November 2011 

NASA/TM–2011-217308 

Design, Optimization, and Evaluation of 

Integrally-Stiffened Al-2139 Panel with Curved 

Stiffeners

David Havens 

Lockheed Martin Aeronautics Company, Marietta, Georgia 

Sandeep Shiyekar 

Virginia Polytechnic Institute and State University, Blacksburg, Virginia 

Ashley Norris 

Lockheed Martin Aeronautics Company, Marietta, Georgia 

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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November 2011 

NASA/TM–2011-217308 

Design, Optimization, and Evaluation of 

Integrally-Stiffened Al-2139 Panel with Curved 

Stiffeners

David Havens 

Lockheed Martin Aeronautics Company, Marietta, Georgia 

Sandeep Shiyekar 

Virginia Polytechnic Institute and State University, Blacksburg, Virginia 

Ashley Norris 

Lockheed Martin Aeronautics Company, Marietta, Georgia 

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 NN L08AA02C) with Ms. Karen M. Brown Taminger as the 

API. We 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, both of 

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

Tests were conducted at NASA Langley Research Center under the Subsonic Fixed Wing 

Project.

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 in the Combined 

Load Test Fixture at NASA Langley Research Center. The panel is representative of a 

large wing engine pylon rib and was optimized for minimum mass subjected to three 

combined load cases. The optimization included constraints on web buckling, material 

yielding, crippling or local stiffener failure, and damage tolerance using a new analysis 

tool named EBF3PanelOpt. Testing was performed for the critical combined 

compression-shear loading configuration. The panel was loaded beyond initial buckling, 

and strains and out-of-plane displacements were extracted from a total of 20 strain gages 

and 6 linear variable displacement transducers. The VIC-3D system was utilized to 

obtain full field displacements/strains in 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. Overall, the panel 

buckled very near to the predicted load in the web regions. 

1 Introduction 

A new analysis tool, EBF3PanelOpt, is being developed for design and optimization of complex 

multifunctional aircraft structural concepts. Application of this new analysis tool is towards pressurized 

non-circular fuselage structures within hybrid wing/body vehicles. In such vehicles, complex structural 

load cases are not well characterized using current design databases. EBF3PanelOpt can be used to 

integrate materials and structural concepts to exploit emerging additive manufacturing processes. These 

processes 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. A secondary goal is to integrate functions such as acoustic damping, adaptive 

active aerodynamic controls, and aeroelastically tailored structures. 

Development of this tool 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

), an additive manufacturing research 

activity 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 structural panel with curved stiffeners. It was desired to select a realistic 

aircraft structural panel with "horizontal" and two "vertical" stiffeners for redesign with curved stiffeners 

and with cut-outs to demonstrate damage tolerance capabilities. A wing-mounted engine pylon rib panel 

was selected. In the case of this panel, the optimization was based on minimum mass subjected to 

constraints on buckling load, yielding, crippling or local stiffener failure, and damage tolerance under a 

combination of compression and shear loads. This optimization effort was used 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 2139-T8. The panel was tested in the NASA LaRC 

Combined Loads Test Fixture (CLTF) [1] under a combined compression-shear loading case. The test 

results were compared against 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 and weaknesses of the 
2 

EBF3PanelOpt tool for the next version 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 for design optimization of curvilinear stiffened panels under in-plane and transverse loading 

[2-5]. The framework named EBF3PanelOpt is an object-oriented script written in PYTHON that 

interfaces with ABAQUS 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 optimizing software such as VisualDoc 

and translates the design data into ABAQUS. A schematic of the EBF3PanelOpt Framework may be 

seen in figure 1. After completion of the FEA, the script reads the results from the output file (*.odv) and 

calculates the responses. The responses include mass, buckling constraint, von Mises stress constraint, 

local crippling constraint, and damage tolerance constraint. The buckling constraint is calculated by: 

1 1

0

d

O (1) 

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

d 1

y

vm

V

V

(2) 

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

imposed using Kreisselmeier-Steinhauser criteria for constraint aggregation as described in [2]. The 

crippling constraint is calculated by: 

หݐݏߪ݂݂݅ ห

ܿܿܨ

൑ ͳ (3) 

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

stress in the stiffener given by: 

°

°

°

 ̄

°

°

°

®

­

d  ̧

 ̧

1

·

 ̈

 ̈

©

§

 ̧

 ̧

1

·

 ̈

 ̈

©

§

!  ̧

 ̧

1

·

 ̈

 ̈

©

§

  



 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

V V

V

V

V

(4) 

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

maximum allowable stress formula, Eq. (4), is obtained from page 444 of [6]. 

The damage tolerance constraint is given by 

K K eff IC d (5)
3 

where KIC is the plane strain fracture toughness. The effective stress intensity factor Keff is computed as: 

2 2 where 0 1 K KK eff I II  dd D D (6)

 

where KI and KII are Mode I and Mode II stress intensity factor, respectively. 

Figure 1. Schematic of EBF3PanelOpt Framework. 

