D.J. Roth and R.P. Tokars

Glenn Research Center, Cleveland, Ohio

R.E. Martin

Cleveland State University, Cleveland, Ohio

R.W. Rauser

The University of Toledo, Toledo, Ohio

J.C. Aldrin

Computational Tools, Inc., Gurnee, Illinois

E.J. Schumacher

Magsoft Corporation, Ballston Spa, New York

Ultrasonic Phased Array Inspection for an

Isogrid Structural Element With Cracks

NASA/TM—2010-216090

March 2010
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D.J. Roth and R.P. Tokars

Glenn Research Center, Cleveland, Ohio

R.E. Martin

Cleveland State University, Cleveland, Ohio

R.W. Rauser

The University of Toledo, Toledo, Ohio

J.C. Aldrin

Computational Tools, Inc., Gurnee, Illinois

E.J. Schumacher

Magsoft Corporation, Ballston Spa, New York

Ultrasonic Phased Array Inspection for an

Isogrid Structural Element With Cracks

NASA/TM—2010-216090

March 2010

National Aeronautics and

Space Administration

Glenn Research Center

Cleveland, Ohio 44135
Acknowledgments

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Level of Review: This material has been technically reviewed by technical management. 
NASA/TM—2010-216090 1 

Ultrasonic Phased Array Inspection for an 

Isogrid Structural Element With Cracks 

D.J. Roth and R.P. Tokars 

National Aeronautics and Space Administration 

Glenn Research Center 

Cleveland, Ohio 44135 

R.E. Martin 

Cleveland State University 

Cleveland, Ohio 44115 

R.W. Rauser 

The University of Toledo 

Toledo, Ohio 43606 

J.C. Aldrin 

Computational Tools, Inc. 

Gurnee, Illinois 60031 

E.J. Schumacher 

Magsoft Corporation 

Ballston Spa, New York 12020 

Abstract 

In this investigation, a T-shaped aluminum alloy isogrid stiffener element used in aerospace 

applications was inspected with ultrasonic phased array methods. The isogrid stiffener element had 

various crack configurations emanating from bolt holes. Computational simulation methods were used to 

mimic the experiments in order to help understand experimental results. The results of this study indicate 

that it is at least partly feasible to interrogate this type of geometry with the given flaw configurations 

using phased array ultrasonics. The simulation methods were critical in helping explain the experimental 

results and, with some limitation, can be used to predict inspection results. 

Introduction 

Integrally-stiffened structures, such as isogrid panels and shells (an example of which is shown in 

Fig. 1(a)) are commonly used in aerospace applications (Ref. 1). These self-stiffened structures are 

effective where low mass, as well as overall stiffness and strength are desired. Common applications 

include propellant tanks and lower stage structures of space launch vehicles. If fasteners are used to attach 

internal structure through the isogrid structure, cracks may originate from the fastener holes. These cracks 

can then propagate through the exterior wall surface, which can be catastrophic for applications such as 

pressurized propellant tanks where the isogrid wall must contain the propellant and maintain pressure. 

Such cracks are not observable from the external surface of the structure until after propagation through 

the exterior wall, and often the interior surface is inaccessible for inspection. Thus, methods for inspection 

of these holes from the exterior isogrid surface are highly desirable. 

The T-shaped element shown in Figure 1(b) is a stiffening subcomponent of an integrally-stiffened 

structure. The upper surface labeled inspection side represents the outerwall of the isogrid, which would 

be the pressure barrier for a propellant tank application. The rib is the interior stiffening component. The 

holes represent points where internal structure would be fastened, and cracks that might form at the 

fastener (e.g., bolt) holes are illustrated. The goal of the inspection would be to detect these cracks from 
NASA/TM—2010-216090 2 

the exterior (top) or inspection side. Ultrasonic inspection is a natural NDE candidate for internal surface 

flaw detection from external surfaces. The geometry of the isogrid element does not easily lend itself to 

ultrasonic inspection since the body, or rib, of the structure is a narrow element perpendicular to and 

projecting from the top. UT inspection could be implemented from the exterior surface, but would likely 

have limited detection capability of primary cracks due to “shadowing” from the rib/stiffener fasteners for 

cracks in certain orientations (Ref. 2). Nevertheless, ultrasonic inspection is still worth considering in this 

case for a number of reasons. These include the study of bulk wave ultrasonic propagation through thin 

elements for practical inspection, and the use of phased array ultrasonics (Refs. 3 to 6) for this type of an 

application. 

