June 2012 

NASA/TP–2012-217584 

Design, Optimization, and Evaluation of 

A1-2139 Compression Panel with Integral 

T-Stiffeners 

Sameer B. Mulani 

Virginia Polytechnic Institute and State University, Blacksburg, Virginia 

David Havens 

Lockheed Martin Aeronautics Company, Marietta, Georgia 

Ashley Norris 

Lockheed Martin Aeronautics Company, Palmdale, California 

R. Keith Bird 

Langley Research Center, Hampton, Virginia 

Rakesh K. Kapania 

Virginia Polytechnic Institute and State University, Blacksburg, Virginia 

Robert Olliffe 

Lockheed Martin Aeronautics Company, Marietta, Georgia 
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June 2012 

NASA/TP–2012-217584 

Design, Optimization, and Evaluation of 

A1-2139 Compression Panel with Integral 

T-Stiffeners 

Sameer B. Mulani 

Virginia Polytechnic Institute and State University, Blacksburg, Virginia 

David Havens 

Lockheed Martin Aeronautics Company, Marietta, Georgia 

Ashley Norris 

Lockheed Martin Aeronautics Company, Palmdale, California 

R. Keith Bird 

Langley Research Center, Hampton, Virginia 

Rakesh K. Kapania 

Virginia Polytechnic Institute and State University, Blacksburg, Virginia 

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 NNL08AA02C) with Ms. Karen M. Brown Taminger as the 

NASA Technical Lead. The authors are thankful to Ms. Taminger for her suggestions. 

The authors would like to thank our partners in the NRA project, Mr. John Barnes and 

Dr. Steve Englestad of Lockheed Martin Aeronautics Company of Marietta, GA, for 

technical discussions. 

Compression tests were conducted at NASA Langley Research Center under the 

Subsonic Fixed Wing Program. Ms. Dawn Jegley of the Structural Mechanics and 

Concepts Branch provided invaluable advice for conducting this compression test. 

The use of trademarks or names of manufacturers in this report is for accurate re porting and does not constitute an 

official endorsement, either expressed or implied, of such products or manufacturers by the National Aeronautics 

and Space Administration. 
Design, Optimization, and Evaluation of Al–2139 Compression Panel with Integral T-Stiffeners

v 

Abstract

A T-stiffened panel was designed and optimized for minimum mass subjected to constraints on 

buckling load, yielding, and crippling or local stiffener failure using a new analysis and design 

tool named EBF3PanelOpt. The panel was designed for a compression loading configuration, a 

realistic load case for a typical aircraft skin-stiffened panel. The panel was integrally machined 

from 2139 aluminum alloy plate and was tested in compression. The panel was loaded beyond 

buckling and strains and out-of-plane displacements were extracted from 36 strain gages and one 

linear variable displacement transducer. A digital photogrammetic system was used to obtain 

full field displacements and strains on the smooth (unstiffened) side of the panel. The 

experimental data were compared with the strains and out-of-plane deflections from a highfidelity nonlinear finite element analysis. The test data indicated that the panel buckled at the 

linear elastic buckling eigenvalue predicted for the panel. The out-of-plane displacement 

measured by the digital photogrammetic system compared well both qualitatively and 

quantitatively with the nonlinear finite element solution in the post-buckling regime. 

Furthermore, the experimental strains compared well with both the linear and nonlinear finite 

element model prior to buckling. The weight of the optimized panel was 20 percent less than 

that of a T-stiffened panel optimized using conventional design techniques. 
Design, Optimization, and Evaluation of Al–2139 Compression Panel with Integral T-Stiffeners

vi

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Design, Optimization, and Evaluation of Al–2139 Compression Panel with Integral T-Stiffeners

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TABLE OF CONTENTS

SECTION 1 Introduction .........................................................................................................1

SECTION 2 EBF3PanelOpt Framework ...............................................................................3

2.1 Parametric Modeling of the Panel ......................................................................................5

SECTION 3 Panel Design and Optimization .........................................................................6

SECTION 4 Panel Manufacturing ........................................................................................11

SECTION 5 Compression Test ..............................................................................................13

SECTION 6 Comparison of Experimental and Analytical Results ...................................16

SECTION 7 Summary and Conclusions ..............................................................................19

SECTION 8 References ..........................................................................................................20

APPENDIX A Strain Gage Locations ......................................................................................22

APPENDIX B Strain Gage Plots...............................................................................................26
Design, Optimization, and Evaluation of Al–2139 Compression Panel with Integral T-Stiffeners

viii

LIST OF TABLES

Table 1. VisualDoc optimization parameters for NSGA-II optimization (ref. 20). ...........7

Table 2. Material properties for Al 2139 used for the panel optimization with 

EBF3PanelOpt. ..........................................................................................................8

Table 3. Design variable bounds and optimal values. ..........................................................8

Table A-1. Location of strain gages on T-stiffened compression test panel. .........................23

LIST OF FIGURES

Figure 1. Schematic of EBF3PanelOpt framework. .............................................................4

Figure 2. Design variables for stiffener curve and T-stiffener cross section. .....................6

Figure 3. Skin panel geometry along with applied in-plane loads. .....................................7

Figure 4. Optimal design responses for the applied in-plane compression. .......................9

Figure 5. Overall dimensions of test panel and skin thickness for each pocket between 

stiffeners. (Dimensions are in inches.) ................................................................10

Figure 6. Dimensions of flanges and webs of T-stiffeners, viewing left half of Section AA from Figure 5. (Dimensions are in inches.) ....................................................10

Figure 7. Location and height of T-stiffeners, viewing Section A-A from Figure 5. 

(Dimensions are in inches.) ...................................................................................11

Figure 8. Picture of the stiffened side of the Al–2139 test panel. .......................................12

Figure 9. Laser scanned surface profile of T-stiffened panel compared to original CAD 

file. ...........................................................................................................................12

Figure 10. Anti-buckling guide. ..............................................................................................13

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

Figure 12. Test panel in compression test system. ................................................................15

Figure 13. Shim locations at top of panel (four right-most stiffeners and right edge of 

panel). .....................................................................................................................15

Figure 14. Posttest photograph showing locations where stiffeners buckled. ....................16

Figure 15. Measured and predicted strain behavior for the skin on the upper right side 

(strain gage A6 location). ......................................................................................17

Figure 16. Measured and predicted strain behavior for the skin on the lower right side 

(strain gage A8 location). ......................................................................................17

Figure 17. Measured and predicted strain behavior for the right-most stiffener (strain 

gage S6 location). ...................................................................................................18

Figure 18. Out-of-plane displacement for panel at end of compression test. .....................19

Figure A-1. Location of strain gages on the stiffened side of the test panel. ........................24

Figure A-2. Strain gage locations on stiffeners A and D. .......................................................25

Figure A-3. Strain gage locations on stiffeners B and C. .......................................................25

Figure A-4. Strain gage locations on stiffeners E and F. ........................................................25

Figure B-1. Predicted and measured strain behavior at strain gage location R1. (Strain 

data are from the compression leg of the rosette gages.) ...................................26

Figure B-2. Predicted and measured strain behavior at strain gage location A1. ...............27

Figure B-3. Predicted and measured strain behavior at strain gage location A2. ...............27

Figure B-4. Predicted and measured strain behavior at strain gage location A3. ...............28