2.1 Parametric Modeling of the Panel 

The design optimization problem of the complex configuration in this study used a baseline configuration 

consisting of a rectangular stiffened panel with two or four curvilinear stiffeners and one or two circular 

cutouts. The loading, material properties, and design constraints for the baseline panel configuration were 

provided by Lockheed Martin Aeronautics Company (Lockheed Martin) as representative of typical 

aircraft structure for this design optimization study. Except where noted, the material used in the design 

examples for FEA was Al 2139-T8. The optimization was performed using two or four blade-type 

curvilinear stiffeners. Shape design variables such as stiffener orientations and curvatures and sizing 

design variables such as stiffener and web dimensions and panel thickness were used. Due to the current 

capability of CAE in ABAQUS, which is limited to creating curved lines by creating y splines throughout 

nodal points only, it is very difficult to handle the issue of the curve going over the domain of the plate. 
4 

Except for the end points of the curve that are on the boundary of the domain, it is in generally difficult to 

know whether or not the curve intersects the boundary of the domain in the optimization problem. 

An “approximate” method was used to overcome the problem in the optimization problem by creating 

curved lines using control points. The Bezier curve-based technique using three control points was used in 

the optimization problem (see figure 2). The Bezier curve equation is in the parametric form as: 

  2 2 1 21 i k j

i k j

x x x x

t tt t

y y y y

­ 1⁄2 ­1⁄2 ­ 1⁄2 ­ 1⁄2 ° ° ®3⁄4 ® 3⁄4 ® 3⁄4 ® 3⁄4    

 ̄ ¿  ̄¿  ̄ ¿ ° °  ̄ ¿ (7)

where t [0,1], and (xi, yi), (xj, yj), (xk, yk) are coordinates of the control points I, J, and K, respectively. 

To create a curved line in ABAQUS using the spline technique passing through points, one more point 

(xm, ym) was interpolated from the Bezier curve at t=0.5 as shown in figure 2, after which a spline curve 

through three points (xi, yi), (xm, ym), (xk, yk) can be created. This spline curve is slightly different from the 

Bezier curve as described, and in some cases, it still intersects the boundary of the domain, although three 

control points lie in the domain of the plate. This method is considered "approximate" because several 

trials are needed to determine the suitable range of these control points. There are 6 design variables 

needed to define the curvilinear stiffeners using this technique. These design variables are used to obtain 

optimal stiffener orientation and curvature, while the sizing design variables present the heights and 

thickness of stiffeners, and thickness of the panel. Tolerances on design variables are used while 

specifying lower and upper bounds on these design variables in order to avoid problems in geometry 

creation. 

a) Create a Bezier Curve using Three Control Points b) Create a Spline throughout Three Points in 

ABAQUS 

Figure 2. Method to Create a Curvilinear Stiffener in ABAQUS 

X

Y

Xi

,Yi

I

J

K

Xj,Yj

Xk,Yk

Xm,Ym

Xm,Ym

Xi,Yi

Xk,Yk
5 

A parametric model was created using Macro Manager in ABAQUS to record the PYTHON script of the 

parametric model. The design variables as described above were labeled in the PYTHON script. This 

script was called stiffened_plate.py.template, which plays the most important role in the program. The 

function of the “stiffened_plate.py.template” script was to carry out analysis to have outputs on buckling, 

damage tolerance, and stress (see figure 1) for evaluating the responses and send them to the optimizer. 

3 Combined Loads Test Fixture 

The Combined Loads Test Fixture (CLTF) was developed by researchers at the NASA Langley Research 

Center (LaRC) to perform combined compression-shear load tests on 24-inch x 28-inch panels [1]. A 

detailed description of the design, assembly, and operation of the test fixture can be found in [1]. Figure 3 

shows the test system without the panel installed. The upper L-shaped shear fixture is bolted to the upper 

compression platen of a 300-kip capacity screw-driven compression test system. The bottom of the lower 

shear fixture rests on roller guides affixed to the lower platen to allow lateral motion. The upright edge of 

the lower shear fixture is attached to a hydraulic ram to apply the shear loads. 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 aluminum tabs while allowing the panel to deform to a parallelogram shape. 

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 provide for a self-reacting shear load mechanism. 

Figure 3. Compression-Shear Test System 

without Test Panel Installed. 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 EBF3PanelOpt software and 

VisualDoc optimization tool. The particle swarm optimization (PSO) [7] was used to estimate the global 

minimum mass satisfying constraints on buckling, crippling and yielding. Detailed optimized design of 

panel is presented in section 4.3. 

Upper 

shear 

fixture

Compression drive column

Lower 

shear 

fixture

Upper 

platen

Lower 

platen

Roller 

guide

Shear 

load 

hydraulic 

ram
6 

4.1 Test Fixture Interface 

Early study of the CLTF indicated that it only transmitted a portion of the compression load into the panel 

while 100% of the shear load was transmitted to the panel [2]. Therefore, to facilitate the loading and 

boundary conditions as closely as possible to those imposed by the CLTF, a reduced grid-point 

interaction model of the test fixture/panel interface is 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, illustrated in figure 5. 

Figure 5. Nonlinear Finite Element Model of Test Fixture/Curvilinear Stiffened Panel Assembly. 

4.2 Nonlinear Finite Element Model 

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

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

nonlinearity and thus is suitable for the post-buckling analysis. The test fixture FEM 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 [1]. The material 

properties used for the test fixture FEM are given in table 1. A linear stress-strain relation was used for 

the test fixture as the fixture's thickness precludes significant material nonlinearity therein. 
7 

Figure 6. Steel Shell Elements in the Nonlinear Test Fixture Model and the Single Point 

Constraints Applied to the Test Fixture Model. 

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. The shear load is introduced in a similar manner to the 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 was provided 

by the EBF3PanelOpt analysis software and modified to include the elastic-plastic material model. Initial 

eccentricity of the panel was provided moving the nodes to match the shape of the first buckling mode, 

scaled to a peak amplitude of 0.0001inch, 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. 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 7. 