Ultrasonic phased array transducers are made of multiple crystals that are electronically pulsed in a 

sequence using a specified delay between pulses to create electronic scanning, beam steering, and/or 

focusing capability. Ultrasonic phased array inspection is gaining wide acceptance and has many 

advantages over conventional A-scan inspection. These advantages include the ability to perform 

scanning with no mechanical movement, the ability to perform angular (sectorial) scans and dynamic 

focusing without setup alteration (thus more feasible and efficient for inspecting complex shapes and 

difficult-to-inspect areas), two-dimensional visualization of results, and similar portability to A-scan 

equipment. 

Ultrasonic phased array inspection results can be difficult to understand due to the complexity of 

angular ultrasound compounded by multiple transducer element excitation. Computational simulation of 

the inspection, or “virtual” inspection, would thus be very desirable to aid in understanding of 

experimental results. Additionally, if such simulation methods are proven accurate, they can then be used 

to predict in a rapid and cost-effective fashion the feasibility and potential outcome of inspections under 

consideration (Ref. 7). 

In this investigation, isogrid test samples with various simulated crack configurations emanating from 

bolt holes were inspected using an ultrasonic phased array method. In concert with actual inspections, 

computational simulations mimicking the actual inspection were performed within the limitations of the 

software. The results are presented from the simplest case (only bolt hole with no flaws) to more complex 

cases where various configurations of flaws are emanating from a bolt hole. 

Test Samples 

Four aluminum 2014 alloy isogrid stiffener element samples were manufactured with notches 

emanating from bolt holes (Fig. 2(a)). The sample length is 15.24 cm. The top of the “T” is 5.08 cm in 

width. The thicknesses of the rib and top are 0.27 and 0.29 cm, respectively. A fillet radius of 0.15 cm 

connects the rib with the top. Notch length and thickness was 0.64 and 0.27 cm (equal to that of the 

isogrid rib thickness), respectively. 
NASA/TM—2010-216090 3 

Phased Array Ultrasonic Method 

The General Electric (GE) Phasor XS portable ultrasonic flaw detector (Fig. 2(a)) was used for the 

actual test part inspection. The phased array probes consisted of a transducer on top of a wedge. The 

transducer employed was a 32 crystal-element linear phased array type with 5 MHz flat focus. The total 

aperture was 16 by 10 mm. The element width was approximately 0.45 mm and the gap (pitch) between 

elements was approximately 0.05 mm. Only 16 of the 32 elements are active at any one time as only 

16 pulser-receivers are available in the instrument. The active aperture area was thus 8 by 10 mm. The 

transducer was attached to a wedge made of Rexolite plastic with incidence angle of approximately 36. 

Figure 2(b) shows a photograph of the probe sitting on the top of the isogrid test sample in a typical 

inspection scenario. The probe was horizontally positioned so that the side of the wedge was 

perpendicular to the axis of the bolt holes. Depending on the specific flaw configurations, the probe might 

be moved horizontally by hand in either direction from a baseline position to achieve prominent 

indications. Generally, the edge of the probe wedge was located near either edge of the bolt hole (see 

Fig. 2(b)). Sectorial scans with inspection/refraction ranges of 20 to 50 (shear wave) and 40 to 70

(shear wave) were performed. Note that for the former range, longitudinal waves are predicted to be 

present up to θS = 29.2 (shear wave angle of refraction) as determined from Snell’s law (Ref. 8): 

L VL s Vs Sin θ /  Sin θ / (1) 

using measured values of shear wave velocity (VS = 0.320 cm/μsec) and longitudinal wave velocity (VL = 

0.656 cm/μsec) for aluminum 2014, and setting SinθL = 1 (θL = angle of refraction for longitudinal waves 

= 90). (See section entitled “Additional Ultrasonic Testing”) 

The situation of having longitudinal waves present in addition to shear waves during an angled 

inspection is actually an undesirable one and probably not often used in practice. It is a complicated 

enough scenario just using one mode due to all of the resulting mode conversions that occur for 

reflections from nonperpendicular incident ultrasonic waves off of internal boundaries. However, because 

of the geometry of the notches with respect to the bolt holes and probe, it was desired to at least attempt 

lower inspection angles. 