Figure B-5. Predicted and measured strain behavior at strain gage location A4. ...............28
Design, Optimization, and Evaluation of Al–2139 Compression Panel with Integral T-Stiffeners

ix

Figure B-6. Predicted and measured strain behavior at strain gage location A5. ...............29

Figure B-7. Predicted and measured strain behavior at strain gage location A6. ...............29

Figure B-8. Predicted and measured strain behavior at strain gage location A7. ...............30

Figure B-9. Predicted and measured strain behavior at strain gage location A8. ...............30

Figure B-10. Predicted and measured strain behavior at strain gage location S1. ...............31

Figure B-11. Predicted and measured strain behavior at strain gage location S2. ...............31

Figure B-12. Predicted and measured strain behavior at strain gage location S3. ...............32

Figure B-13. Predicted and measured strain behavior at strain gage location S4. ...............32

Figure B-14. Predicted and measured strain behavior at strain gage location S5. ...............33

Figure B-15. Predicted and measured strain behavior at strain gage location S6. ...............33
Design, Optimization, and Evaluation of Al–2139 Compression Panel with Integral T-Stiffeners

x 

Nomenclature

3D three-dimensional 

BDF bulk data format 

CAD computer aided design

CFD computational fluid dynamics

EBF3 electronic beam free-form fabrication

FEA finite element analysis

FEM finite element model 

FSW friction stir welding

GA genetic algorithm

LaRC Langley Research Center

LVDT linear variable displacement transducer

NASA National Aeronautics and Space Administration 

NC numerically controlled

NRA NASA research announcement

NSGA-II non-dominated sorting algorithm 

PSO particle swarm optimization

a1 a multiplication constant for allowable crippling stress calculation 

a2 an exponent for allowable crippling stress calculation 

bn length of nth component of the stiffener cross section, inch 

E Young’s modulus, psi 

Fcc allowable crippling stress for whole stiffener, psi 

Fccn allowable crippling stress of nth component of the stiffener cross-section, psi 

hw height of the web, inch 

n number of components in the stiffener cross section 

tf flange thickness, inch 

tn thickness of nth component of the stiffener cross-section, inch 

tp panel pocket thickness, inch 

tw web thickness, inch 

wf flange width, inch

x,y,z rectilinear coordinate basis

λ0 buckling eigenvalue 

ε strain

σvm von Mises stress, psi

σstiff minimum principle stress in the stiffener, psi

σy yield stress, psi

ν Poisson’s ratio 
Design, Optimization, and Evaluation of Al–2139 Compression Panel with Integral T-Stiffeners

1 

 SECTION 1

INTRODUCTION

Stiffened panels are integral parts of aerospace, automobile, and ship structures due to their high 

stiffness-to-weight ratio as compared to unstiffened panels. These stiffened panels are designed 

to withstand the buckling, yielding, and crippling of the applied in-plane loads; hence, the 

optimality of these structures depends upon the appropriate dimensions of the plate and stiffeners 

and the appropriate stiffener locations. Traditionally, these stiffening members, which have a 

uniform cross section, are straight and riveted to the panels or to the parent structures to ease the 

manufacturing process. Over the years optimization frameworks using discrete numbers of 

straight stiffeners, like Hypersizer (ref. 1), PASCO (ref. 2), PANDA (ref. 3), and VICONOPT 

(ref. 4) have been developed to optimize stiffened panels. These frameworks rely on the 

Rayleigh-Ritz method or the finite strip method to do analysis, but they have some limitations 

when optimizing panels, especially non-rectangular panels, with nonuniform in-plane loading. 

More information about these limitations can be found in references 4 and 5. Thus, traditional 

design methodology has a limited design space to achieve a desired performance. A designer can 

use the enhanced design space by employing curved, nonuniform thickness stiffening members, 

as well as panel thicknesses, without using riveted joints. This design philosophy uses the 

concept of unitized structures, meaning that the stiffening members become integral to the 

structures, leading to a monolithic construction of the vehicle and a reduced count of total parts 

for an assembly (ref. 6). 

Mankind’s wish for future aerospace vehicles to be multifunctional and have improved 

performance has led to better vehicles. Additional requirements like fuel efficiency (to combat

unstable fuel prices) and reduced emissions have become of prime importance in the last decade. 

Yet, airlines stipulate that a 20 percent improvement in direct operating cost is necessary to 

justify introducing an all-new aircraft into their fleets (ref. 6). The aircraft industry is thus forced 

to continuously reduce the weight of the aircraft. With that goal in mind, National Aeronautics 

and Space Administration (NASA) has initiated several NASA Research Announcement (NRA) 

contracts for future aircraft designs that are fuel efficient and have met requirements for reduced

emissions and noise. Three different aircraft configurations were included in the NRA as future 

aerospace vehicles: 1) hybrid wing/body, 2) truss-braced wing, and 3) double bubble. These 

vehicles would have pressurized noncircular fuselage structures and complex wing geometry. 

Traditional aircraft designs have led designers to have the confidence and experience of 

designing such structures using both the knowledge-base that has been built over the years and 

various other rules-of-thumb. There is a lack of experience in both the knowledge of the 

structural loads and the resulting design of complex, multi-functional, aircraft structural concepts 

for future aerospace vehicles. 

During the last three decades, there has been tremendous progress in computer-aided design 

(CAD), the finite element method (FEM), computational fluid dynamics (CFD), and multiphysics modeling using numerical methods. It has led to better analyses of vehicles and reduced 

the need for extensive experimentation. Because of better analysis tools and the availability of 

parallel processing, the optimization algorithms have improved substantially. Earlier, gradientbased optimization methods were popular due to their efficiency. Currently, global heuristic 

optimization techniques, such as genetic algorithm (GA), particle swarm optimization (PSO), 
Design, Optimization, and Evaluation of Al–2139 Compression Panel with Integral T-Stiffeners

2 

and ant-colony optimization, are increasingly used more because of available computational 

power and the need for global optimal solutions. 

In recent years, topology optimization methods for continuum structures have increased in 

popularity. Bendsoe and Kikuchi developed the theoretical foundation for the topology 

optimization methodology in 1988 (ref. 7). The commercial software, Altair OptiStruct (ref. 8), 

was developed and released in 1994 and used the topology optimization approach. In topology 

optimization, the density or elastic modulus of each finite element is allowed to vary between 

lower and upper bounds (ref. 9). Hence, the number of design variables in the topology 

optimization is equal to or greater than the number of finite elements. Another issue with 

topology optimization is the creation of the checker board pattern. To remove a checker board 

pattern generated during the topology optimization, different filtering schemes are used that add 

further computational cost. So, topology optimization is very computationally-intensive in its 

current format. Thus, the method can be impractical for everyday design. Furthermore, the 

manufacturability of the optimal design is not guaranteed. 

However, recent new metallic manufacturing processes such as friction stir welding (FSW) (ref. 

10) and electron beam freeform fabrication (EBF3

) (ref. 11) 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. 7). Therefore, considering a design space in 

which stiffeners can take a curvilinear profile rather than a straight profile may result in a 

reduction in mass for the same structural design requirements. By using these innovative 

manufacturing techniques with curvilinear stiffening, the design engineer can build unitized 

structures with fewer parts, lower weight, less material wastage, and multifunctionality. In 

addition, these attributes make unitized structures good candidates for manufacturing in space. 

