Evaluation of the Submodeling Technique for 

Analyzing Electronic Components 

by Brian M. Powers and David A. Hopkins 

ARL-TR-3627 October 2005

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Army Research Laboratory 

Aberdeen Proving Ground, MD 21005-5069 

ARL-TR-3627 October 2005 

Evaluation of the Submodeling Technique for 

Analyzing Electronic Components 

Brian M. Powers and David A. Hopkins 

Weapons and Materials Research Directorate, ARL 

Approved for public release; distribution is unlimited. 
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4. TITLE AND SUBTITLE 

 Evaluation of the Submodeling Technique for Analyzing Electronic 

 Components 

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 622618.H80

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6. AUTHOR(S) 

 Brian M. Powers and David A. Hopkins (both of ARL)

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U.S. Army Research Laboratory 

Weapons and Materials Research Directorate 

Aberdeen Proving Ground, MD 21005-5069

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 Approved for public release; distribution is unlimited.

13. SUPPLEMENTARY NOTES 

14. ABSTRACT 

The use of submodeling in a finite element model for structural response is investigated for a simple structure representative of

an electronic circuit board subjected to projectile launch conditions. The basic technique and rationale for submodeling are 

discussed. The consequences of sampling rate when one is using the global model’s response as input for the local model’s 

response are also highlighted. Aditionally, the effect of submodeling in introducing artificial high frequency response is shown. 

Finally, it is shown that with proper selection of model parameters, submodeling can provide accurate stress results of electronic 

components in conditions similar to gun launch. 

15. SUBJECT TERMS

 electronic components; finite elements; submodeling 

16. SECURITY CLASSIFICATION OF:

19a. NAME OF RESPONSIBLE PERSON

 Brian M. Powers 

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Unclassified

b. ABSTRACT

Unclassified

c. THIS PAGE

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 410-306-1961

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ii
Contents 

List of Figures iv

List of Tables iv

1. Introduction 1

2. Sample Problem 2

3. Results 4

4. Conclusions 5

5. References 8

Distribution List 9 

iii
List of Figures 

Figure 1. Finite element model layout with electronic chip. ......................................................... 2 

Figure 2. Velocity load curve applied to base of support ring....................................................... 3 

Figure 3. Global model with coarse representation of board......................................................... 4 

Figure 4. Submodel domain........................................................................................................... 4 

Figure 5. Contour plots of Von Mises stress (psi) at t = 0.6 ms for (a) the baseline case, 

(b) 100-point load curve, and (c) 1000-point load curve. ....................................................... 6 

Figure 6. Comparison of the Von Mises stress in a representative element in a lead for the 

baseline case and the two submodels...................................................................................... 7 

Figure 7. FFTs of data from figure 6. ............................................................................................ 7 

List of Tables 

Table 1. Material properties of model components. ...................................................................... 3 

iv
1. Introduction 

The need for computational techniques to efficiently handle multiple length scales is increasingly

important as finite element (FE) models become more detailed and complex. This is especially 

pronounced in structures containing electronic components. One example of interest is smart 

munitions, which are often evaluated in a dynamic analysis that simulates gun launch. The 

length scale of the electronics is typically orders of magnitude smaller than the overall size of the 

structure. This can lead to very small element sizes and a very large number of elements when 

mesh uniformity is imposed. In explicit dynamic analyses, the time increment is chosen, based 

on stability criteria (i.e., Courant condition) and is directly dependent upon the element size; see, 

for example, (1). Consequently, as the element size decreases, so does the time step; this results 

in an increase in the computational time that can be excessive, often restrictively so in the case of 

large models with very small components. 

One way to alleviate this problem is to use global-local modeling approaches, one method of 

which is often referred to as “submodeling”. A review of submodeling and other modeling 

global/local approaches is included in (2). The commercial FE package ABAQUS1 includes a 

submodeling technique. This report explores whether the submodeling technique has applicability for modeling structures with electronic components using the technique available in 

ABAQUS. 