Additional Ultrasonic Testing 

The 5 MHz shear and longitudinal wave ultrasonic velocity measurements were performed on one of 

the isogrid stiffener element test samples using a precision contact ultrasonic method (Ref. 9). The shear 

and longitudinal wave velocity values for the test sample were measured to be 0.320 and 0.656 cm/μsec, 

respectively. 
NASA/TM—2010-216090 4 

Ultrasonic Simulation 

In this investigation, CIVA 9.1a software was utilized to model the phased array ultrasonic inspection 

of the isogrid stiffener element. The CIVA software allows bulk wave beam field predictions using the 

elastodynamics pencil method, and flaw response predictions using Kirchhoff, GTD or Born models for 

beam/flaw interaction (Refs. 10 to 17). CIVA can model many bulk wave inspection scenarios including 

A-scan, B-scan, C-scan, and S-scan (sectorial scan). The software has many powerful options available 

including the ability to compute delay laws for phased array ultrasonic setups (Refs. 6 and 18) and the 

ability to overlay resulting beam profiles and beam/flaw responses onto the model of the part. Beam 

profile visualizations show ultrasound propagation directions, focal spot locations, modes, and beam 

widths. Components requiring flaw response predictions need to be chosen from the directory of preexisting specimen shapes, imported as two-dimensional DXF files, or drawn in two-dimensional profile in 

the computer-aided-design (CAD) facility included in the CIVA software. After the two-dimensional 

profile is created or imported, it is subsequently extruded to create the three-dimensional solid model. 

(Three-dimensional solid models can be imported into CIVA, but currently only for beam field 

predictions.) Materials can be added from the existing CIVA material library, or defined by the user. 

Subsequently, flaws can be added from the existing CIVA flaw library or imported from/created in a 

CAD facility. Reference 5, and Figure 3, explain the simulation process steps in more detail. 

The geometry of the isogrid test sample presents somewhat of a problem for the two-dimensional 

CAD facility in CIVA with regards to predicting flaw response. If one considers the initial twodimensional geometries prior to extrusion for the isogrid sample three-dimensional solid model, there are 

two possibilities. The first two-dimensional geometry that can be considered is that of a “T” shape. In this 
NASA/TM—2010-216090 5 

case, the “T” shape of selected dimensions can be extruded longitudinally the appropriate length so that it 

creates the isogrid three-dimensional solid model. Call this the “T” configuration. However, in this 

situation, the bolt hole cannot be incorporated into the initial two-dimensional “T” and still account for 

interaction between the bolt hole and the flaw. (A hole can be incorporated into the “T” threedimensional solid model configuration after extrusion by addition of a circular flaw which is actually 

done in this investigation to consider ultrasonic reflection from just the bolt hole. But addition of the bolt 

hole and additional flaws results in improper modeling of the ultrasonic interactions between the bolt hole 

and the planar flaw simulating the notch/crack. CIVA is not configured to model flaw-flaw interaction. If 

backwall reflections between the holes and flaws are not expected to be significant, then the modeling is 

accurate when the holes are drawn as flaws.) 

The second two-dimensional geometry that can be considered is a rectangle that has a discontinuous 

hole in it for the purpose of connecting the hole to (part of) the backwall (bottom surface). CIVA requires 

the bolt hole to be drawn as part of the backwall to correctly model the ultrasonic interaction between the 

bolt hole and the notches, including any corner trap effects between the hole and flaw. Extrusion can thus 

take place in the thickness direction which results in a three-dimensional solid model with bolt hole. 

However, in this case, the top of the “T” is missing so that the ultrasonic probe is actually modeled as 

sitting on top of the thickness. This “I” configuration does not accurately simulate the actual inspection 

condition, but it was the only choice for simulation using CIVA for flaw response that includes 

interactions with the bolt hole and backwall. For the beam profile, both “I” and “T” geometries and 

subsequent extrusions were performed in order to compare beam profiles for both solid models. 

For the CAD modeling in the CIVA two-dimensional CAD facility, all sides were color-coded as 

front, back, side, and interface so that the ultrasonic probe attached itself properly, and the beam field and 

flaw response predictions were calculated correctly. Only one material zone needed to be defined since 

the entire part was the same material. (This is in contrast to the study of Reference 5 where the part was 

divided into four distinct zones since weld material was different from base material.) As already noted, 

the (discontinuous) hole was made a part of the backwall as required to correctly model interaction 

between surfaces and flaws. The CIVA software has interface screens for the user to describe the 

transducer crystal element characteristics and geometry, phased array crystal assembly, inspection/scan 

parameters, wedge material and geometry, test sample material and geometry, flaw material and 

geometry, and computation parameters. The model parameters selected matched closely with actual 

experimental parameters. The notch/crack was modeled as a planar flaw. The flaws were added after the 

CAD model was completed. 

