shear strain than was seen for gages 5 and 6. In the linear region, the 

linear model accurately predicts the shear strain. For the flat side of the panel (strain gage 22), the 
20 

nonlinear FEA and the test response are nearly indistinguishable. However, for the stiffened side of the 

panel (strain gage 21), the measured response is substantially different from the predicted response in the 

post buckling region. 

-0.007

-0.006

-0.005

-0.004

-0.003

-0.002

-0.001

0.000

0.001

0.002

0.003

0.0 0.5 1.0 1.5 2.0 2.5

Load Factor

Strain

Figure 21. Comparison of the test, nonlinear FEM, and the linear test fixture/panel assembly 

responses for axial strain gages 21A and 22A (εyy). (Strain is presented in units of 

in/in.) 

-0.0030

-0.0025

-0.0020

-0.0015

-0.0010

-0.0005

0.0000

0.0005

0.0010

0 0.5 1 1.5 2 2.5

Load Factor

Strain

Figure 22. Comparison of the test, nonlinear FEM, and the linear test fixture/panel assembly 

responses for shear strain extracted from strain gages rosettes 21 and 22 (εxy). (Strain 

is presented in units of in/in.) 
21 

8 Summary and Conclusions 

A new analysis tool, EBF3PanelOpt, has been developed for design and optimization of complex 

multifunctional aircraft structural concepts. The tool was used to design and optimize a baseline 

structural panel with curved stiffeners. The panel was optimized for minimum mass subjected to 

constraints on buckling load, yielding, and crippling or local stiffener failure. The panel was designed for 

a combined compression-shear loading configuration that is a realistic load case for a typical aircraft wing 

panel. The optimized panel design was used to fabricate an integrally-machined test panel using 

aluminum alloy 7075-T851. The panel was tested at NASA LaRC in the Combined Load Test Fixture 

under combined compression-shear loading. The test results were compared against analytical results 

obtained using MSC Nastran. Both a linear FEA which was generated by EBF3PanelOpt and a detailed 

nonlinear FEA were compared with the test results in an attempt to verify the accuracy of assumptions 

and modeling techniques utilized by the EBF3PanelOpt software. 

From the comparison of the numerical test results and the finite element analysis the following 

observations were made: 

 The panel buckled at the predicted linear buckling eigenvalue. Pre-test modifications to the test 

fixture FE modeling which interfaces with EBF3PanelOpt corrected the linear buckling 

eigenvalue . 

 Before buckling, the strains and deflections were accurately predicted by EBF3PanelOpt with the 

exception of the shear strain at the center of the panel. The shear strain in this region was overpredicted by a factor of 2. 

 The out-of-plane deflection measured by the VIC-3D image correlation system indicated good 

qualitative comparison between the FEA and the test results; however, the panel experienced 

substantially less out-of-plane deflection than predicted by the nonlinear FEA at a load factor of 

1.0. 

 Comparison of the post-buckled response to the nonlinear finite element model revealed 

substantial discrepancies. Gages located in the corners of the panel showed very accurate post 

buckling predictions by the FEA while the predictions for gages along the center line of the panel 

were substantially erroneous. 

It should be noted that it is not surprising that the post-buckling response was not predicted well 

by the analysis. The post-buckling response depends heavily on synergistic effects of modeling 

inaccuracies. Within the nonlinear finite element model, springs were used to introduce the load into the 

panel. The stiffness of these springs was tuned and correlated to previous test data. 

The accuracy of the predicted response before buckling is a substantial accomplishment and 

indicates that the information utilized by EBF3PanelOpt to predict the buckling, Von Mises and crippling 

constraints are accurate. 

Furthermore, this study has shown that it is critical for the user to correctly apply the loading and 

boundary conditions when using EBF3PanelOpt. For the current design, a superelement representing the 

test fixture was used to constrain the panel and apply the loading. This approach is limited to the test 

fixture and would require substantial changes to the EBF3PanelOpt script. EBF3PanelOpt currently also 

allows for uniform loading and uniform clamped or free edge boundary conditions. While this covers a 

variety of loading configurations, it is not generic. It is recommended that EBF3PanelOpt provide the 

most generality in applying the boundary conditions and loading. 
22 

9 References 

1. Bendsoe, M. and Kikuchi, N., “Generating Optimal Topologies in Optimal Design using a 

Homogenization Method,” Computer Methods in Applied Mechanics and Engineering, 71, pp. 197–

224, 1988. 