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

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

assigned. The fasteners, highlighted in yellow, are shown figure 6. 

Table 1. Material Properties used in the Nonlinear Finite Element Model. 

15-5 (or 17-4) H1025 Stainless Steel Al 2139-T8 

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

Poisson’s ratio, ν 0.32 0.33 

Yield Stress, [ksi] 152.9 68.1 
8 

Figure 7. Finite Element Model of test panel. 

4.3 Optimization of Two and Four Curvilinear Stiffeners 

A baseline panel design from Lockheed Martin (shown in figure 8) was used to perform the optimization 

with multi-constraints imposed on buckling, damage tolerance, vonMises stress, and crippling under two 

load cases (see figure 9). Two curvilinear stiffeners were used for the optimized design and were created 

by the “approximate” Bezier curve using three control points as described above. The design variable 

scheme is shown in figure 10. The baseline is a clamped edge, complex panel with two cutouts. Load 

case (a) presents the panel under maximum compression load and load case (b) presents the panel under 

maximum tension load. The panel was designed with two rings around two cutouts and with two or four 

curvilinear stiffeners. 
9 

Figure 8. Lockheed Martin Baseline. 

Figure 9. Scheme for Multi-Load Cases. 

28 in

24 in

3.389 in

7.717 in

4.923 in

9.564 in 

U3 = 0, UR1 = 0

U3 = 0, UR1 = 0

U3 = 0

UR2 = 0 U3 = 0

UR2 = 0

x1

x2

a) Maximum Compression Load Case b) Maximum Tension Load Case

801 lb/in

253 lb/in

90 lb/in

854 lb/in

293 lb/in

124 lb/in
10 

Figure 10. Design Variables for Optimization Problem with Two Curvilinear Stiffeners. 

The optimization results of the Lockheed Martin baseline using two curvilinear stiffeners with multiconstraints under two load cases are summarized in table 2. The constraints on buckling and on crippling 

are active and become critical while the constraints on vonMises stress and damage tolerance in this 

problem are not critical. This conclusion confirmed the investigation on the fracture, stress and buckling 

analysis of the baseline for doing the optimization problem. Therefore, to save computation, the inactive 

constraints were checked after the optimization for the optimal configuration. In this case, the damage 

tolerance constraint was 0.0806 while the damage tolerance criterion for the stress concentrations around 

cutouts was also satisfied, with the damage tolerant constraint being 0.7436. 

Table 2. Optimization results for Lockheed Martin Cutout-panel with Multi-Constraints under 

Multi-Load Cases: In the Case of Two Curvilinear Stiffeners.

control points

control points

x1

x2 x3

x4 x5

x11

x7

x6

x10

x8

x9

x12

x13

x16

x17

x14(ring thickness)

x15(ring thickness)
11 

Table 3. Optimal Design Variables for Lockheed Martin Cutout-panel with Multi-Constraints 

under Multi-Load Cases: Case of Two Curvilinear Stiffeners.

Table 3 shows the optimal parameters for all 17 design variables. The optimal design configuration is 

shown in figure 11 and the first four buckling mode shapes are shown in figure 12. The eigenvalues of the 

first four buckling modes of the optimal design configuration are very similar. During the panel 

optimization process, the eigenvalues of the first nine buckling modes were extracted and analyzed. The 

optimization was carried out using the Particle Swarm Optimization (PSO) with 40 particles after 69 

iterations (see figure 13). The 69-iteration PSO result was used as the starting point for the GradientBased Optimization (GBO).The converged results of the GBO were obtained after 7 iterations and are 

shown in figure 14. 
12 

Figure 11. Optimal Design Configuration for Lockheed Martin Panel using PSO and Gradient 

Based Optimization: Case of Two Curvilinear Stiffeners 

Figure 12. First Four Buckling Mode Shapes and eigenvalues for the Optimal Design 

Configuration using Two Curvilinear-Stiffeners. 

Mode 1 = 0.9999 Mode 2 = 1.0199 

Mode 3 = 1.0871 Mode 4 = 1.1753 
13 

 

Figure 13. Optimization History for the Objective Function (Mass) and Buckling Constraint for 

Optimization of Lockheed Martin Panel using the PSO algorithm with 69 Iterations 

0.7 

0.75 

0.8 

0.85 

0.9 

0.95 

1 

0 10 20 30 40 50 60 70 80 

Buckling Constraint 

Design Iteration 

Response History 

6.5 

6.65 

6.8 

6.95 

7.1 

7.25 

7.4 

7.55 

7.7 

7.85 

8 

0 10 20 30 40 50 60 70 80 

Mass (lbf) 

Design Iteration 

Objective Function History 
14 

Figure 14. Optimization History for the Objective Function (Mass) and Buckling Constraint for 

Optimization of Lockheed Martin Panel using the GBO algorithm with 7 Iterations. 

6.5 

6.52 

6.54 

6.56 

6.58 

6.6 

0 1 2 3 4 5 6 7 8 

Mass (lbf) 

Design Iteration 

Objective Function History 

0.994 

0.995 

0.996 

0.997 

0.998 

0.999 

1 

0 1 2 3 4 5 6 7 8 

Buckling Constraint 

Design Iteration 

Response History 
15 

Innovative capabilities in the programming code were developed by VPI in version 2 of EBF3PanelOpt. 