The “half-skip” sound path interaction with the flaw was chosen in the computation parameters. 

When the half-skip option is chosen, beam-flaw interactions that are in the direct sound path from the 

probe to the flaw and vice-versa are considered. Additionally, waves incident on flaws after reflection off 

the backwall and reflections from the flaws off the backwall towards the probe are also taken into 

account. This option therefore enables the computation of corner (trap) echoes, or more generally, echoes 

resulting from the inward and/or outward reflection off flaws via the backwall. Therefore, for the halfskip option, the echoes taken into account can include the specular reflections, tip diffractions, and 

corner-like echoes. 

Backwall echoes were included in the computation (surface echoes were not included so as not to 

clutter up the displays). Shadowing was included since in some of the flaw configurations, the shadowing 

effect of a flaw onto the echo-response from other flaws or from component geometry might need to be 

considered. Sectorial scans were simulated using similar angles for the experimental phased array. A 

computation zone was selected that encompassed the bolt hole area. Computation accounted for mode 

conversion, but did not account for material noise or attenuation in this study. These are options which 

can be modeled, but increase computation time. The computed delay laws controlling the sector scan 

were not compared with the actual delay laws for the instrument because the latter are not readily 

exportable from the instrument. The overall flaw response calculation computes the signal received by the 

probe as the summation of individual contributions for the various resulting wave modes. The 

computation mode was two-dimensional—the planar flaw was meshed along its profile vertically-
NASA/TM—2010-216090 6 

perpendicular to the sound beam projection. The Kirchhoff approximation (Ref. 19) was used in the flaw 

response calculations. The Kirchhoff approximation assumes that the elastic wave is entirely scattered by 

the flaw. The flaw is meshed and the wave scattered by the flaw is the product of amplitude and timedependent functions of incident wave and complex scattering coefficient at each meshed location. The 

Kirchhoff approximation relies on the assumption that each point at the flaw surface contributes as if it 

was part of an infinite plane (no interaction with neighboring points). The Kirchhoff approximation is 

assumed to give accurate results for flaws providing specular or near specular reflection over planar or 

volumetric flaws. Quantitative error is expected to increase when the scattered direction moves away 

from the specular direction. 

The Kirchhoff approximation is a high frequency approximation, valid when 2πa/λ >> 1 (i.e., when 

the flaw length (a) is significantly greater than the wavelength (λ)). In this case, the aluminum alloy has a 

shear wave velocity around 0.320 cm/μsec and at a frequency of 5 MHz, the wavelength is approximately 

0.64 mm (using wavelength = velocity/frequency). Then, 2π*2.64 mm/0.64 mm ~26 (planar flaw length 

of about four times larger than the ultrasonic wavelength) which satisfies the Kirchhoff criterion. 

Beam Profile Simulation Results 

Figure 4 shows beam profile results for several shear wave inspection angles for the extruded “T” 

solid model. The beam profiles are overlaid on top of the solid model. Focusing on the computation zone 

within the test sample, one can see ultrasonic propagation directions, focal spot locations, modes, and 

beam widths. The single red and green lines show the center lines for shear and longitudinal wave 

propagation, respectively. It can be seen that at inspection angles (shear wave) up to around 29, both 

shear and longitudinal waves are shown to be present. 
NASA/TM—2010-216090 7 

Figure 5 shows a comparison of the beam profiles for the “I” and “T” solid models indicating some 

differences in resulting beams within the sample. This is most likely due to the additional ultrasonic 

interactions between the fillet area and ribwall for the “T” model. This interaction is explained by viewing 

Figure 6 which shows the likely paths of beams (and reflections off of a bolt hole) when a fillet is present. 
NASA/TM—2010-216090 8 

Flaw Response Experimental and Simulation Results 

Figure 7 shows experimental and simulation results for the case where no flaws are emanating from a 

bolt hole (using “T” model for simulation since only flaw is bolt hole). Simulation shows the strong direct 

echo off of the bolt hole (an extension of the backwall) which agrees with experimental results. Angle of 

maximum amplitude is different by about 7 between simulation and experiment. Any slight differences 

in the setup, transducer model, and CAD model (including hole size and location) between simulation and 

experimentation would affect the angle (position) of max amplitude. 