Additional benefits of unitized structures are found in reference 12. The use of the unitized 

structure is expected to grow exponentially by the year 2020 (ref. 6). Boeing (ref. 13) developed 

an integrally stiffened fuselage concept whose 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.

Since 2007, an analysis and design tool, EBF3PanelOpt (ref. 14–17), has been under 

development for the design and optimization of complex aircraft structural concepts at the 

Virginia Polytechnic Institute and State University (Virginia Tech). EBF3PanelOpt is a tool for 

optimization of stiffened panel and shell structures in which stiffeners are not limited by 

traditional manufacturing techniques. Using curved stiffeners broadens the design space without 

substantially adding to the computational cost of the optimization. EBF3PanelOpt is being 

developed to exploit the emerging additive manufacturing processes that offer the ability to 

efficiently fabricate complex structural configurations. Initially, EBF3PanelOpt was supported 

with two or four curvilinear blade-stiffeners, but subsequently, it was extended to support 

multiple load-cases and nonuniform panel thicknesses. For blade-stiffened panels, in-plane loads 

are always applied through the plate only, not through the stiffeners. For very high in-plane 

compression loadings, non-blade stiffeners like T, L, J or hat stiffeners are efficient in load 

resistance. So, in the last phase, EBF3PanelOpt was modified to support curvilinear T stiffeners 

and with the stiffeners loaded (ref. 17). The ultimate goal is to enhance aircraft performance and 

environmental responsibility through reductions in weight, emissions, and cabin noise, and to 
Design, Optimization, and Evaluation of Al–2139 Compression Panel with Integral T-Stiffeners

3 

integrate functions such as acoustic damping, adaptive active aerodynamic controls, and 

aeroelastically tailored structures.

The tool development is being conducted under an NRA contract at Virginia Tech with support 

and aircraft manufacturing expertise provided through a subcontract with Lockheed Martin 

Aeronautics Company (LM Aero). The work is complementary to the EBF3 additive 

manufacturing research activities at NASA LaRC. 

This paper describes the final phase of the development of the EBF3PanelOpt using curvilinear 

T-stiffeners. To analyze the advantage of EBF3PanelOpt , the baseline panel was optimized 

with mass minimization as an objective and subjected to constraints on the buckling load, 

yielding, and crippling or on local stiffener failure under compression loading. The optimized 

panel design was used to fabricate an integrally-machined test panel with aluminum alloy 

Al−2139. The panel was tested at NASA LaRC under uniaxial compression loading. The test 

results were compared against a high-fidelity nonlinear finite element analysis (FEA) of the test 

panel. During the experimentation, the panel buckled at a critical limit load predicted by 

EBF3PanelOpt and nonlinear FEA. The elastic strains calculated by the nonlinear FEA model 

matched within just a few percent of the measured values. Even the post-buckling analysis 

matched within 5 percent of the measured values for strains and loads. The biggest achievement 

was a 20 percent mass reduction for the T-stiffened panel design using EBF3PanelOpt over a 

conventionally optimized panel using current industry practice. 

 SECTION 2

EBF3PANELOPT FRAMEWORK

In the initial stages of the EBF3PanelOpt optimization framework, blade-stiffened panels under 

multiple load cases could be optimized with EBF3PanelOpt, but the stiffeners were not directly 

loaded during the application of in-plane compression. For larger magnitudes of in-plane 

compression along with the shear forces, the optimal panel requires the stiffener cross section 

having a larger moment of area away from neutral axis to resist the buckling efficiently. Hence, 

the optimal panel design would have non-blade stiffeners like T, L, or a hat cross section for the 

stiffeners, but note that these cross sections would be optimal if the stiffeners were loaded 

directly in compression. So, EBF3PanelOpt has been updated to support the curvilinear 

T-stiffeners for panel designs along with the options: 1) loads through the stiffeners and plate, 

and 2) loads through the plate only (ref. 17). 

The EBF3PanelOpt optimization framework shown in Fig. 1 is an object-oriented script written 

in Python that interfaces MSC.PATRAN and MSC.NASTRAN to perform FEA on a panel with 

curvilinear T-type stiffeners. It calculates the mass of the panel and constraints on yielding, 

buckling, and crippling or local failure of the panel. For further information see reference 17 by 

Mulani, Duggirala and Kapania. 
Design, Optimization, and Evaluation of Al–2139 Compression Panel with Integral T-Stiffeners

4 

Figure 1. Schematic of EBF3PanelOpt framework. 

During the optimization, after reading the design variables, Python writes a PATRAN session 

file, launches PATRAN, and executes this session file to update the geometry of the stiffened 

panel. After successful execution of the session file, it writes the input file (using the bulk data 

file or bdf) for NASTRAN. After the successful execution of this NASTRAN (bdf) file, a code 

written in Python reads the NASTRAN response file (f06) and calculates the responses like the 

buckling factor, von Mises stress, and crippling stress. These responses are fed to the optimizer 

to generate new designs or to make a decision regarding the optimization process. During the 

execution of PATRAN and NASTRAN, if any error occurs or if the run takes more time than the 

allocated time, these processes will be terminated and default responses will be sent with 

“pass/fail” as an active constraint. Many other checks are implemented to monitor the successful 

completion of geometry, meshing whole geometry, and evaluation of finite element analysis. 

Here, the optimization goal is to minimize the mass of the panel with the constraints on global 

buckling, von Mises stress, and crippling or local failure of the stiffeners. The buckling 

constraint is calculated by:

1 1

0

≤

λ

(1) 

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

≤ 1

y

vm

σ

σ (2) 
Design, Optimization, and Evaluation of Al–2139 Compression Panel with Integral T-Stiffeners

5 

where σvm is the von Mises stress, and σy is the material yield strength. The von Mises stress 

constraint is imposed using the Kreisselmeier-Steinhauser criteria for constraint aggregation as 

described in reference 18. The crippling constraint was calculated by:

≤ 1

cc

stiff

F

σ (3) 

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

maximum allowable stress in the stiffener with a complex cross section that is calculated with

the weighted formula given by: 

n n n cc

n

cc

n n

n

bt F

F

b t =

∑

∑

(4)

where bn, tn, n and Fccn are length, thickness of the stiffener’s individual component, total 

number of components of the stiffener cross section, and maximum allowable crippling stress for

an individual component of the stiffener given by: 

2

2 2

1

1 1

/ , 1

/ / , 1

a

y

y

cc a a

y y

y

b E

a

t

F

bE bE

a a

t t

σ

σ

σ σ

σ

−

− −

      >       = 

      ≤         

(5)

where E is the Young’s modulus of the stiffener material, b and t are the length and the thickness 

of the stiffener cross-section member, respectively. The coefficients a1 and a2 are 0.61525 and 

0.78387, respectively, for the stiffener member that is free at one end and connected to another 

member or structure at the other end. For the stiffener member that is connected at both ends, a1

and a2 are 1.1819 and 0.7782, respectively. The maximum allowable stress formula, Eq. 5, was 

obtained from page 444 of reference 19. 