Submodeling employs two models, as detailed in (3). In this report, the global model represents 

the entire structure and contains a coarse representation of the domain of interest (e.g., an 

electronic chip). The entire global model is sufficiently refined to accurately calculate the 

displacement solution on the boundary of the domain of interest. Subsequently, the solution 

obtained from the global model along the boundary of interest is applied as a displacement 

boundary condition on the submodel. 

The submodel is a highly refined model of the domain of interest. The primary assumption of 

submodeling is that the structural details of the submodel do not significantly affect the solution 

in the global model. In most practical applications, there are no known a priori methods for 

determining the validity of this assumption. It is therefore left to the analyst to determine the 

validity of this assumption, based on prior experience. 

 1ABAQUS, which is not an acronym, is a registered trademark of ABAQUS, Inc.

1
2. Sample Problem 

The submodeling technique was applied to a simplified geometry of an electronic component. 

The purpose of the example is to demonstrate how the technique can be applied to structural 

elements of an FE model with large differences in length scales. The length scales chosen are 

representative of those seen in typical smart munitions applications. Figure 1 shows the layout 

of the electronics with respect to the outer shell and the supporting structure. The electronics 

consist of two structures representing capacitors which are modeled as monolithic material, and 

a small outline integrated circuit (SOIC) eight-lead chip. The support ring has a 3-inch diameter, 

while the width of the leads on the chip is on the order of 0.010 inch. The scale difference is 

thus on the order of 300 to 1. This is an intermediate level of disparity in length scales and is 

typical for smart munitions. 

Figure 1. Finite element model layout with electronic chip. 

The full baseline model uses 116,000 elements, with 47,000 elements comprising the chip. 

“Tied surface” contact is used at the interface between the chip and the support. All material 

properties are linear elastic and are summarized in table 1. The loading is applied by prescribing 

the velocity of the nodes on the lower surface of the outer ring. The velocity-time history is 

shown in figure 2. The defined termination time for the model is 1.4 ms. This time span was 

chosen so that the model would execute in a reasonable amount of time on available hardware. 

The initial time step is 4.24x10-9 seconds. The model requires more than 200,000 time steps to 

complete the analysis. 

2
Table 1. Material properties of model components. 

Density (lb⋅s

2

/in4) Modulus (Msi1

) Poisson’s Ratio

Ring and Support 7.33x10-4 30.0 0.3

Board 1.48x10-4 28.6 0.14

Chip (AD623) 1.14x10-4 2.31 0.25

Chip Leads 3.55x10-4 17.5 0.3

Capacitor 1.31x10-4 15.1 0.17

Solder Cap 7.98x10-4 5.2 0.4 1

Msi = millions of psi 

0

5000

10000

15000

20000

25000

30000

35000

40000

0 0.0002 0.0004 0.0006 0.0008 0.001 0.0012 0.0014 0.0016

Time (s)

Velocity (in/s)

Figure 2. Velocity load curve applied to base of support ring. 

The global model uses the mesh from the baseline model for the outer ring and supports and is 

shown in figure 3. The geometry of the chip is replaced with a coarser mesh of shell elements 

with offset contact used to maintain the centerline location of the board with respect to the support 

structure. The shell elements are defined to have the thickness of the board. Discrete mass 

elements are attached to nodes at the approximate locations of the lead attachment points. The 

mass of these elements is distributed to match the total mass of the capacitors and the chip. The 

total number of elements in the global model is 70,000. It is assumed that the stiffness of the chip 

does not appreciably affect the overall response of the structure away from the chip location. 

As an additional consideration, the time-dependent fidelity of the boundary conditions that are 

applied to the submodel is known to affect the results (3). To determine these effects, two 

different sets of results are extracted from the global model and are subsequently used as boundary 

conditions for the submodel. Specifically, 100 and 1000 result states are used as input. This has 

the effect of essentially using two load curves that are discretized at different time intervals, 

1.4x10-5 seconds and 1.4x10-6 seconds, respectively, for the different number of results states. 