The main objective was the design optimization of a curvilinear stiffened panel. Using the same 

simulation of loading, constraints and design criterion as per the two curvilinear stiffener cases, a four 

stiffener design was also optimized using the program. The resulting design was a panel with a weight of 

6.820 lbf, which was 6.8 % less than the weight of the Lockheed Martin baseline with straight stiffeners. 

To validate these results of design optimization, Lockheed Martin generated experimental results for 

comparison. Figure 15 shows the panel with four curved stiffeners optimized using EBF3PanelOpt v2.0 

with maximum von Mises stress and mode I eigenvalue contours. 

Figure 15. VT Optimized Panel using EBF3PanelOpt v2.0. 

EBF3PanelOpt v2.0 predicted that the panel was buckling critical for the maximum compressive load 

case. A CATIA model of this panel was generated and used to manufacture the innovative panel design as 

shown in figure 16. 

Figure 16. Panel Design for Manufacturing 
16 

5 Panel Manufacturing 

A solid model of the curvilinear stiffened panel was converted to a detailed CAD file in CATIA 

V5 by Lockheed Martin. The geometry is included with 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 17). 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 is included with stiffener 

run-outs at the ends. 

The baseline optimized test article was then machined with blade stiffeners. This panel was 

machined from 2-inch thick aluminum alloy 2139-T8 plate stock and all required tolerances were met 

after the initial panel was determined to require some rework. 

After the panel was machined and inspected, 4140 steel tabs conforming to the NASA combined 

loading fixture drawings [1] were adhesively bonded using Hysol EA9395 with 0.005-inch diameter glass 

micro-balloons added for bond-line control. These bonds were cured at room temperature for 24 hours 

then postcured at 200 oF to prevent any residual thermal expansion stresses at the bond-line. The panel 

was then crated and shipped to NASA LaRC for testing. The machined panel is shown in figure 17. 

A surface profile of the test panel was generated using laser scanning techniques. Figure 18 

shows the deviation of the laser-scanned surface from that of the original CAD file of the panel. The 

center region of the panel has surface profile of the original CAD file. However, the laser scan data 

indicate that the top and bottom ends of the panel are bowed approximately 0.1 inch towards the stiffener 

side of the panel. 

Figure 17. Picture of the Al-2139 Test Panel without Steel Tabs. 
17 

Figure 18. Out-of-plane distortion of fabricated test panel measured by scanning laser profilometer. 

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 three LVDTs were attached to the shear fixture 

to measure shear displacement. 

A total of 20 strain gages were attached to the skin of the panel. Ten of the gages were 

0°/45°/90° rosettes and 10 of the gages were uniaxial gages aligned parallel to the compression load 

direction. In addition, 6 more uniaxial gages were attached to selected stiffeners. A description of the 

strain gage locations is provided in appendix A. Both sides of the panel were 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 6 LVDTs 

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. Two VIC-3D systems were configured to obtain full-field stereophotogrammetic 

displacement/strain measurements on the upper half and the lower half of stiffened side of panel. In 

addition to the VIC-3D cameras, video cameras were set up to record behavior of both the skin and 

stiffened sides of the panel during the test. Figure 19 shows the test system with the panel installed and 

ready for testing. 

TOP BOTTOM

+0.100

0.000

-0.100

inches
18 

Figure 19. Compression-Shear Test System with Test Panels Installed. 

The test system was configured to apply compression load and shear load simultaneously at a 

load ratio of 0.316 (shear load y compression load). 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 ensure 

that the instrumentation was operational and that the load ratio was correct. The data acquisition and 

VIC-3D systems were started and load application was initiated. When the panel attained a compression 

load of 36,800 lbs and a shear load of 11,400 lbs a buckling event occurred and the compression load 

decreased rapidly by 600 lbs. The shear load controller was not able to adequately follow the 

compression load command signal and rapid oscillations in the shear actuator began. The test was 

stopped and the panel was unloaded. Once the load was removed, no apparent permanent panel 

deformation was observed. 

The shear load controller tuning was adjusted and the compression-shear test was initiated again. 

Loading proceeded past the maximum load attained during the first test without event. Several loud 

"pops" were heard during loading. The panel attained a compression load of 54,600 lbs and a shear load 

of 16,800 lbs, at which point a very loud bang occurred. The shear load dropped to zero, but the 

compression load kept increasing and the test panel appeared to remain intact. The test was stopped and 

the panel was unloaded. It was discovered that the bolt connecting the shear load cell to the shear load 

frame had fractured, resulting in the loud noise and the loss of shear load. Inspection of the test system 

indicated that the shear load train hydraulic ram was operating in a direction opposite to the planned 

direction, thus applying a tensile load to the shear load cell bolt and resulting in bolt fracture. Removal of 

the panel from the test frame also revealed that three of the steel tabs had debonded from the edge of the 

panel. These debonds most likely were the source of the popping sounds during the test. 

Post-test inspection of the panel showed a small permanently deformed area in the top center 

region near strain gage #A1. Figure 20 shows post-test photographs of the skin and stiffened sides of the 

test panel illustrating regions where the tabs debonded and the permanent buckled occurred. Figure 21 

shows the extent of the buckled region. In the figure, one of the debonded steel tabs was placed on-edge 

across the buckled region to give a straight-edge reference for the amount of buckling. The skin buckled 

about 0.050 inch towards the stiffener side of the panel. 