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. Height of the web, thicknesses of the flange and web, and flange width of uniform 

T-stiffener cross section are sizing design variables apart from the plate pocket thicknesses. In 

EBF3PanelOpt, stiffener curve or profile is defined using third order uniform rational B-spline 

using two endpoints and a control point. The interpolation of the perimeter of the panel and panel 

surface yields endpoints and the control point for the stiffener. So, four design variables are 

required to define the stiffener curve, two for endpoints and two for the control point. As shown 

in Fig. 2(a), design variables x1 and x4 define endpoints of the stiffener, and design variables x2

and x3 indicate the control points for the typical stiffener curve. Figure 2(b) shows the typical 

cross section of the stiffener along with the terminology of its parts.
Design, Optimization, and Evaluation of Al–2139 Compression Panel with Integral T-Stiffeners

6 

(a) Shape design variables. (b) T-stiffener cross section.

Figure 2. Design variables for stiffener curve and T-stiffener cross-section. 

The EBF3PanelOptcode has an option for the placement of stiffeners to use the symmetry of the 

panel. The stiffeners are placed symmetrically with respect to x and y axes using the ”Symmetric 

Design” option; only even numbers of stiffeners are used, and the design variables related to only 

half of the stiffeners are given during the optimization. When the stiffeners are loaded in 

compression using the option ”Stiffener Loads,” the user has to use the ”Symmetric Design” 

option. There is another option, called “Nonuniform Thickness,” that provides the different 

thickness values for the panel pockets formed by the intersection of the stiffeners. For additional 

information of these options, refer to the work by Mulani, Duggirala, and Kapania (ref. 17). 

 SECTION 3

PANEL DESIGN AND OPTIMIZATION

Initially, a 24-inch by 28-inch stiffened panel with six T-stiffeners was optimized with different 

options for stiffener placement. The stiffener endpoints were allowed to move on the horizontal 

edges only so that the stiffeners would align in the vertical direction or major compression 

direction (ref. 17). Figure 3 shows the boundary conditions and the applied loads. During the 

optimization using EBF3PanelOpt, the loads were applied through the stiffeners with the option 

“Stiffener Loads” along with “Nonuniform Thickness” option for panel pockets and “Symmetric 

Design” for stiffener placement. The optimization was carried out using the “Genetic Algorithm” 

with 34 particles and 1000 iterations using VisualDoc (ref. 20) commercial optimization 

software. Currently, the non-dominated sorting algorithm (NSGA-II) (ref. 21) supports real 

design variables in VisualDoc. Table 1 provides the optimization parameters for this algorithm 

used for the analysis. For the details regarding the definition of the parameters, see reference 20. 

Sizing design variables like panel pocket thickness, web and flange thickness, web heights, and 

flange widths are allowed to change during the optimization, apart from the shape variables of 

the curvilinear T-stiffeners. The objective of the optimization was to minimize the mass of the 

panel with the constraints on the buckling, crippling, and yielding. 

Three different optimal designs were obtained, and it was found that the majority of stiffeners 

were straight. Hence, a fourth optimal design was obtained with six straight stiffeners equally 

 
Design, Optimization, and Evaluation of Al–2139 Compression Panel with Integral T-Stiffeners

7 

distributed on the panel using only the sizing design variables. So, 20 particles were used to 

simulate GA optimization for the final design. 

Figure 3. Skin panel geometry along with applied in-plane loads.

Table 1. VisualDoc optimization parameters for NSGA-II optimization (ref. 20). 

Optimization Parameter Value

Probability of Crossover 0.95

Probability of Mutation 0.10

Distribution Index for Crossover 10.00

Distribution Index for Mutation 15.00

Maximum number of iterations 1000

The panel was designed for a limit load of 85,440 lbs in compression against buckling, crippling, 

and yielding. Table 2 gives the material properties of the aluminum alloy used in the panel 

optimization. Table 3 gives the design variables along with their lower and upper bounds and 

with their optimal values for the final optimal panel. Figure 4 shows the thickness distribution, 

buckling mode shape, and von Mises stress distribution of the optimal design. Here, von Mises 

stress is normalized with respect to yield stress of the material, and the maximum stress is only 

76 percent of the yield stress. 
Design, Optimization, and Evaluation of Al–2139 Compression Panel with Integral T-Stiffeners

8 

Table 2. Material properties for Al 2139 used for the panel optimization with 

EBF3PanelOpt. 

Property Value

Young’s modulus, [Msi] 10.6

Poisson’s ratio 0.33

Yield stress, [ksi] 61.9

Density, [lb/inch3] 0.0975

Table 3. Design variable bounds and optimal values.

Design Variable Lower 

Bound

Upper 

Bound

Optimized 

Design

Stiffener 1 Web Height, hw1, [inch] 0.3937 1.9685 1.5328

Stiffener 2 Web Height, hw2, [inch] 0.3937 1.9685 1.2763

Stiffener 3 Web Height, hw3, [inch] 0.3937 1.9685 1.5892

Stiffener 1 Web Thickness, tw1, [inch] 0.0394 0.3150 0.0606

Stiffener 2 Web Thickness, tw2, [inch] 0.0394 0.3150 0.0942

Stiffener 3 Web Thickness, tw3, [inch] 0.0394 0.3150 0.0653

Stiffener 1 Flange Width, wf1, [inch] 0.3937 1.9685 0.3623

Stiffener 2 Flange Width, wf2, [inch] 0.3937 1.9685 0.8218

Stiffener 3 Flange Width, wf3, [inch] 0.3937 1.9685 0.4792

Stiffener 1 Flange Thickness, tf1, [inch] 0.0394 0.3150 0.0803

Stiffener 2 Flange Thickness, tf2, [inch] 0.0394 0.3150 0.0846

Stiffener 3 Flange Thickness, tf3, [inch] 0.0394 0.3150 0.0532

Panel Pocket 1 Thickness, tp1, [inch] 0.0394 0.1575 0.0888

Panel Pocket 2 Thickness, tp2, [inch] 0.0394 0.1575 0.0919

Panel Pocket 3 Thickness, tp3, [inch] 0.0394 0.1575 0.0845

Panel Pocket 4 Thickness, tp4, [inch] 0.0394 0.1575 0.0942

Panel Pocket 5 Thickness, tp5, [inch] 0.0394 0.1575 0.0829

Panel Pocket 6 Thickness, tp6, [inch] 0.0394 0.1575 0.0907

Panel Pocket 7 Thickness, tp7, [inch] 0.0394 0.1575 0.0872
Design, Optimization, and Evaluation of Al–2139 Compression Panel with Integral T-Stiffeners

9 

(a) Thickness distribution 

(in inches). 

(b) Linear buckling 

mode shape.

(c) Von Mises stress 

distribution.

Figure 4. Optimal design responses for the applied in-plane compression. 

The final optimized panel had six stiffeners with the dimensions of each stiffener, as well as each 

web segment between stiffeners, being optimized individually. Figure 5 shows the overall 

dimensions of the panel and the skin thickness in the individual pockets between stiffeners. 

Figures 6 and 7 show the dimensions of the T-stiffeners and the location of the stiffeners on the 

panel, respectively. The stiffener dimensions and locations are symmetric about the vertical 

centerline of the panel. However, the pocket thickness dimensions are not symmetric. The 

resultant panel had a weight of 8.3 lbs. 

For comparative purposes, a baseline panel with six uniform T-stiffeners and a uniform web 

thickness was designed and optimized with conventional techniques, specifically a combination 

of HyperSizer and NASTRAN Solution 200. This conventional panel had a weight of 10.4 lbs. 

Thus, the panel that was designed and optimized with EBF3PanelOpt was able to achieve a 

weight reduction of 20 percent compared to the conventionally-optimized panel. 