3
Figure 3. Global model with coarse representation of board. 

The submodel consists of the detailed geometry of the electronics package and a small adjacent

section of the supports. The domain of the submodel is shown in figure 4. As mentioned, the 

displacement results from the global model were applied along the outer edges of the supports. 

Figure 4. Submodel domain. 

3. Results 

All analyses were run on an SGI (Silicon Graphics, Inc.) Origin 3900. The baseline model was 

analyzed with 32 processors and took approximately 1,100 total CPU (central processing unit) 

hours (or about 34 hours/CPU). The global model was run on a single processor and took 6 CPU 

4
hours. The two submodel analyses, one using 100 global result states and the other using 1000 

states, took approximately 900 total CPU hours each on 32 processors (or about 28 hours/CPU). 

For this model, the overall reduction in analysis time was not significant. 

The results from the two submodel cases are compared to the baseline model as shown in figure 5. 

Figure 5 shows contour plots of the Von Mises stress at time t = 0.6 ms for the three cases. For 

this geometry, the highest stress is in the leads. Figure 6 compares the stress-time history for a 

representative element in a lead. The results for both submodels are generally in good agreement 

with the global model, but the stress peaks for the 100-point case overshoot the global model. The 

1000-point results match the peaks and valleys of the global model better. The reason for the 

difference in the results is entirely attributable to the use of a coarser loading function in the case 

of the 100-point curve versus the 1000-point curve. 

It is known a priori that the submodeling technique might introduce high frequency content into 

the solution, but it is unknown how the solution would be affected. A fast Fourier transform (FFT) 

was performed on the data in figure 6 and is presented in figure 7. An FFT assumes the data to be 

periodic, but the data are finite in length, which causes error because of leakage (4). Non-zero 

values in the data at the starting and ending times create jumps in the data when they are expanded 

from a finite time to become periodic. These jumps create spurious, non-physical frequencies in 

the FFT. These spurious frequencies can be minimized with the use of a window on the data to 

force the starting and ending times of the signal to be zero so that no jumps appear in the periodic 

representation. For this study, a Hamming window was applied to the data before the FFT was 

calculated. While the frequency content of the response below 10 KHz matches very well, the 

time resolution for the loading function for the submodel introduces high frequency response into 

the solution for both cases. 

4. Conclusions 

The submodeling analysis technique in ABAQUS has been shown to be applicable to dynamics 

analysis involving electronic components. While submodeling can lead to artificial high frequency 

content in the final results, proper care in selecting the frequency of global model output can 

minimize these effects. As shown in the sample problem, sufficient accuracy in the stress results 

of the submodel can be realized if we consider the desired frequency response range. If we 

subsequently sample the global loading finely enough, any high frequency content introduced will 

be above the frequency range of interest. 

5
(a) 

(b) 

(c) 

Figure 5. Contour plots of Von Mises stress (psi) at t = 0.6 ms for (a) the baseline 

case, (b) 100-point load curve, and (c) 1000-point load curve. 

6
Figure 6. Comparison of the Von Mises stress in a representative element in a lead for the baseline case and the two

submodels. 

Figure 7. FFTs of data from figure 6. 

7
5. References 

1. Hughes, T.R.J. The Finite Element Method: Linear Static and Dynamic Finite Element 

Analysis. Prentice-Hall: Englewood Cliffs, NJ, 1987. 

2. Minnicino, M.; D. Hopkins. Overview of Reduction Methods and Their Implementation into 

Finite Element Local-to-Global Techniques; ARL-TR-3340; U.S. Army Research 

Laboratory: Aberdeen Proving Ground, MD, September 2004. 

3. ABAQUS Analysis User’s Manual Version 6.4, 2003. 

4. Ewins, D. J. Modal Testing: Theory and Practice. Research Studies Press: Letchworth, 

England, 1984. 