Combined

Load

test

fixture

Test

panel 

Self-reacting

shear 

load 

bar

Shear 

load 

hydraulic 

ram
19 

Figure 20. Post-Test Photograph of Test Panel with Debonded Tabs and Small Buckled Region. 

Figure 21. Post-Test Photograph of Test Panel showing Buckled Region. 

12 in.

Buckled region

Tab 

debond

Skin Side Stiffener Side

~ 0.050 in.
20 

7 Comparison of Results 

Buckling

The first mode buckling test results are shown in Figure 22. This buckling occurs in the top 

center panel near strain gage A1. The solid blue line represents the predicted eigenvalue (or buckling 

load level) at a load factor of 0.77 which very closely matches our test data. 

Normally, EBF3PanelOpt would not allow such a design to occur as it would violate the criteria 

for the panel to remain stable to limit load (an eigenvalue of 1.0). However, the panel design was 

optimized using a positive shear load (defined in Figure 9). The original analysis using a positive shear 

load predicted a buckling load factor level of 1.23 for the web at this panel location (i.e. this web should 

not buckle until 123% of limit load is achieved). However, as discussed previously, an anomaly in the 

test setup caused a negative shear load to be applied to the test panel. By reversing the shear load 

direction and using the same load magnitude, EBF3PanelOpt predicted a buckling load factor of 0.77 

which matched the test results for an applied negative shear. This result that indicates that the direction of 

applied shear can have a significant effect on the design of curvilinear stiffened structure that is buckling 

critical. Based on this result, all of the predictions contained in this report are based on negative shear 

loading to allow a direct comparison to the test performed. 

The test fixture also plays a role in comparing the EBF3PanelOpt results to the test results. As 

discussed in Section 4.3, the optimization used a clamped edge boundary condition with fully applied 

load. The test fixture (Section 4.1) only transmits a portion of the compression load into the panel, and 

has neither simple nor fully clamped edges. Using a FEM for predictions has minimized the discrepancy 

between the design and test data; however, some differences may still remain due to the nature of using a 

FEM representation. 

Figure 22. EBF3PanelOpt First Mode Buckling Prediction and Test Results. (Strain is 

presented in inch/inch.) 
21 

The next buckling mode test results are shown in Figure 23. The buckling is visible in the strain 

gage data for the upper and lower surface around a load factor of 0.93. The solid blue line shows the 

predicted eigenvalue at 0.93. This gage is near the center of the panel and represents the first “global” 

buckling mode (meaning multiple webs are affected by this mode shape). 

Appendix C contains the data for all of the strain gages and the EBF3PanelOpt predictions for 

this test. Overall the panel buckled very near the predicted load factor level for each of the web regions. 

Based on the test results, the panel failed by buckling as predicted by the sizing mode and the buckling 

load compared well to that predicted by EBF3PanelOpt. 

Figure 23. EBF3PanelOpt Second Mode Buckling Prediction and Test Results. (Strain is 

presented in inch/inch.) 

 
22 

Out-of-Plane Displacement

Six LVDT’s were used during the test to monitor the out of plane displacement of the panel. All 

of the LVDT’s were arranged on the flat side of the panel. Using the cutouts for positional reference, the 

locations are shown below in Figure 24 as D1 – D6. 

Figure 24. LVDT Locations on Flat Side of Panel. 
23 

The out-of-plane displacement predictions did not match the test results . However, this poor 

correlation is not surprising due to the fabrication issues discussed in Section 5.0. A cross section through 

the center of the panel is shown below in Figure 25. The neutral axis for this section is approximately 

0.08 inch toward the stiffener side of the compression load line causing an induced moment that would 

cause the test panel to deflect to the stiffener side of the panel (a positive LVDT reading). This is the 

configuration modeled in the FEM and used for out-of-plane displacement predictions. Unfortunately, 

the top and bottom of the panel were warped 0.1 inch toward the stiffener side of the panel, effectively 

shifting the neutral axis at the center of the panel to be located 0.02 inch toward the web side of the 

applied compression load line. This neutral axis shift will cause the panel to deflect towards the web 

(flat) side of the panel (a negative LVDT reading). 

Figure 25. Panel Center Cross Section w/ Neutral Axis Shift. 

The shift in the neutral axis due to panel warpage can be seen in the test results shown in Figure 

26 for LVDT D1 at the center of the panel. The predicted behavior for deflection to the stiffener side is 

represented in the positive displacement values. The actual behavior showing deflection to the flat side is 

represented in the negative LVDT displacement values. 

Figure 26. Test Panel Center Out-of Plane-Displacement. 

Neutral Axis Warped Panel Load Line 

FEM Panel Load Line 
24 

Although a “warped” FEM could be generated and used for predictions, it was decided that such 

an exercise would only serve to correlate the strain levels for the one-of-a-kind FEM and would not 

accomplish any further validation of EBF3PanelOpt’s buckling optimization capability. The effect of this 

0.1-inch out-of-plane warpage in this panel was not included in the panel analysis in this present study. 

Additionally, the LVDT’s were located using the results from positive shear predictions. The 

intent was to place them at peak deflection points for the predicted buckled shape. Because the test was 

actually performed using an applied negative shear, the locations of the LVDT’s may not be as 

meaningful as they are no longer located at their intended position on the buckled web. Appendix C 

contains the data for all 6 LVDT locations (D1-D6). 