 
Design, Optimization, and Evaluation of Al–2139 Compression Panel with Integral T-Stiffeners

10

Figure 5. Overall dimensions of test panel and skin thickness for each pocket 

between stiffeners. (Dimensions are in inches.)

Figure 6. Dimensions of flanges and webs of T-stiffeners, viewing left half of 

Section A-A from Fig. 5. (Dimensions are in inches.)

4x R 0.25

4x 0.25

4x R 0.12

R 0.12 

TYP

28.00 CL SYM

24.50

CL

1.618 0.061

0.822

0.080

0.362

0.085

0.065

0.053

0.479

0.094
Design, Optimization, and Evaluation of Al–2139 Compression Panel with Integral T-Stiffeners

11

Figure 7. Location and height of T-stiffeners, viewing Section A-A from Fig. 5. 

(Dimensions are in inches.)

 SECTION 4

PANEL MANUFACTURING

The final test panel was 28 inches tall by 24 inches wide and was machined from 2-inch thick 

2139 aluminum plate using numerically controlled (NC) programming generated from a CAD 

file supplied by LM Aero. When the decision was made to apply only compression loading to 

this panel, the manufacturing effort was greatly simplified, compared to the previous combined 

loading test articles. The pad-ups and stiffener drop-off regions along the periphery of the test 

panel, as well as the bonded-on steel tabs, were no longer required to accommodate load 

introduction. The top and bottom ends of this panel were simply machined flat and parallel to 

ensure that an even distribution of loading was applied from the test machine platens. There 

were two deviations from the basic panel design cross section that were included in the test panel 

to simulate both vertical and lateral panel continuity during testing. The first was the minor padups in the webs between the stiffeners at the top and bottom (loaded) ends of the panel. These 

were included to prevent a non-representative local web buckling at the loaded ends. The other 

deviation was to include a 0.25-inch extension of the web on each side of the panel to 

accommodate the anti-buckling guides, which would serve to simulate the next stiffener in an 

actual continuing panel. Post-machining inspection indicated that all stringent dimensional 

tolerance constraints specified on the manufacturing drawing were met. The panel was crated 

and shipped to NASA LaRC for final inspection, strain gage installation, and testing. Figure 8

shows a picture of the final machined panel. 

CL

1.661 1.364

3.648

7.060

10.503

R 0.12 TYP R 0.12 TYP
Design, Optimization, and Evaluation of Al–2139 Compression Panel with Integral T-Stiffeners

12

Figure 8. Picture of the stiffened side of the Al–2139 test panel. 

Once the panel was received at NASA LaRC, a surface profile of the test panel was generated 

laser scanning techniques. Figure 9 shows the deviation of the laser-scanned surface from that of 

the original CAD file of the panel. The center region of the panel had a surface profile similar to 

that of the original CAD file. However, one edge of the panel was bowed approximately 0.050 

inch toward the smooth side. The other edge of the panel had a small twist such that the top 

corner bowed toward the smooth side and the bottom corner bowed toward the stiffener side by 

about 0.050 inch. 

Figure 9. Laser scanned surface profile of T-stiffened panel compared to original 

CAD file.

Top

y, 90°

x, 0°

Right

0.050 in.

0

-0.050

BOTTOM

TOP
Design, Optimization, and Evaluation of Al–2139 Compression Panel with Integral T-Stiffeners

13

 SECTION 5

COMPRESSION TEST

A compression test was conducted on the T-stiffened panel at NASA LaRC with a 300,000-lb 

capacity hydraulic test machine. Linear variable displacement transducers (LVDTs) were 

attached to three corners of the upper compression platen to measure panel compression 

displacement. 

A total of 36 strain gages were attached to the panel skin and stiffeners. Two of the gages were 

0°/45°/90° rosettes and 34 of the gages were uniaxial gages aligned parallel to the compression 

load direction. Appendix A provides a description of the strain gage locations. The smooth 

(unstiffened) side of the panel was spray-painted with a speckled pattern to facilitate strain and 

displacement measurements with a Vic-3D (three dimensional) automated stereophotogrammetic 

technique. The panel was installed into the test machine with one LVDT located 0.75 inch above 

the center point of the panel on the stiffened side to measure out-of-plane displacement. 

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

of one 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 and strain measurements on the smooth side of panel. In 

addition to the Vic-3D cameras, two video cameras were set up to record panel behavior during 

the test.

Anti-buckling guides were attached to the two edges of the panel to prevent premature buckling 

(see Fig. 10). The guides were tightened to the point where they were lightly clamping the panel 

but still allowed the panel to freely slide up and down within the guides. Teflon tape was applied 

to the edges of the panel to provide a low friction surface between the anti-buckling guides and 

the panel.

Figure 10. Anti-buckling guide.

Test Panel

Anti-Buckling Guide

TOP VIEW

Test Panel

Anti-Buckling 

Guide
Design, Optimization, and Evaluation of Al–2139 Compression Panel with Integral T-Stiffeners

14

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

the stiffened side and smooth side of the panel in the test system. A one-inch thick steel plate 

was situated between the bottom of the panel and the lower compression platen to prevent the 

panel from scarring the platen during testing. Similarly, a 0.03-inch thick sheet of titanium was 

positioned between the top of the panel and the upper compression platen. The panel was 

positioned in the test system such that the applied load was directly over the neutral axis of the 

panel cross section. The test system was configured to apply a compression load in stroke 

control at a displacement rate of 0.010 inch/minute. Preliminary tests were conducted up to a 

maximum compression load of 25,000 lbs to insure that all of the instrumentation was 

operational and that the panel was aligned and loading uniformly. Although a tight tolerance 

was put on the parallelism between the top and bottom edges of the panel, the preliminary tests 

indicated that 0.0015-inch thick foil shims were needed at the top of the panel in five locations. 

Figure 13 shows a picture of the shim locations. The data acquisition and Vic-3D systems were 

started, and the load application was initiated. Stiffener buckling events occurred at different 

load levels because the panel had three pairs of stiffeners with each pair having different 

dimensions and different buckling resistance levels. The first buckling event occurred at 

approximately 85,000 lbs. The load continued to increase to 133,500 lbs at which point the final 

pair of stiffeners buckled, and the load began to slowly decrease. The test was stopped at this 

point, and the panel was unloaded back to zero load. All six stiffeners buckled during the test, 

but the panel did not exhibit an abrupt catastrophic failure. Figure 14 shows a picture of the 

panel with buckled stiffeners following the compression test. The outermost stiffeners (A and D) 

buckled first, followed by the innermost stiffeners (B and C). Stiffeners E and F buckled last and 

do not show any significant nonlinearity in the figure because the test was stopped as soon as 

these stiffeners exhibited the onset of buckling. 

Figure 11. Compression test system with test panel installed. 

Upper Platen

Lower Platen

Anti-Buckling Guide

Test Panel
Design, Optimization, and Evaluation of Al–2139 Compression Panel with Integral T-Stiffeners

15

(a) Stiffened side. (b) Smooth side.

Figure 12. Test panel in compression test system. 

Figure 13. Shim locations at top of panel (four right-most stiffeners and right 

edge of panel).

Shims

Test 

Panel
Design, Optimization, and Evaluation of Al–2139 Compression Panel with Integral T-Stiffeners

16

Figure 14. Post-test photograph showing locations where stiffeners buckled.