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ATTN M MILLER F CRILLEY 

14000 NW 58 CT 

MIAMI LAKES FL 33014

 2 FOSTER MILLER 

ATTN M ROYLANCE W ZUKAS 

195 BEAR HILL RD

 WALTHAM MA 02354-1196

1 ROM DEVELOPMENT CORP

ATTN R O MEARA 

 136 SWINEBURNE ROW 

 BRICK MARKET PLACE 

NEWPORT RI 02840

 2 TEXTRON SYSTEMS 

ATTN M TREASURE T FOLTZ 

 1449 MIDDLESEX ST 

LOWELL MA 01851 

13
NO. OF 

COPIES ORGANIZATION

1 O GARA HESS & EISENHARDT 

ATTN M GILLESPIE 

9113 LESAINT DR 

FAIRFIELD OH 45014 

1 MILLIKEN RESEARCH CORP 

ATTN M MACLEOD 

PO BOX 1926 

 SPARTANBURG SC 29303

1 CONNEAUGHT INDUSTRIES INC 

ATTN J SANTOS 

PO BOX 1425 

COVENTRY RI 02816 

 1 ARMTEC DEFENSE PRODUCTS 

ATTN S DYER 

85 901 AVE 53

PO BOX 848

 COACHELLA CA 92236

3 PACIFIC NORTHWEST LAB 

ATTN M SMITH G VAN ARSDALE 

 R SHIPPELL 

PO BOX 999

 RICHLAND WA 99352

1 ALLIANT TECHSYSTEMS INC 

4700 NATHAN LN N 

 PLYMOUTH MN 55442-2512

 1 APPLIED COMPOSITES 

ATTN W GRISCH 

333 NORTH SIXTH ST 

ST CHARLES IL 60174

 1 CUSTOM ANALYTICAL 

ENG SYS INC 

ATTN A ALEXANDER 

13000 TENSOR LANE NE 

 FLINTSTONE MD 21530 

 1 AAI CORP 

ATTN DR N B MCNELLIS

PO BOX 126

HUNT VALLEY MD 21030-0126

1 OFC DEPUTY UNDER SEC DEFNS 

ATTN J THOMPSON 

1745 JEFFERSON DAVIS HWY 

CRYSTAL SQ 4 STE 501 

 ARLINGTON VA 22202

NO. OF 

COPIES ORGANIZATION

3 ALLIANT TECHSYSTEMS INC 

ATTN J CONDON E LYNAM 

 J GERHARD 

WV01 16 STATE RT 956 

PO BOX 210

ROCKET CENTER WV 26726-0210

 1 PROJECTILE TECHNOLOGY INC 

 515 GILES ST

HAVRE DE GRACE MD 21078

 1 PRATT & WHITNEY 

ATTN C WATSON 

400 MAIN ST MS 114 37

EAST HARTFORD CT 06108

 5 NORTHROP GRUMMAN 

ATTN B IRWIN K EVANS

D EWART J MCGLYNN 

 A SHREKENHAMER 

BLDG 160 DEPT 3700

1100 W HOLLYVALE ST 

AZUSA CA 91701

 1 BRIGS COMPANY 

ATTN J BACKOFEN 

2668 PETERBOROUGH ST 

 HERNDON VA 22071-2443 

1 ZERNOW TECHNICAL SERVICES 

ATTN L ZERNOW 

425 W BONITA AVE STE 208 

SAN DIMAS CA 91773

2 GENERAL DYNAMICS OTS 

 FLINCHBAUGH DIV

ATTN K LINDE T LYNCH 

PO BOX 127

RED LION PA 17356 

1 GKN WESTLAND AEROSPACE 

ATTN D OLDS 

 450 MURDOCK AVE 

MERIDEN CT 06450-8324

 1 BOEING ROTORCRAFT 

ATTN P HANDEL 

800 B PUTNAM BLVD 

 WALLINGFORD PA 19086 

14
NO. OF 