Strain Predictions

A total of 20 strain gages were attached in back-to-back fashion to the skin of the panel. Ten of 

the gages were type CEA13-250UR-350 rosettes (0°/45°/90°) rosettes with the 90° direction oriented 

parallel to the compression load direction. For the strain gage rosettes, the minimum principal strain was 

calculated from the 0°, 90° and 45° components. Ten of the gages were type CEA00-250UW-350 

uniaxial gages oriented parallel to the compression load direction. In addition, 6 more uniaxial gages 

were attached to the selected stiffeners. Three of these gages were attached to the stiffener and three to 

the skin directly behind the stiffener on the flat side of the panel. These gages were aligned in the 

direction of the stiffener. The primary function of the strain gages are to capture the onset of buckling 

which is why all of the gages are installed “back to back”. The secondary functions of the strain gages 

are to record the strain levels in each of the panel for test monitoring and comparison to predictions. 

However, because this panel is sized by buckling and not strength, correlation to magnitude is not critical 

so long as the test results show buckling to occur as predicted. 

Although the onset of buckling, as previously discussed, match the test results very well, the 

magnitudes for the strain predictions did not match the test results well. This is not surprising due to the 

fabrication issues discussed in Section 5.0 and the shift in neutral axis (discussed in out of plane 

displacement results) which caused a change in direction for the induced moment. Moments due to small 

out of plane displacement (that do not change the overall stiffness of the panel) will affect the strain 

readings at the outer fibers in the compression direction (vertical rosette leg component), however, will 

not affect the critical buckling load or the buckling results. The FEM predicted an out of plane deflection 

towards the stiffener side of the panel. The induced tension should lower the compressive strains on the 

stiffener side of the panel and increase them on the flat side of the panel. The warped test panel, however, 

deflected towards the flat side of the panel inducing tension (or a reduction in compression) on the flat 

side of the panel and adding to the compression of the stiffener side of the panel. Figure 27 shows the 

predicted strains and test strains. 

The results of the predicted behavior versus the test behavior can be seen in this figure. The 

predicted behavior has lower compressive strains on the stiffener side (R1S) and higher compressive 

strains on the flat (or web) side (R1W). This behavior is consistent with the prediction assuming out of 

plane deflection towards the stiffener side. The actual behavior shows lower compressive strains on the 

flat (or web) side (R1W Min Prin) and higher compressive strains on the stiffener side (R1S Min Prin). 

This behavior is consistent with a reversal in induced moment caused by the warpage in the panel. 

The predicted eigenvalue (0.93) from EBF3PanelOpt shown in Figure 27 (blue vertical line) 

matches well with the onset of buckling seen in the test data (green and orange curves). This match is a 
25 

strong indication that the moment reversal caused by the panel warping will change the strain readings, 

but is not of sufficient magnitude to have an effect on the buckling load level (which is in line with the 

equations that govern the critical buckling load which are not influenced by moment). The strains from 

the non-linear FEM run (blue and purple curves) indicated a higher predicted loading as depicted in the 

higher negative strain readings occurring at a lower percent of limit load. It is not apparent why the nonlinear analysis produced this higher local loading; however, it did predict the onset of buckling to occur at 

the same strain level as the linear analysis. Appendix C contains the data for all of the strain gages. 

Figure 27. EBF3PanelOpt First Mode Buckling Prediction, Strain Predictions and Test Results. 

(Strain is presented in inch/inch.) 

Figure 28 shows the strain readings from strain gage R2 in the lower right corner of the panel. 

Yield failure of the material initiated in this corner of the panel, as indicated by the strain reading at a load 

factor of 2.48 times the analytically derived limit load. This failure load correlated well with the 

analytical prediction of that occurrence at a load factor of 2.60 times limit load in the same location. A 

load cell bolt failure ended testing at a load factor of 2.65. The load factor (X-axis) for this figure 

extends further then the other data shown in this report (and appendix C). All of the data contained in this 

report and in appendix C reflect the first test that was halted prematurely (load factor of 1.9) due to the 

shear load cell controller issue discussed previously in Section 6. Once the anomaly in the shear 

controller was corrected, a second test was performed. Unfortunately, the panel was plastically deformed 
26 

during the first test which altered some of the subsequent strain readings during the second test. Although 

the second test strain readings cannot be compared to prediction, we were able to take the panel to failure 

to compare location and load level to our predictions. 

Figure 28. Strain Gage R2 Test Data to Failure. (Strain is presented in inch/inch.) 

 
27 

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 structural panel 

with curved stiffeners. The panel was optimized for minimum mass subjected to combined in-plane loads 

with constraints on buckling load, yielding, and crippling or local stiffener failure. The resulting design 

was a panel with a weight of 6.820 lbf, which was about 7% less than the weight of the Lockheed Martin 

baseline panel with straight stiffeners. The optimized panel design was used to fabricate an integrallymachined test panel using aluminum alloy 2139-T8. The panel was tested under a combined 

compression-shear loading configuration that is a realistic load case for a large wing pylon rib panel. 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: 

x Test results show that the panel failed by buckling as predicted by the sizing mode and the 

buckling occurred at a load close to that predicted by EBF3PanelOpt. 

x Material yielding begins to occur in the lower corner at a load factor of 2.48, closely matching the 

predicted behavior and load. Loading continued to a load factor of 2.65 when a load cell bolt 

failure occurred, ending the testing. 

x The strain and deflection predictions, especially in the post buckled region, do not match well to 

the test results due to the severe warping in the panel. The warp was large enough to shift the 

neutral axis of the panel to the opposite side of the applied load resulting in a reversal in direction 

of both out of plane deflection and moment (induced from the eccentricity). 