 SECTION 6

COMPARISON OF EXPERIMENTAL AND ANALYTICAL RESULTS

The test results from strain gages and 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. For all the results, the nondimensional 

load factor was used to indicate the load 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 panel model. Appendix A describes the location of the strain gages. The 

responses from the complete set of strain gages were plotted against the load factor from the 

nonlinear finite element model and the experimental results in Appendix B. 

Figure 15 shows the measured and predicted strain behavior for the T-stiffened panel skin on the 

upper right side (strain gage A6). The dashed curves represent test measurements from strain 

gages on the stiffened side (A6S) and on the smooth or "web" side (A6W). The solid curves are 

predictions. The vertical line represents the limit load generated by EBF3PanelOpt, which 

corresponds to a load factor of 1.0 or 85,440 lbs compression. Figure 16 shows the same 

information for the skin on the lower right side (strain gage A8). The data show that the panel 

buckled at the limit load as predicted. 

A E B C F D

Buckled 

Stiffeners

Buckled 

Stiffeners
Design, Optimization, and Evaluation of Al–2139 Compression Panel with Integral T-Stiffeners

17

Figure 15. Measured and predicted strain behavior for the skin on the upper right 

side (strain gage A6 location).

Figure 16. Measured and predicted strain behavior for the skin on the lower right 

side (strain gage A8 location).

-0.015

-0.01

-0.005

0

0.005

0.01

0.015

0.02

0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40 1.60 1.80

Strain (in/in)

Load Factor

Location A8 Strain Prediction

A8W Predict A8S Predict EBF3 Linear EV1 A8W Test A8S Test

-0.08

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40 1.60 1.80

Strain (in/in)

Load Factor

Location A6 Strain Prediction

A6W Predict A6S Predict EBF3 Linear EV1 A6W Test A6S Test
Design, Optimization, and Evaluation of Al–2139 Compression Panel with Integral T-Stiffeners

18

The panel design was optimized such that the two outermost stiffeners (A and D) should also 

buckle at the limit load, followed by the two center stiffeners (B and C), and finally the middle 

stiffeners (E and F). Figure 17 shows the strain gage test data and predicted responses for the 

right-most stiffener (D). Strain gages S6A and S6B are located on the stiffener cap, and strain 

gage S6C is located on the smooth side of the panel directly behind that stiffener. The results 

indicate that this stiffener did buckle at the predicted limit load. Examination of all of the strain 

gage data for the stiffeners (not shown) showed that the stiffeners buckled in the sequence 

predicted, with the final set of stiffeners buckling at a load factor value of approximately 1.5. 

Figure 17. Measured and predicted strain behavior for the right-most stiffener 

(strain gage S6 location).

Comparison of predicted mode shapes matched very well with the test data recorded on the 

Vic-3D system. Figure 18 shows the out-of-plane displacement predicted and measured for the 

final buckled shape of the panel. 

-0.025

-0.02

-0.015

-0.01

-0.005

0

0.005

0.01

0.015

0.02

0.025

0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40 1.60 1.80

Strain (in/in)

Load Factor

Location S6 Strain Prediction

S6A Predict S6B Predict S6C Predict EBF3 Linear EV1

S6A Test S6B Test S6C Test
Design, Optimization, and Evaluation of Al–2139 Compression Panel with Integral T-Stiffeners

19

(a) Prediction. (b) Vic-3D measurement.

Figure 18. Out-of-plane displacement for panel at end of compression test.

As shown in Fig. 15–17, the predicted elastic strains were within just a few percent of the elastic 

strains from the test data. This result was typical for all of the strain gage locations (see 

Appendix B). The test data do show, however, that post buckling occurred at different load 

levels than predicted for some of the strain gage locations. This difference may be a reflection of 

post-buckling load redistribution within the panel not occurring as the analysis predicted. 

However, post-buckling behavior was reasonably predicted (both strain levels and modes) 

considering the highly nonlinear behavior of the panel. EBF3PanelOpt is a linear optimization

code and does not rely on post-buckled behavior for optimization. 

Analytical predictions indicated that catastrophic failure would occur rapidly in the load factor 

range of 1.40 to 1.49, with ultimate failure occurring at load factor of 1.49. The test data show 

catastrophic failure occurred at a load factor of 1.54. However, the test data did not show the 

predicted rapid failure because the test was conducted in displacement-control while the 

predictions were based on load-control conditions. Regardless, the ultimate failure occurred

within 5 percent of the predicted load level. 

In addition to good agreement between the prediction and the measurement for the strain 

behavior and buckling loads, the predicted buckling mode shapes matched very well with the test 

data recorded on the Vic-3D system. Figure 18 shows that the prediction and the Vic-3D 

measurement for out-of-plane displacement at the end of the test were very similar to each other.

 SECTION 7

SUMMARY AND CONCLUSIONS

A T-stiffened panel was designed and optimized for minimum mass subjected to constraints on 

buckling load, yielding, and crippling, or to local stiffener failure a new analysis tool named 

EBF3PanelOpt. The panel was designed for a compression loading configuration that is a 

realistic load case for a typical aircraft skin-stiffened panel. The panel was integrally machined 

from 2139 aluminum alloy plate and was tested in compression. The panel was loaded beyond 
Design, Optimization, and Evaluation of Al–2139 Compression Panel with Integral T-Stiffeners

20

buckling and strains, and out-of-plane displacements were extracted from 36 strain gages and 

one linear variable displacement transducer. A digital photogrammetic system was used to 

obtain full field displacements and strains on the smooth (unstiffened) 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. This design, optimization, and testing activity yielded 

the following conclusions: 

• The panel optimized with EBF3PanelOpt with individually-optimized T-stiffeners had a 

weight that was 20 percent lower compared to a conventionally-optimized panel with 

uniform stiffeners. 

• The panel is buckling-critical at limit load, as predicted by EBF3PanelOpt. 

• Elastic strain predictions were within just a few percent of the measured values, further 

confirming the prediction that the panel was not strength-critical. This result implies the 

optimization routine correctly analyzed the critical failure mode and sizing (optimizing) 

accordingly. 

• Post-buckled analysis (not required for EBF3PanelOpt validation) was reasonably 

representative of the panel behavior during testing, and catastrophic failure occurred

within 5 percent of the predicted load level. 

 SECTION 8

REFERENCES

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Post Buckling Using Hypersizer,” 43rd AIAA/ASME/ASCE/AHS/ASC Structures, 

Structural Dynamics, and Materials Conference, No. AIAA–2002–1222, Denver, 

Colorado, 22–25 April 2002. 

2. Anderson, M. S. and Stroud, W. J., “General Panel Sizing Computer Code and Its 

Application to Composite Structural Panels,” AIAA Journal, Vol. 17, No. 8, 1979, pp. 

892–897. 

3. Bushnell, D., “Theoretical Basis of the PANDA Computer Program for Preliminary 

Design of Stiffened Panels Under Combined In-plane Loads,” Computers and Structures, 

Vol. 27, No. 4, 1987, pp. 541–563. 

4. Butler, R., Tyler, A. A., and Cao, W., “Optimum Design and Evaluation of Stiffened 

Panels with Practical Loading,” Computers and Structures, Vol. 52, No. 6, 1994, pp. 

1107–1118. 

5. Stroud, W. J., Greene, W. H., and Anderson, M. S., “Buckling Loads of Stiffened 

Panels Subjected to Combined Longitudinal Compression and Shear: Results Obtained 

With PASCO, EAL and STAGS Computer Programs,” Technical Paper 2215, NASA, 

1984. 