COPIES ORGANIZATION

 5 SIKORSKY AIRCRAFT 

ATTN G JACARUSO J ADELMANN

T CARSTENSAN B KAY 

S GARBO MS S330A 

6900 MAIN ST 

PO BOX 9729 

 STRATFORD CT 06497-9729

 1 AEROSPACE CORP 

ATTN G HAWKINS M4 945

2350 E EL SEGUNDO BLVD

EL SEGUNDO CA 90245

 2 CYTEC FIBERITE 

ATTN M LIN W WEB 

1440 N KRAEMER BLVD

 ANAHEIM CA 92806 

 2 UDLP 

ATTN G THOMAS M MACLEAN 

PO BOX 58123

SANTA CLARA CA 95052 

 2 UDLP 

ATTN R BRYNSVOLD 

P JANKE MS 170 

4800 E RIVER RD 

 MINNEAPOLIS MN 55421-1498

 1 LOCKHEED MARTIN 

 SKUNK WORKS 

ATTN D FORTNEY 

 1011 LOCKHEED WAY

 PALMDALE CA 93599-2502

1 NORTHRUP GRUMMAN CORP 

ELECTRONIC SENSORS & SYSTEMS DIV 

ATTN E SCHOCH MS V 16

1745A W NURSERY RD

 LINTHICUM MD 21090

 1 GDLS DIVISION 

ATTN D BARTLE 

PO BOX 1901 

 WARREN MI 48090 

 2 GDLS 

ATTN D REES M PASIK 

PO BOX 2074 

 WARREN MI 48090-2074

NO. OF 

COPIES ORGANIZATION

 1 GDLS 

 MUSKEGON OPER 

ATTN M SOIMAR 

76 GETTY ST

 MUSKEGON MI 49442

 1 GENERAL DYNAMICS 

 AMPHIBIOUS SYS 

 SURVIVABILITY LEAD 

ATTN G WALKER 

991 ANNAPOLIS WAY 

 WOODBRIDGE VA 22191 

6 INST FOR ADVANCED TECH 

ATTN H FAIR I MCNAB 

P SULLIVAN S BLESS 

W REINECKE C PERSAD

3925 W BRAKER LN STE 400

 AUSTIN TX 78759-5316

 1 ARROW TECH ASSOC 

1233 SHELBURNE RD STE D8 

SOUTH BURLINGTON VT 05403-7700

 1 R EICHELBERGER 

 CONSULTANT

409 W CATHERINE ST 

BEL AIR MD 21014-3613

 1 SAIC

ATTN G CHRYSSOMALLIS 

8500 NORMANDALE LAKE BLVD

 SUITE 1610

 BLOOMINGTON MN 55437-3828

1 UCLA MANE DEPT ENGR IV 

ATTN H T HAHN

LOS ANGELES CA 90024-1597 

1 UMASS LOWELL 

 PLASTICS DEPT 

ATTN N SCHOTT 

1 UNIVERSITY AVE 

LOWELL MA 01854 

1 IIT RESEARCH CAR 

ATTN D ROSE 

 201 MILL ST 

 ROME NY 13440-6916

1 GA TECH RESEARCH INST 

GA INST OF TCHNLGY 

ATTN P FRIEDERICH

 ATLANTA GA 30392

15
NO. OF 

COPIES ORGANIZATION

1 MICHIGAN ST UNIV

 MSM DEPT 

ATTN R AVERILL

 3515 EB 

EAST LANSING MI 48824-1226

1 PENN STATE UNIV

ATTN R S ENGEL 

 245 HAMMOND BLDG

UNIVERSITY PARK PA 16801

1 PENN STATE UNIV

ATTN C BAKIS 

 212 EARTH ENGR 

 SCIENCES BLDG 

UNIVERSITY PARK PA 16802

 1 PURDUE UNIV

SCHOOL OF AERO & ASTRO 

ATTN C T SUN 

W LAFAYETTE IN 47907-1282

1 UNIV OF MAINE 

ADV STR & COMP LAB 