Figure 8 shows experimental and simulation results for examination of indications related to the bolt 

hole and downward-extending flaw (using “I” model for simulation since bolt hole and flaws are present). 

For the sector angle range 40 to 70, only shear waves will be refracted in the part since the critical angle 

for longitudinal waves has been reached at 29.2 as was derived earlier (see Eq. (1)). In this case, four 

distinct corresponding echoes are identified in the experiment and simulation. The four corresponding 

echo indications are identified as that from the bolt hole, corner trap echoes related to the backwall – flaw 

– hole path (incomplete shadowing), flaw – backwall/backwall – flaw path, and backwall – hole path. 

Additionally, it is plausible that a creeping wave echo (Ref. 20) would be present at about the same time 

as shown for indication 2 and might be the primary indication for 2 in the experiment. Also, a fillet echo 

is likely present in the experimental results directly in line with indication 3 but slightly later in time in 

the experiment. 
NASA/TM—2010-216090 9 

 
NASA/TM—2010-216090 10 

Figure 9 shows experimental and simulation results (reset for sector angle range 20 to 50) for one 

flaw extending upward from the bolt hole at a 45 angle, one flaw extending downward, and with the 

probe position moved over the bolt hole so that examination of indications related to the bolt hole and 

upward-extending flaw could be examined. In this case, three distinct corresponding echoes are identified 

common to the experiment and simulation. These indications are for tip diffraction from the upper flaw, 

bolt hole reflection, and a corner trap echo related to the downward-extending flaw – backwall path. The 

backwall – hole path echo seen in Figure 7 is no longer present because the transducer has been moved 

over the bolt hole. To see the tip diffraction echo, the gain was adjusted higher in post-processing. 

Additionally, a possible creeping wave (Ref. 20) is identified for the experiment which travels around the 

bolt hole and is reflected at the intersection of the bolt hole and the downward-extending flaw. Again, a 

prominent fillet echo (indication 3) is likely present in the experimental results directly in line with 

indication 2 (echo from bolt hole) but slightly later in time in the experiment. This is not seen in the 

simulation since the fillet is not present in the “I” model. 

 
NASA/TM—2010-216090 11 

Figure 10 shows experimental and simulation results for the case where one flaw extends laterally 

(away from the probe) and one flaw extends downward from a bolt hole. The transducer has again been 

moved nearly directly over the bolt hole. Two echoes are common to the experiment and simulation. In 

addition to the bolt hole direct echo, a tip diffraction echo from the laterally-extending flaw is observed in 

both the simulation (very light indication) and experiment. It is also possible that the reflection from the 

laterally-extending flaw is due partially and possibly primarily to a creeping wave signal (Ref. 20) which 

will not be seen in the simulation. Tip diffraction echoes can be modeled correctly in CIVA with regards 

to their time-of-flight position, but not with respect to amplitude unless a calibration feature is utilized. 

Conclusions and Future Efforts 

This article describes experimental and simulation results for phased array ultrasonic inspection of an 

aluminum alloy isogrid stiffener element containing notches emanating from bolt holes. Good qualitative 

agreement was observed between experimental results and modeling predictions with regards to flaw 

response indications. The simulations were extremely important in helping to understand experimental 

results, even though the isogrid stiffener element solid model could not include the top section of the 

isogrid element for flaw response calculations. In a few cases, indications seen in the experimental results 

and expected from the simulation were not seen. The simulation software cannot currently model 

creeping waves, but future versions are being developed to address this limitation. The simulations 

compared well enough to the experimental results in a qualitative sense that the researchers would have 
NASA/TM—2010-216090 12 

confidence in using them to predict significant inspection results. Future simulation work with isogrid 

stiffener element samples will be performed which examine other flaw configurations and in which CIVA 

batch processing capabilities are utilized to perform parametric studies. It would be interesting to vary 

flaw size, transducer frequency, and include material noise and attenuation in simulations in order to 

approximate limits of detectability for various inspection scenarios. 

References 

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Independent Assessment, NASA Engineering and Safety Center, RP-08-85, v1.1, August, 2008. 

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Olympus NDT, 2007. 