6. 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. 
Design, Optimization, and Evaluation of Al–2139 Compression Panel with Integral T-Stiffeners

21

7. Bendsoe, M. and Kikuchi, N., “Generating Optimal Topologies in Optimal Design Using 

a Homogenization Method,” Computer Methods in Applied Mechanics and Engineering, 

Vol. 71, pp. 197–224, 1988. 

8. 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. 

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

Applications, Springer-Verlag, Berlin, 2003. 

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

International Conference on Aluminum Alloys, 1998. 

11. 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, 8–10 April 2002, pp. 51–56. 

12. 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. 

13. 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. 

14. Mulani, S. B., Joshi, P., Li, J., Kapania, R. K., and Shin, Y. S., “Optimal Design of 

Unitized Structures Using Response Surface Approaches,” Journal of Aircraft, Vol. 47, 

No. 6, 2010, pp. 1898–1906. 

15. Mulani, S. B., Slemp, W. C. H., and Kapania, R. K., “Development of a Framework for 

Design Optimization of Planar Panels Using Curvilinear Stiffeners,” Aeromat 2010 

Conference and Exposition, Bellevue, Washington, 20–24 June 2010. 

16. Mulani, S. B., Slemp, W. C. H., and Kapania, R. K., “EBF3PanelOpt: A Curvilinearly 

Stiffened Panel Optimization Framework for Multiple Load Cases,” 13th AIAA/ISSMO 

Multidisciplinary Analysis Optimization Conference, Fort Worth, Texas, 13–15 

September 2010, AIAA–2010–9238. 

17. Mulani, S. B., Duggirala, V., and Kapania, R. K., “Curvilinearly T-Stiffened Panel 

Optimization Framework under Multiple Load Cases Using Parallel Processing,” 53rd 

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

Conference, Honolulu, Hawaii, 23–26 April 2012. 
Design, Optimization, and Evaluation of Al–2139 Compression Panel with Integral T-Stiffeners

22

18. Kreisselmeier, G. and Steinhauser, R., “Systematic Control Design by Optimizing a 

Vector Performance Index,” Proceeding IFAC Symposium on Computer-Aided Design of 

Control Systems, Zurich, Switzerland, 1979, pp. 113–117. 

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

1997. 

20. VisualDOC 6.2, Design Optimization Software, Vanderplaats Research and 

Development, Colorado Springs, CO–80906. 

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Genetic Algorithm: NSGA-II”, IEEE Transactions on Evolutionary Computation,” Vol. 

6, No. 2, 2002, pp. 182–197. 

APPENDIX A

STRAIN GAGE LOCATIONS 

A total of 36 strain gages were attached to the test panel. Two of the strain gages were type 

CEA–00–250UR–350 rosettes (0°/45°/90°) with the 90° direction oriented parallel to the 

compression load direction. The rosettes were attached to the skin in back-to-back fashion at the 

center point of the panel. Twenty-two of the gages were type CEA–00–250UW–350 uniaxial 

gages oriented parallel to the compression load direction. Sixteen of these gages were attached 

to the skin in back-to-back fashion in various locations remote from the stiffeners. In addition, 

six of these gages were attached to the skin on the smooth side of the panel directly behind each 

of the six stiffeners. The remaining 12 gages were type CEA–00–125UN–350 uniaxial gages 

oriented parallel to the compression load direction and were attached to the stiffener cap (two

gages per stiffener). 

Table A-1 shows an itemized list of the strain gages and their locations on the panel. Figure A-1

shows the strain gage locations on the skin on the stiffened side of the panel. The corresponding 

gages for the smooth side of the panel are directly behind those shown in the figure. The 

intersection of the vertical and horizontal centerlines is designated as the zero position point on 

the panel. The positive horizontal direction (x) on this drawing is pointing to the left on the 

stiffened side of the panel. The positive vertical direction (y) is pointing upward. The stiffener 

labels from left to right are A, E, B, C, F, and D. These labels are based on the stiffener section 

cut labels on the original panel drawing. Fig. A-2, A-3, and A-4 show the strain gage locations 

for each stiffener. 
Design, Optimization, and Evaluation of Al–2139 Compression Panel with Integral T-Stiffeners

23

Table A-1. Location of strain gages on T-stiffened compression test panel. 

gage ID gage type orient. x (in) y (in) location

R1W1 rosette 0° 0.00 0.00 skin on smooth side of panel

R1W2 rosette 45° 0.00 0.00 skin on smooth side of panel

R1W3 rosette 90° 0.00 0.00 skin on smooth side of panel

R1S1 rosette 0° 0.00 0.00 skin on stiffened side of panel

R1S2 rosette 45° 0.00 0.00 skin on stiffened side of panel

R1S3 rosette 90° 0.00 0.00 skin on stiffened side of panel

A1W axial 90° 3.43 0.00 skin on smooth side of panel

A1S axial 90° 3.43 0.00 skin on stiffened side of panel

A2W axial 90° 0.00 4.50 skin on smooth side of panel

A2S axial 90° 0.00 4.50 skin on stiffened side of panel

A3W axial 90° –3.43 0.00 skin on smooth side of panel

A3S axial 90° –3.43 0.00 skin on stiffened side of panel

A4W axial 90° 0.00 –4.50 skin on smooth side of panel

A4S axial 90° 0.00 –4.50 skin on stiffened side of panel

A5W axial 90° 10.30 8.00 skin on smooth side of panel

A5S axial 90° 10.30 8.00 skin on stiffened side of panel

A6W axial 90° –10.30 8.00 skin on smooth side of panel

A6S axial 90° –10.30 8.00 skin on stiffened side of panel

A7W axial 90° 10.30 –8.00 skin on smooth side of panel

A7S axial 90° 10.30 –8.00 skin on stiffened side of panel

A8W axial 90° –10.30 –8.00 skin on smooth side of panel

A8S axial 90° –10.30 –8.00 skin on stiffened side of panel

S1A axial 90° stiffener A 4.50 cap on stiffener A

S1B axial 90° stiffener A 4.50 cap on stiffener A

S1C axial 90° 1.71 4.50 skin on smooth side of panel behind stiffener A

S2A axial 90° stiffener E –4.50 cap on stiffener E

S2B axial 90° stiffener E –4.50 cap on stiffener E

S2C axial 90° –1.71 –4.50 skin on smooth side of panel behind stiffener E

S3A axial 90° stiffener B 0.00 cap on stiffener B

S3B axial 90° stiffener B 0.00 cap on stiffener B

S3C axial 90° 5.14 0.00 skin on smooth side of panel behind stiffener B

S4A axial 90° stiffener C 0.00 cap on stiffener C

S4B axial 90° stiffener C 0.00 cap on stiffener C

S4C axial 90° 1.71 0.00 skin on smooth side of panel behind stiffener C

S5A axial 90° stiffener F 8.00 cap on stiffener F

S5B axial 90° stiffener F 8.00 cap on stiffener F

S5C axial 90° 1.71 8.00 skin on smooth side of panel behind stiffener F

S6A axial 90° stiffener D –8.00 cap on stiffener D

S6B axial 90° stiffener D –8.00 cap on stiffener D

S6C axial 90° 1.71 –8.00 skin on smooth side of panel behind stiffener D
Design, Optimization, and Evaluation of Al–2139 Compression Panel with Integral T-Stiffeners

24

Figure A-1. Location of strain gages on the stiffened side of the test panel.