It should be noted that it is not surprising that the post-buckling response is 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 are used to introduce the load into the panel. The 

stiffness of these springs have been 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 to allow the user to correctly apply the loading 

and boundary conditions when using EBF3PanelOpt. EBF3PanelOpt currently allows for uniform 

loading and uniform clamped, simple or free edge boundary conditions. 
28 

References 

1. Baker, D.J., “Combined Load Test Fixture," Technical Memorandum ARL-TR-3726, Army 

Research Lab, Hampton, VA, February 2006. 

2. 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. 

3. 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 

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

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

4. 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 17th AIAA/ASME/AHS Adaptive 

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

5. 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 17th AIAA/ASME/AHS Adaptive Structures Conference, Palm Springs, 

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

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

7. 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. 

 
29 

Appendix A 

Strain Gage Locations 

A total of 20 strain gages were attached in back-to-back fashion to the skin of the panel. Ten of 

the gages were type CEA13-250UR-350 rosettes (0°/45°/90°) with the 90° direction oriented parallel to 

the compression load direction. Ten of the gages were type CEA00-250UW-350 uniaxial gages oriented 

parallel to the compression load direction. Six additional uniaxial gages were attached to the selected 

stiffeners. Three of these gages were attached to the stiffener and three to the skin directly behind the 

stiffener on the flat side of the panel. These gages were aligned in the direction of the stiffener. 

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 stiffener side of the panel. The corresponding gages for the flat 

side of the panel are directly behind those shown in the figure. 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 bottom stiffener is Stiffener A and the top stiffener is Stiffener D. 

The left-hand stiffener is Stiffener B and the right-hand stiffener is Stiffener C. The strain gage locations 

for Stiffeners A, B, and C are shown in figures A2, A3, and A4, respectively. 
30 

Table A1. Location of Strain Gages on Compression-Shear Test Panel. 

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

A1S uniaxial 90° 0.93 11.70 Skin on stiffener side of panel A1

A1W uniaxial 90° 0.93 11.70 Skin on flat side of panel

A2S uniaxial 90° -5.01 9.67 Skin on stiffener side of panel A1

A2W uniaxial 90° -5.01 9.67 Skin on flat side of panel

A3S uniaxial 90° 1.64 -9.54 Skin on stiffener side of panel A1

A3W uniaxial 90° 1.64 -9.54 Skin on flat side of panel

A4S uniaxial 90° 10.00 0.00 Skin on stiffener side of panel A1

A4W uniaxial 90° 10.00 0.00 Skin on flat side of panel

A5S uniaxial 90° -10.00 0.00 Skin on stiffener side of panel A1

A5W uniaxial 90° -10.00 0.00 Skin on flat side of panel

R1AS rosette 0° 1.19 -3.46 Skin on stiffener side of panel A1

R1BS rosette 45° 1.19 -3.46 Skin on stiffener side of panel A1

R1CS rosette 90° 1.19 -3.46 Skin on stiffener side of panel A1

R1AW rosette 0° 1.19 -3.46 Skin on flat side of panel

R1BW rosette 45° 1.19 -3.46 Skin on flat side of panel

R1CW rosette 90° 1.19 -3.46 Skin on flat side of panel

R2AS rosette 0° 8.15 -11.40 Skin on stiffener side of panel A1

R2BS rosette 45° 8.15 -11.40 Skin on stiffener side of panel A1

R2CS rosette 90° 8.15 -11.40 Skin on stiffener side of panel A1

R2AW rosette 0° 8.15 -11.40 Skin on flat side of panel

R2BW rosette 45° 8.15 -11.40 Skin on flat side of panel

R2CW rosette 90° 8.15 -11.40 Skin on flat side of panel

R3AS rosette 0° -9.40 -11.10 Skin on stiffener side of panel A1

R3BS rosette 45° -9.40 -11.10 Skin on stiffener side of panel A1

R3CS rosette 90° -9.40 -11.10 Skin on stiffener side of panel A1

R3AW rosette 0° -9.40 -11.10 Skin on flat side of panel

R3BW rosette 45° -9.40 -11.10 Skin on flat side of panel

R3CW rosette 90° -9.40 -11.10 Skin on flat side of panel

R4AS rosette 0° -5.34 4.50 Skin on stiffener side of panel A1

R4BS rosette 45° -5.34 4.50 Skin on stiffener side of panel A1

R4CS rosette 90° -5.34 4.50 Skin on stiffener side of panel A1

R4AW rosette 0° -5.34 4.50 Skin on flat side of panel

R4BW rosette 45° -5.34 4.50 Skin on flat side of panel

R4CW rosette 90° -5.34 4.50 Skin on flat side of panel

R5AS rosette 0° 8.53 9.52 Skin on stiffener side of panel A1

R5BS rosette 45° 8.53 9.52 Skin on stiffener side of panel A1

R5CS rosette 90° 8.53 9.52 Skin on stiffener side of panel A1

R5AW rosette 0° 8.53 9.52 Skin on flat side of panel

R5BW rosette 45° 8.53 9.52 Skin on flat side of panel

R5CW rosette 90° 8.53 9.52 Skin on flat side of panel

S1S uniaxial 90° 4.68 -0.29 Stiffener C A4

S1W uniaxial 90° 4.68 -0.29 Skin on flat side of panel behind Stiffener C

S2S uniaxial 90° -1.45 -5.20 Stiffener B A3

S2W uniaxial 90° -1.45 -5.20 Skin on flat side of panel behind Stiffener B

S3S uniaxial 90° -4.29 -6.45 Stiffener A A2

S3W uniaxial 90° -4.29 -6.45 Skin on flat side of panel behind Stiffener A
31 

Figure A1. Location of Strain Gages on Stiffener Side of Panel. 
32 

Figure A2. Location of strain gages on Stiffener A. 