2. Schramm, U. and Zhou, M., “Recent Developments in the Commercial Implementation of Topology 

Optimization,” IUTAM Symposium on Topological Design Optimization of Structures, Machines 

and Materials: Solid Mechanics and Its Applications, Vol. 137, Part 6, 2006, pp. 239-248, DOI 

10.1007/1-4020-4752-5_24. 

3. Bendsoe, M. and Sigmund, O., Topology Optimization: Theory, Methods, and Applications. 

Springer-Verlag, Berlin, 2003. 

4. Schramm, U. and Zhou, M., Tang, P.S., and Harte, C., “Topology Layout of Structural Designs and 

Buckling,” 10th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference, Albany, 

New York, Aug. 30-1, 2004, AIAA-2004-4636. 

5. D. Bushnell, “PANDA2 — Program for Minimum Weight Design of Stiffened, Composite, Locally 

Buckled Panels,” Computers and Structures Vol. 25, 1987, pp. 469–605. 

6. W. Akl, A. El-Sabbagh, A. Baz, “Optimization of the Static and Dynamic Characteristics of Plates 

with Isogrid Stiffeners,” Finite Elements in Analysis and Design, Vol. 44, No. 8, May 2008, Pages 

513-523, DOI: 10.1016/j.finel.2008.01.015. 

7. Nicholas, E. D., “Developments in the Friction-Stir Welding of Metals,” ICAA-6: 6th International 

Conference on Aluminum Alloys, 1998. 

8. Taminger, K. M. B., Hafley, R. A., and Dicus, D. L., “Solid Freeform Fabrication: An Enabling 

Technology for Future Space Missions,” Keynote Lecture for 2002 International Conference on 

Metal Powder Deposition for Rapid Manufacturing Metal Powder Industries Federation, San 

Antonio, TX, April 8-10, 2002, pp. 51-56. 

9. Chan, K., Harter, J., Grandt, A. F., and Honeycutt, K., “Enhanced Crack Growth Methodology and 

Analyses for Unitized Structures,” Ninth Joint FAA/DoD/NASA Conference on Aging Aircraft, 

Atlanta, GA, 6–9 March 2006. 

10. Renton, W. J., Olcott, D., Roeseler, W., Batzer, R., Baron, W., and Velicki, A., “Future of Flight 

Vehicle Structures (2000–2023),” Journal of Aircraft, Vol. 41, No. 5, 2004, pp. 986–997. 

doi:10.2514/1.4039. 

11. Pettit, R. G., Wang, J. J., and Toh, C., “Validated Feasibility Study of Integrally Stiffened Metallic 

Fuselage Panels for Reducing Manufacturing Costs,” NASA CR-2000-209342, The Boeing 

Company, Long Beach, CA. 

12. Gurav, S. P. and Kapania, R. K., “Development of Framework for the Design Optimization of 

Unitized Structures,” 50th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and 

Materials Conference, Palm Springs, CA, May 4-7, 2009, AIAA2009-2186. 

13. Joshi, P., Mulani, S. B., Kapania, R. K. and Shin, Y. S., "Optimal Design of Unitized Structures 

with Curvilinear Stiffeners Using Response Surface Methodology", AIAA-2008-2304, 49th 
23 

AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference and the 

16th AIAA/ASME/AHS Adaptive Structures Conference, Schaumburg, IL, Apr. 7-10, 2008. 

14. Joshi, P., Mulani, S. B., Gurav, S. P., and Kapania, R. K., "Design Optimization for Minimum Sound 

Radiation from Point-Excited Curvilinearly Stiffened Panel", 50th AIAA/ASME/ASCE/AHS/ASC 

Structures, Structural Dynamics, and Materials Conference and the 17th AIAA/ASME/AHS 

Adaptive Structures Conference, Palm Springs, California, May 4-7, 2009, AIAA-2009-2649. 

15. Dang, T. D., Kapania, R. K. and Gurav, S. P., “Optimization of Unitized Structures under Damage 

Tolerance Constraints,” 50th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and 

Materials Conference and the 17th AIAA/ASME/AHS Adaptive Structures Conference, Palm 

Springs, California, May 4-7, 2009, AIAA-2009-2550. 

16. Baker, D.J., “Combined Load Test Fixture,” NASA Technical Memorandum TM-2010-216211, 

March 2010. 