ATTN R LOPEZ ANIDO 

5793 AEWC BLDG 

 ORONO ME 04469-5793

1 JOHNS HOPKINS UNIV

APPLIED PHYSICS LAB 

ATTN P WIENHOLD 

11100 JOHNS HOPKINS RD

 LAUREL MD 20723-6099

 1 UNIV OF DAYTON

ATTN J M WHITNEY 

 COLLEGE PARK AVE 

DAYTON OH 45469-0240 

 5 UNIV OF DELAWARE 

CTR FOR COMPOSITE MTRLS 

ATTN J GILLESPIE M SANTARE 

S YARLAGADDA S ADVANI

 D HEIDER 

 201 SPENCER LAB

 NEWARK DE 19716

1 DEPT OF MTRLS 

SCIENCE & ENGRG 

UNIV OF IL AT URBANA-CHAMPAIGN

ATTN J ECONOMY 

1304 W GREEN ST 115B 

 URBANA IL 61801 

NO. OF 

COPIES ORGANIZATION

1 MISSISSIPPI STATE UNIV 

DEPT OF AEROSPACE ENGRG 

ATTN A J VIZZINI 

MISSISSIPPI STATE MS 39762 

 1 DREXEL UNIV 

ATTN A S D WANG

3141 CHESTNUT ST 

 PHILADELPHIA PA 19104 

3 UNIV OF TEXAS AT AUSTIN 

CAR FOR ELECTROMECHANICS

ATTN J PRICE A WALLS 

 J KITZMILLER 

10100 BURNET RD

 AUSTIN TX 78758-4497

 1 SOUTHWEST RESEARCH INST 

ENGR & MATL SCIENCES DIV 

ATTN J RIEGEL 

6220 CULEBRA RD 

PO DRAWER 28510 

SAN ANTONIO TX 78228-0510

 ABERDEEN PROVING GROUND

 1 DIRECTOR 

US ARMY RSCH LABORATORY 

ATTN AMSRD ARL CI OK TECH LIB 

BLDG 4600 

 1 US ARMY ATC 

ATTN CSTE DTC AT AC I W C FRAZER

 BLDG 400

 1 DIR USARL 

ATTN AMSRD ARL CI

 BLDG 

 1 DIR USARL 

ATTN AMSRD ARL O AP EG M ADAMSON

BLDG 

 1 DIR USARL 

ATTN AMSRD ARL SL BB D BELY

 BLDG 328

 2 DIR USARL 

ATTN AMSRD ARL WM J SMITH 

 D LYON

 BLDG 4600 

16
NO. OF 

COPIES ORGANIZATION

 2 DIR USARL 

ATTN AMSRD ARL WM B CHIEF 

 T KOGLER 

BLDG 4600 

 2 DIR USARL 

ATTN AMSRD ARL WM BC P PLOSTINS

J NEWILL 

 BLDG 390

 3 DIR USARL 

ATTN AMSRD ARL WM BD B FORCH 

R PESCE-RODRIGUEZ B RICE 

 BLDG 4600 

 3 DIR USARL 

ATTN AMSRD ARL WM BD P CONROY

C LEVERITT A ZIELINSKI 

 BLDG 390

 2 DIR USARL 

ATTN AMSRD ARL WM BE R LIEB 

 M LEADORE

 BLDG 4600 

 1 DIR USARL 

ATTN AMSRD ARL WM BF

 S WILKERSON

 BLDG 390

 2 DIR USARL 

ATTN AMSRD ARL WM M J MCCAULEY 

 S MCKNIGHT 

 BLDG 4600 

 2 DIR USARL 

ATTN AMSRD ARL WM MA

L GHIORSE E WETZEL 

 BLDG 4600 

 22 DIR USARL 

ATTN AMSRD ARL WM MB

J BENDER T BOGETTI 

J BROWN L BURTON 

R CARTER K CHO W DE ROSSET 

G DEWING R DOWDING

W DRYSDALE R EMERSON 

D GRAY D HOPKINS R KASTE 

L KECSKES M MINNICINO 

B POWERS D SNOHA 