A5S

A1S

A2S

A3S

A4S

A7S A8S

A6S
Design, Optimization, and Evaluation of Al–2139 Compression Panel with Integral T-Stiffeners

25

Figure A-2. Strain gage locations on stiffeners A and D.

Figure A-3. Strain gage locations on stiffeners B and C.

Figure A-4. Strain gage locations on stiffeners E and F.
Design, Optimization, and Evaluation of Al–2139 Compression Panel with Integral T-Stiffeners

26

APPENDIX B

STRAIN GAGE PLOTS

The following figures show the data from each strain gage attached to the T-stiffened 

compression panel compared to the strain behavior prediction at that location. Also shown on 

each plot is the predicted buckling load factor as calculated from the linear eigenvalue generated 

from EBF3PanelOpt. A description of the strain gage locations is provided in Appendix A. 

Figure B-1. Predicted and measured strain behavior at strain gage location R1. 

(Strain data are from the compression leg of the rosette gages.)

-0.006

-0.004

-0.002

0.000

0.002

0.004

0.006

0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40 1.60 1.80

Strain (in/in)

Load Factor

R1W3 Predict R1S3 Predict EBF3 Linear EV1

R1W3 Test R1S3 Test
Design, Optimization, and Evaluation of Al–2139 Compression Panel with Integral T-Stiffeners

27

Figure B-2. Predicted and measured strain behavior at strain gage location A1.

Figure B-3. Predicted and measured strain behavior at strain gage location A2.

-0.006

-0.004

-0.002

0.000

0.002

0.004

0.006

0.008

0.010

0.012

0.014

0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40 1.60 1.80

Strain (in/in)

Load Factor

A1W Predict A1S Predict EBF3 Linear EV1

A1W Test A1S Test

-0.010

-0.008

-0.006

-0.004

-0.002

0.000

0.002

0.004

0.006

0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40 1.60 1.80

Strain (in/in)

Load Factor

A2W Predict A2S Predict EBF3 Linear EV1

A2W Test A2S Test
Design, Optimization, and Evaluation of Al–2139 Compression Panel with Integral T-Stiffeners

28

Figure B-4. Predicted and measured strain behavior at strain gage location A3.

Figure B-5. Predicted and measured strain behavior at strain gage location A4.

-0.005

0.000

0.005

0.010

0.015

0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40 1.60 1.80

Strain (in/in)

Load Factor

A3W Predict A3S Predict EBF3 Linear EV1

A3W Test A3S Test

-0.010

-0.005

0.000

0.005

0.010

0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40 1.60 1.80

Strain (in/in)

Load Factor

A4W Predict A4S Predict EBF3 Linear EV1

A4W Test A4S Test
Design, Optimization, and Evaluation of Al–2139 Compression Panel with Integral T-Stiffeners

29

Figure B-6. Predicted and measured strain behavior at strain gage location A5.

Figure B-7. Predicted and measured strain behavior at strain gage location A6.

-0.050

-0.040

-0.030

-0.020

-0.010

0.000

0.010

0.020

0.030

0.040

0.050

0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40 1.60 1.80

Strain (in/in)

Load Factor

A5W Predict A5S Predict EBF3 Linear EV1

A5W Test A5S Test

-0.080

-0.060

-0.040

-0.020

0.000

0.020

0.040

0.060

0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40 1.60 1.80

Strain (in/in)

Load Factor

A6W Predict A6S Predict EBF3 Linear EV1

A6W Test A6S Test
Design, Optimization, and Evaluation of Al–2139 Compression Panel with Integral T-Stiffeners

30

Figure B-8. Predicted and measured strain behavior at strain gage location A7.

Figure B-9. Predicted and measured strain behavior at strain gage location A8.

-0.030

-0.020

-0.010

0.000

0.010

0.020

0.030

0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40 1.60 1.80

Strain (in/in)

Load Factor

A7W Predict A7S Predict EBF3 Linear EV1

A7W Test A7S Test

-0.020

-0.010

0.000

0.010

0.020

0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40 1.60 1.80

Strain (in/in)

Load Factor

A8W Predict A8S Predict EBF3 Linear EV1

A8W Test A8S Test
Design, Optimization, and Evaluation of Al–2139 Compression Panel with Integral T-Stiffeners

31

Figure B-10. Predicted and measured strain behavior at strain gage location S1.

Figure B-11. Predicted and measured strain behavior at strain gage location S2.

-0.100

-0.050

0.000

0.050

0.100

0.150

0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40 1.60 1.80

Strain (in/in)

Load Factor

S1A Predict S1B Predict S1C Predict EBF3 Linear EV1

S1A Test S1B Test S1C Test

-0.020

-0.010

0.000

0.010

0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40 1.60 1.80

Strain (in/in)

Load Factor

S2A Predict S2B Predict S2C Predict EBF3 Linear EV1

S2A Test S2B Test S2C Test
Design, Optimization, and Evaluation of Al–2139 Compression Panel with Integral T-Stiffeners

32

Figure B-12. Predicted and measured strain behavior at strain gage location S3.

Figure B-13. Predicted and measured strain behavior at strain gage location S4.

-0.060

-0.040

-0.020

0.000

0.020

0.040

0.060

0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40 1.60 1.80

Strain (in/in)

Load Factor

S3A Predict S3B Predict S3C Predict EBF3 Linear EV1

S3A Test S3B Test S3C Test

-0.010

0.000

0.010

0.020

0.030

0.040

0.050

0.060

0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40 1.60 1.80

Strain (in/in)

Load Factor

S4A Predict S4B Predict S4C Predict EBF3 Linear EV1

S4A Test S4B S4C Test
Design, Optimization, and Evaluation of Al–2139 Compression Panel with Integral T-Stiffeners

33

Figure B-14. Predicted and measured strain behavior at strain gage location S5.

Figure B-15. Predicted and measured strain behavior at strain gage location S6.

-0.020

-0.010

0.000

0.010

0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40 1.60 1.80

Strain (in/in)

Load Factor

S5A Predict S5B Predict S5C Predict EBF3 Linear EV1

S5A Test S5B Test S5C Test

-0.020

-0.010

0.000

0.010

0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40 1.60 1.80

Strain (in/in)

Load Factor

S6A Predict S6B Predict S6C Predict EBF3 Linear EV1

S6A Test S6B Test S6C Test
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Design, Optimization, and Evaluation of A1-2139 Compression Panel with 

Integral T-Stiffeners

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Mulani, Sameer B.; Havens, David; Norris, Ashley; Bird, R. Keith; 

Kapania, Rakesh K.; Olliffe, Robert

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14. ABSTRACT

A T-stiffened panel was designed and optimized for minimum mass subjected to constraints on buckling load, yielding, and 

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

compression loading configuration, a realistic load case for a typical aircraft skin-stiffened panel. The panel was integrally 

machined from 2139 aluminum alloy plate and was tested in compression. The panel was loaded beyond buckling and strains 

and out-of-plane displacements were extracted from 36 strain gages and one linear variable displacement transducer. A digital 

photogrammetic system was used to obtain full field displacements and strains on the smooth (unstiffened) 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.

15. SUBJECT TERMS

T-stiffeners; compression testing; finite element analysis; integral structures; structural optimization

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