17. Niu, M.C.Y., ed. Airframe Stress Analysis and Sizing. 2nd. Hong Cong: Conmilit Press, 1997. 

18. Venter, G. and Sobieszczanski-Sobieski, J. “Particle Swarm Optimization,” 43rd 

AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, Denver, 

CO, April 22-25, 2002, AIAA2002-1235. 

19. “Metallic Materials and Elements for Aerospace Vehicle Structures,” Department of Defense 

Handbook, MIL-HDBK-5J, January 31, 2003. 
24 

Appendix A 

Strain Gage Locations 

A total of 32 strain gages were attached to the baseline compression-shear curvilinear-stiffened 

test panel. Six of the strain gages were Micro-Measurements (Vishay Precision Group, Inc.) type 

CEA13-250UR-350 rosettes (0°/45°/90°) with 0° direction oriented parallel to the compression load 

direction. Three of these rosettes were attached to the skin on the stiffened side of the panel and three 

were attached to the skin on the flat side of the panel. The other 26 gages were Micro-Measurements 

(Vishay Precision Group, Inc.) type CEA00-250UW-350 uniaxial gages oriented parallel to the 

compression load direction. Ten of these uniaxial gages were attached to the skin on the stiffened side of 

the panel and ten were attached to the skin on the flat side of the panel. Four of the uniaxial gages were 

attached to the stiffeners. The remaining two uniaxial gages were attached to the skin on the flat side of 

the panel directly behind the two stiffeners. 

Table A1 shows an itemized list of the strain gages and their location on the panel. Figure A1 

shows the strain gage locations on the top half of the panel and figure A2 shows the strain gage locations 

on the bottom half of the panel. The intersection of the vertical and horizontal centerlines is considered to 

be the zero position point on the panel. When viewing the stiffened side of the panel, the positive 

horizontal direction (x) is moving to the right. The positive vertical direction (y) is moving upward. The 

left-hand stiffener is Stiffener A and the right-hand stiffener is Stiffener B. Figure A3 and figure A4 

show the strain gage locations attached to Stiffeners A and B, respectively. 
25 

Table A1. Location of strain gages on baseline compression-shear test panel. 