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5. Roth, D.J., Tokars, R.P., Martin, R.E., Rauser, R.W., Aldrin, J.C., and Schumacher, E.J., Ultrasonic 

Phased Array Inspection Simulations of Welded Components at NASA, Materials Evaluation, 

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6. Mahaut S., Chatillon S., Kerbrat E., Porré J., Calmon P., and Roy O., “New features for phased array 

techniques inspections: simulation and experiments,” 16th World Conf on Non Destructive Testing, 

Montréal, 2004. 

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Applications to Aerospace Structures,” Materials Evaluation vol. 66. no. 1 pp. 53–59 (2008). 

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9. Roth, D.J., Kiser, J.D., Swickard, S.M., Szatmary, S., and Kerwin, D., “Quantitative Mapping of Pore 

Fraction Variations in Silicon Nitride Using an Ultrasonic Contact Scan Technique,” Research in 

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11. Achenbach, J.D., “Measurement Models for Quantitative Ultrasonics,” Journal of Sound and 

Vibration, vol. 159, 1992, pp. 385–401. 

12. Rose, J.L., Ultrasonic Waves in Solid Media. Cambridge, Cambridge University Press, 1999. 

13. Gengembre N., “Pencil method for ultrasonic beam computation,” Proc. of the 5th World Congress 

on Ultrasonics, Paris, 2003. 

14. Raillon R. and Lecoeur-Taïbi I., “Transient elastodynamic model for beam flaw interaction. 

Application to nondestructive testing,” Ultrasonics, 2000 38 527–530. 

15. Darmon M., Calmon P. and Bele C., “Modeling of the ultrasonic response of inclusions in steels,” in 

Review of progress in QNDE, vol. 22A, AIP publishing, 2003, pp. 101–108. 

16. Lonne, S., de Roumilly, L., Le Ber, L., Mahaut, S. and Cattiaux, G., “Experimental Validation of 

CIVA Ultrasonic Simulations,” International Conference on NDE in Nuclear Industry (ICNDE), 

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Obtained with CIVA at CEA: Beam Modeling and Flaw Signal Prediction,” in Review of progress in 

QNDE, vol. 26B, AIP publishing, 2007, pp. 1870–1877. 

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Ultrasonic Phased-Arrays Applications,” in Review of progress in QNDE, vol. 26A, AIP publishing, 

2007, pp. 799–805. 

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Plenum Press, New York, 1998. 

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“Case Study for the Implementation of an Automated Ultrasonic Technique to Detect Fatigue Cracks 

in Aircraft Weep Holes,” Materials Evaluation, vol. 59, no. 11, p. 1313, (2001). 
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9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES)

National Aeronautics and Space Administration 

Washington, DC 20546-0001 

10. SPONSORING/MONITOR'S

 ACRONYM(S)

NASA 

11. SPONSORING/MONITORING

 REPORT NUMBER

NASA/TM-2010-216090 

12. DISTRIBUTION/AVAILABILITY STATEMENT

Unclassified-Unlimited 

Subject Categories: 38 and 71 

Available electronically at http://gltrs.grc.nasa.gov 

This publication is available from the NASA Center for AeroSpace Information, 443-757-5802

13. SUPPLEMENTARY NOTES

Submitted to the Materials Evaluation 

14. ABSTRACT

In this investigation, a T-shaped aluminum alloy isogrid stiffener element used in aerospace applications was inspected with ultrasonic 

phased array methods. The isogrid stiffener element had various crack configurations emanating from bolt holes. Computational simulation 

methods were used to mimic the experiments in order to help understand experimental results. The results of this study indicate that it is at 

least partly feasible to interrogate this type of geometry with the given flaw configurations using phased array ultrasonics. The simulation 

methods were critical in helping explain the experimental results and, with some limitation, can be used to predict inspection results.

15. SUBJECT TERMS

Nondestructive evaluation; Structures; Crack; Metal alloy; Stiffener element; Computational simulation; Ultrasonics; Isogrid; 

Modeling; Phased array 

16. SECURITY CLASSIFICATION OF: 17. LIMITATION OF

 ABSTRACT

UU 

18. NUMBER

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 PAGES

18 

19a. NAME OF RESPONSIBLE PERSON

STI Help Desk (email:help@sti.nasa.gov) 

a. REPORT

U 

b. ABSTRACT

U 

c. THIS 

PAGE

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19b. TELEPHONE NUMBER (include area code)

443-757-5802 

Standard Form 298 (Rev. 8-98)

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