Figure A3. Location of strain gages on Stiffener B. 

Figure A4. Location of Strain Gages on Stiffener C 

(Gages aligned along stiffener length)

(Gages aligned along stiffener length)

(Gages aligned along stiffener length)
33 

Appendix B 

Location of LVDTs for Out-of-Plane Displacement Measurement 

A total of 6 linear variable displacement transducers (LVDTs) were attached to the compressionshear test panel to measure out-of-plane displacement. The LVDTs were attached to the flat side of the 

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

buckling of the skin towards the stiffener 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 photos of (a) the top half and (b) the bottom half of the flat side of the panel with 

the LVDTs attached. The intersection of the vertical and horizontal centerlines of the panel 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. 

Table B1. Location of LVDTs on Compression-Shear Test Panel.

LVDT no. X (in.) Y (in.)

D1 1.2 -3.6

D2 -4.8 10.0

D3 9.7 2.8

D4 -9.4 -11.3

D5 8.5 9.9

D6 0.8 12.2
34 

Figure B1. Location of LVDTs on Flat Side of Test Panel for Out-of-Plane Displacement 

Measurement: (a) Top Half of Panel; (b) Bottom Half of Panel. 

D1

D4

D3

D5

D6

D2

(a)

(b)
35 

Appendix C 

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

The results from each LDVT and strain gage are plotted in figures C1-C17. For the strain gage 

rosettes, the minimum principal strain was calculated from the 0°, 90° and 45° components using the 

following equation: 

1 H

2 H

3 H

Principal Stresses with

0-45-900 Rosette:

1 3 2 2

/ 12 23

2 ( )( ) 21 1 MAX MINE H H

V HH HH

Q Q

a o 

 r   « »   ¬ 1⁄4

The minimum principal strain predictions from the nonlinear finite analysis are also included in the strain 

plots. For the LVDT data, positive displacement is towards the stiffener side of the panel. Refer to 

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

Figure C1. Strain Gage R1 Data. (Strain is presented in inch/inch). 
36 

Figure C2. Strain Gage R2 Data. (Strain is presented in inch/inch). 

Figure C3. Strain Gage R3 Data. (Strain is presented in inch/inch). 
37 

Figure C4. Strain Gage R4 Data. (Strain is presented in inch/inch). 

Figure C5. Strain Gage R5 Data. (Strain is presented in inch/inch). 
38 

Figure C6. Strain Gage A1 Data. (Strain is presented in inch/inch). 

Figure C7. Strain Gage A2 Data. (Strain is presented in inch/inch). 
39 

Figure C8. Strain Gage A3 Data. (Strain is presented in inch/inch). 

Figure C9. Strain Gage S1 Data. (Strain is presented in inch/inch). 
40 

Figure C10. Strain Gage S2 Data. (Strain is presented in inch/inch). 

Figure C11. Strain Gage S3 Data. (Strain is presented in inch/inch).
41 

Figure C12. D1 LVDT Data. 

Figure C13. D2 LVDT Data. 
42 

Figure C14. D3 LVDT Data. 

Figure C15. D4 LVDT Data. 
43 

Figure C16. D5 LVDT Data. 

Figure C17. D6 LVDT Data.
REPORT DOCUMENTATION PAGE Form Approved

OMB No. 0704-0188

2. REPORT TYPE 

Technical Memorandum

 4. TITLE AND SUBTITLE

Design, Optimization, and Evaluation of Integrally-Stiffened A1-2139 

Panel With Curved Stiffeners 

5a. CONTRACT NUMBER

 6. AUTHOR(S)

Havens, David; Shiyekar, Sandeep; Norris, Ashley; Bird, Richard K.; 

Kapania, Rakesh K.; 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 is 

representative of a large wing engine pylon rib and was optimized for minimum mass subjected to three combined load cases. The optimization included 

constraints on web buckling, material yielding, crippling or local stiffener failure, and damage tolerance using a new analysis tool named EBF3PanelOpt. 

Testing was performed for the critical combined compression-shear loading configuration. The panel was loaded beyond initial buckling, and strains and 

out-of-plane displacements were extracted from a total of 20 strain gages and 6 linear variable displacement transducers. The VIC-3D system was utilized to 

obtain full field displacements/strains in 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. Overall, the panel buckled very near to the predicted load in the web regions. 

15. SUBJECT TERMS

Curvilinear stiffeners; Finite element analysis; Load tests; Structural design; Structural optimization

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collection of information, including suggestions for reducing this burden, to Department of Defense, Washington Headquarters Services, Directorate for Information Operations and 

Reports (0704-0188), 1215 Jefferson Davis Highway, Suite 1204, Arlington, VA 22202-4302. Respondents should be aware that notwithstanding any other provision of law, no person 

shall be subject to any penalty for failing to comply with a collection of information if it does not display a currently valid OMB control number.

PLEASE DO NOT RETURN YOUR FORM TO THE ABOVE ADDRESS.

1. REPORT DATE (DD-MM-YYYY)

01- 11 - 2011