gage no. gage type orient. x (in) y (in) location Figure

1 uniaxial 0° 0 1.58 skin on stiffened side of panel A1

2 uniaxial 0° 0 1.58 skin on flat side of panel A1

3 uniaxial 0° 0 0.22 skin on stiffened side of panel A1

4 uniaxial 0° 0 0.22 skin on flat side of panel A1

5A rosette 0° 0 -0.68 skin on stiffened side of panel A2

5B rosette 90° 0 -0.68 skin on stiffened side of panel A2

5C rosette 45° 0 -0.68 skin on stiffened side of panel A2

6A rosette 0° 0 -0.68 skin on flat side of panel A2

6B rosette 90° 0 -0.68 skin on flat side of panel A2

6C rosette 45° 0 -0.68 skin on flat side of panel A2

7 uniaxial 0° 0 -1.51 skin on stiffened side of panel A2

8 uniaxial 0° 0 -1.51 skin on flat side of panel A2

9 uniaxial 0° 0 -2.71 skin on stiffened side of panel A2

10 uniaxial 0° 0 -2.71 skin on flat side of panel A2

11 uniaxial 0° 0 -3.53 skin on stiffened side of panel A2

12 uniaxial 0° 0 -3.53 skin on flat side of panel A2

13 uniaxial 0° 0 -4.35 skin on stiffened side of panel A2

14 uniaxial 0° 0 -4.35 skin on flat side of panel A2

15 uniaxial 0° -7.88 -0.68 skin on stiffened side of panel A2

16 uniaxial 0° -7.88 -0.68 skin on flat side of panel A2

17 uniaxial 0° 7.88 -0.68 skin on stiffened side of panel A2

18 uniaxial 0° 7.88 -0.68 skin on flat side of panel A2

19 uniaxial 0° 7.88 -8.40 skin on stiffened side of panel A2

20 uniaxial 0° 7.88 -8.40 skin on flat side of panel A2

21A rosette 0° 7.88 -11.98 skin on stiffened side of panel A2

21B rosette 90° 7.88 -11.98 skin on stiffened side of panel A2

21C rosette 45° 7.88 -11.98 skin on stiffened side of panel A2

22A rosette 0° 7.88 -11.98 skin on flat side of panel A2

22B rosette 90° 7.88 -11.98 skin on flat side of panel A2

22C rosette 45° 7.88 -11.98 skin on flat side of panel A2

23A rosette 0° -7.88 10.82 skin on stiffened side of panel A1

23B rosette 90° -7.88 10.82 skin on stiffened side of panel A1

23C rosette 45° -7.88 10.82 skin on stiffened side of panel A1

24A rosette 0° -7.88 10.82 skin on flat side of panel A1

24B rosette 90° -7.88 10.82 skin on flat side of panel A1

24C rosette 45° -7.88 10.82 skin on flat side of panel A1

25 uniaxial 0° -7.88 5.95 skin on stiffened side of panel A1

26 uniaxial 0° -7.88 5.95 skin on flat side of panel A1

27 uniaxial 0° --- -6.70 Stiffener A A3

28 uniaxial 0° --- -6.70 Stiffener A A3

29 uniaxial 0° --- -6.70 skin on flat side of panel directly behind Stiffener A A3

30 uniaxial 0° --- 5.52 Stiffener B A4

31 uniaxial 0° --- 5.52 Stiffener B A4

32 uniaxial 0° --- 5.52 skin on flat side of panel directly behind Stiffener B A4
26 

Figure A1. Location of strain gages on top half of test panel. 

Figure A2. Location of strain gages on bottom half of test panel. 

Figure A3. Location of strain gages on Stiffener A. 

(Gages aligned along stiffener length)
27 

Figure A4. Location of strain gages on Stiffener B. 

(Gages aligned along stiffener length)
28 

Appendix B 

Location of LVDTs for Out-of-Plane Displacement Measurement 

A total of 5 linear variable displacement transducers (LVDTs) were attached to the baseline 

compression-shear curvilinear-stiffened test panel. The LVDTs were attached to the smooth side of the 

panel using mounting brackets attached to the test machine. The LVDTs were configured such that an 

outward buckling of the smooth side of the panel would result in a positive displacement reading on the 

data acquisition system. 

Table B1 shows an itemized list of the LVDTs and their location on the panel. Figure B1 shows 

the LVDT locations. All of the LVDTs were positioned on the bottom half of the test panel. The 

intersection of the vertical and horizontal centerlines is considered to be the zero position point on the 

panel. When viewing the stiffened side of the panel, the positive horizontal direction (x) is moving to the 

right. The positive vertical direction (y) is moving upward. The left-hand stiffener is Stiffener A and the 

right-hand stiffener is Stiffener B. 

Table B1. Location of LVDTs on baseline compression-shear test panel. 

LVDT 

Number 

x [inch] y [inch] 

4 -8.0 -2.7 

5 6.9 -12.2 

6 7.4 -6.9 

7 8.5 -2.7 

9 -1.0 -2.7 

Figure B1. Location of LVDTs on test panel. 
29 

Appendix C 

Supplemental Data from Strain Gages and the Out-of-Plane LDVTs 

The results from each LDVT and strain gage are plotted below. For the strain gage rosettes, the 

shear strain was deduced from the 0°, 90° and 45° components as described in the text. Refer to 

appendix A for strain gage locations and appendix B for out-of-plane LVDT locations. 

-0.08

-0.07

-0.06

-0.05

-0.04

-0.03

-0.02

-0.01

0

0.01

0.0 0.5 1.0 1.5 2.0 2.5

Load Factor

Displacement (in)

Figure C1. Comparison of the test, nonlinear FEM, and the linear test fixture/panel assembly 

responses for LVDT 4 (positive deflection is measured towards the stiffeners). 
30 

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.0 0.5 1.0 1.5 2.0 2.5

Load Factor

Displacement (in)

Figure C2. Comparison of the test, nonlinear FEM, and the linear test fixture/panel assembly 

responses for LVDT 5 (positive deflection is measured towards the stiffeners). 

0

0.05

0.1

0.15

0.2

0.25

0.3

0.0 0.5 1.0 1.5 2.0 2.5

Load Factor

Displacement (in)

Figure C3. Comparison of the test, nonlinear FEM, and the linear test fixture/panel assembly 

responses for LVDT 6 (positive deflection is measured towards the stiffeners). 
31 

-0.0020

-0.0016

-0.0012

-0.0008

-0.0004

0.0000

0.0 0.5 1.0 1.5 2.0 2.5

Load Factor

Strain

Figure C4. Comparison of the test, nonlinear FEM, and the linear test fixture/panel assembly 

responses for axial strain gages 1 and 2 (εyy). (Strain is presented in units of 

inch/inch.) 

-0.0020

-0.0016

-0.0012

-0.0008

-0.0004

0.0000

0.0 0.5 1.0 1.5 2.0 2.5

Load Factor

Strain

Figure C5. Comparison of the test, nonlinear FEM, and the linear test fixture/panel assembly 

responses for axial strain gages 3 and 4 (εyy). (Strain is presented in units of inch/inch.) 
32 

-0.0024

-0.0020

-0.0016

-0.0012

-0.0008

-0.0004

0.0000

0.0 0.5 1.0 1.5 2.0 2.5

Load Factor

Strain

Figure C6. Comparison of the test, nonlinear FEM, and the linear test fixture/panel assembly 

responses for axial strain gages 7 and 8 (εyy). (Strain is presented in units of inch/inch.) 

 

-0.0016

-0.0012

-0.0008

-0.0004

0.0000

0.0 0.5 1.0 1.5 2.0 2.5

Load Factor

Strain

Figure C7. Comparison of the test, nonlinear FEM, and the linear test fixture/panel assembly 

responses for axial strain gages 8 and 9 (εyy). (Strain is presented in units of inch/inch.) 
33 

-0.0024

-0.0020

-0.0016

-0.0012

-0.0008

-0.0004

0.0000

0.0 0.5 1.0 1.5 2.0 2.5

Load Factor

Strain

Figure C8. Comparison of the test, nonlinear FEM, and the linear test fixture/panel assembly 

responses for axial strain gages 11 and 12 (εyy). (Strain is presented in units of 

inch/inch.) 

-0.0030

-0.0025

-0.0020

-0.0015

-0.0010

-0.0005

0.0000

0.0005

0.0 0.5 1.0 1.5 2.0 2.5

Load Factor

Strain

Figure C9. Comparison of the test, nonlinear FEM, and the linear test fixture/panel assembly 

responses for axial strain gages 13 and 14 (εyy). (Strain is presented in units of 

inch/inch.) 
34 

-0.0035

-0.0030

-0.0025

-0.0020

-0.0015

-0.0010

-0.0005

0.0000

0.0005

0.0010

0.0 0.5 1.0 1.5 2.0 2.5

Load Factor

Strain

Figure C10. Comparison of the test, nonlinear FEM, and the linear test fixture/panel assembly 

responses for axial strain gages 15 and 16 (εyy). (Strain is presented in units of 

inch/inch.) 

-0.0040

-0.0030

-0.0020

-0.0010

0.0000

0.0010

0.0020

0.0 0.5 1.0 1.5 2.0 2.5

Load Factor

Strain

Figure C11. Comparison of the test, nonlinear FEM, and the linear test fixture/panel assembly 

responses for axial strain gages 17 and 18 (εyy). (Strain is presented in units of 

inch/inch.) 
35 

-0.0040

-0.0030

-0.0020

-0.0010

0.0000

0.0010

0.0020

0.0 0.5 1.0 1.5 2.0 2.5

Load Factor

Strain

Figure C12. Comparison of the test, nonlinear FEM, and the linear test fixture/panel assembly 

responses for axial strain gages 19 and 20 (εyy). (Strain is presented in units of 

inch/inch.) 

0.0000

0.0005

0.0010

0.0015

0.0020

0.0025

0.0 0.5 1.0 1.5 2.0 2.5

Load Factor

Strain

Figure C13. Comparison of the test, nonlinear FEM, and the linear test fixture/panel assembly 

responses for strain gages 21 and 22 perpendicular to the direction of the dominant 

compressive loading (εxx). (Strain is presented in units of inch/inch.) 
36 

-0.0050

-0.0040

-0.0030

-0.0020

-0.0010

0.0000

0.0010

0.0020

0.0 0.5 1.0 1.5 2.0 2.5

Load Factor

Strain

Figure C14. Comparison of the test, nonlinear FEM, and the linear test fixture/panel assembly 

responses for axial strain gages 23 and 24 (εyy). (Strain is presented in units of 

inch/inch.) 

 

-0.0005

0.0000

0.0005

0.0010

0.0015

0.0020

0.0025

0.0 0.5 1.0 1.5 2.0 2.5

Load Factor

Strain

Figure C15. Comparison of the test, nonlinear FEM, and the linear test fixture/panel assembly 

responses for strain gages 23 and 24 perpendicular to the direction of the dominant 

compressive loading (εxx). (Strain is presented in units of inch/inch.) 
37 

-0.0008

-0.0006

-0.0004

-0.0002

0.0000

0.0002

0.0004

0.0006

0.0008

0 0.5 1 1.5 2 2.5

Load Factor

Strain

Figure C16. Comparison of the test, nonlinear FEM, and the linear test fixture/panel assembly 

responses for shear strain extracted from strain gages rosettes 23 and 24 (εxy). (Strain 

is presented in units of inch/inch.) 

-0.0035

-0.0025

-0.0015

-0.0005

0.0005

0.0015

0.0 0.5 1.0 1.5 2.0 2.5

Load Factor

Strain

Figure C17. Comparison of the test, nonlinear FEM, and the linear test fixture/panel assembly 

responses for axial strain gages 25 and 26 (εyy). (Strain is presented in units of 

inch/inch.) 
38 

-0.001

0.000

0.001

0.002

0.003

0.004

0.005

0.006

0.007

0.0 0.5 1.0 1.5 2.0 2.5

Load Factor

Strain

Figure C18. Comparison of the test, nonlinear FEM, and the linear test fixture/panel assembly 

responses for axial strain gages 27 and 28 (εyy) (see figure A3 for gage locations). 

(Strain is presented in units of inch/inch.) 

-0.003

-0.0025

-0.002

-0.0015

-0.001

-0.0005

0

0.00 0.50 1.00 1.50 2.00 2.50

Load Factor

Strain

Figure C19. Comparison of the test, nonlinear FEM, and the linear test fixture/panel assembly 

responses for axial strain gages 29 (εyy). (Strain is presented in units of inch/inch.) 
39 

-0.001

0.000

0.001

0.002

0.003

0.004

0.005

0.0 0.5 1.0 1.5 2.0 2.5

Load Factor

Strain

Figure C20. Comparison of the test, nonlinear FEM, and the linear test fixture/panel assembly 

responses for axial strain gages 30 and 31 (εyy) (see figure A4 for gage locations). 

(Strain is presented in units of inch/inch.) 

-0.0035

-0.003

-0.0025

-0.002

-0.0015

-0.001

-0.0005

0

0.00 0.50 1.00 1.50 2.00 2.50

Load Factor

Strain

Figure C21. Comparison of the test, nonlinear FEM, and the linear test fixture/panel assembly 

responses for axial strain gages 32 (εyy). (Strain is presented in units of inch/inch.) 
REPORT DOCUMENTATION PAGE Form Approved

OMB No. 0704-0188

2. REPORT TYPE 

Technical Publication

 4. TITLE AND SUBTITLE

Design, Optimization and Evaluation of Integrally Stiffened Al 7050 Panel

with Curved Stiffeners

5a. CONTRACT NUMBER

 6. AUTHOR(S)

Slemp, Wesley C. H.; Bird, R. Keith; Kapania, Rakesh K.; Havens, David; 

Norris, Ashley; Olliffe, Robert

 7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES)

NASA Langley Research Center

Hampton, VA 23681-2199

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National Aeronautics and Space Administration

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Availability: NASA CASI (443) 757-5802

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14. ABSTRACT

A curvilinear stiffened panel was designed, manufactured, and tested in the Combined Load Test Fixture at NASA Langley 

Research Center. The panel was optimized for minimum mass subjected to constraints on buckling load, yielding, and 

crippling or local stiffener failure using a new analysis tool named EBF3PanelOpt. The panel was designed for a combined 

compression-shear loading configuration that is a realistic load case for a typical aircraft wing panel. The panel was loaded 

beyond buckling and strains and out-of-plane displacements were measured. The experimental data were compared with the 

strains and out-of-plane deflections from a high fidelity nonlinear finite element analysis and linear elastic finite element 

analysis of the panel/test-fixture assembly. The numerical results indicated that the panel buckled at the linearly elastic 

buckling eigenvalue predicted for the panel/test-fixture assembly. The experimental strains prior to buckling compared well 

with both the linear and nonlinear finite element model.

15. SUBJECT TERMS

Buckling; Curvilinear stiffeners; Finite element analysis; Integrally-stiffened structure; Load Tests; Structural optimization

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561581.02.08.07.15.15 

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01- 09 - 2011