J SOUTH M STAKER 

J SWAB J TZENG 

 BLDG 4600 

NO. OF 

COPIES ORGANIZATION

 11 DIR USARL 

ATTN AMSRD ARL WM MC J BEATTY

R BOSSOLI E CHIN 

S CORNELISON D GRANVILLE 

B HART J LASALVIA

J MONTGOMERY F PIERCE 

E RIGAS W SPURGEON 

 BLDG 4600

 11 DIR USARL 

ATTN AMSRD ARL WM MD P DEHMER 

B CHEESEMAN R DOOLEY 

G GAZONAS S GHIORSE 

M KLUSEWITZ W ROY J SANDS 

S WALSH D SPAGNUOLO S WOLF 

 BLDG 4600 

 2 DIR USARL 

ATTN AMSRD ARL WM RP J BORNSTEIN 

 C SHOEMAKER 

 BLDG 1121 

 1 DIR USARL 

ATTN AMSRD ARL WM T B BURNS 

 BLDG 309

 1 DIR USARL 

ATTN AMSRD ARL WM TA W GILLICH

 BLDG 309

 7 DIR USARL 

ATTN AMSRD ARL WM TA M BURKINS 

B GOOCH T HAVEL C HOPPEL 

E HORWATH J RUNYEON

 M ZOLTOSKI 

 BLDG 393

 1 DIR USARL 

ATTN AMSRD ARL WM TB P BAKER 

 BLDG 309

 1 DIR USARL 

ATTN AMSRD ARL WM TC R COATES

 BLDG 309

 4 DIR USARL 

ATTN AMSRD ARL WM TD D DANDEKAR 

M RAFTENBERG S SCHOENFELD

 T WEERASOORIYA 

 BLDG 4600 

 2 DIR USARL 

ATTN AMSRD ARL WM TE CHIEF 

J POWELL 

 BLDG 1116A 

17
NO. OF 

COPIES ORGANIZATION

 1 LTD 

 R MARTIN 

 MERL 

 TAMWORTH RD 

HERTFORD SG13 7DG 

 UK 

 1 CIVIL AVIATION

 ADMINSTRATION

 T GOTTESMAN 

PO BOX 8 

BEN GURION INTRNL AIRPORT 

 LOD 70150

 ISRAEL

 1 AEROSPATIALE 

 S ANDRE 

A BTE CC RTE MD132

316 ROUTE DE BAYONNE 

 TOULOUSE 31060

 FRANCE 

 1 DRA FORT HALSTEAD

P N JONES 

SEVEN OAKS KENT TN 147BP 

 UK 

1 SWISS FEDERAL ARMAMENTS 

 WKS 

 W LANZ 

 ALLMENDSTRASSE 86

 3602 THUN

 SWITZERLAND 

1 DYNAMEC RESEARCH LAB

 AKE PERSSON 

 BOX 201 

SE 151 23 SODERTALJE 

 SWEDEN

1 ISRAEL INST OF TECHLGY

 S BODNER 

FACULTY OF MECHANICAL 

 ENGR 

 HAIFA 3200

 ISRAEL

 1 DSTO

WEAPONS SYSTEMS DIVISION

 N BURMAN RLLWS 

 SALISBURY 

 SOUTH AUSTRALIA 5108 

 AUSTRALIA 

NO. OF 

COPIES ORGANIZATION

1 DEF RES ESTABLISHMENT

 VALCARTIER 

 A DUPUIS 

2459 BLVD PIE XI NORTH

 VALCARTIER QUEBEC 

 CANADA

PO BOX 8800 COURCELETTE 

 GOA IRO QUEBEC 

 CANADA

 1 ECOLE POLYTECH 

 J MANSON 

 DMX LTC 

CH 1015 LAUSANNE

 SWITZERLAND 

1 TNO DEFENSE RESEARCH 

 R IJSSELSTEIN 

ACCOUNT DIRECTOR 

 R&D ARMEE

PO BOX 6006 

 2600 JA DELFT 

 THE NETHERLANDS 

2 FOA NATL DEFENSE RESEARCH

 ESTAB 

DIR DEPT OF WEAPONS &

 PROTECTION 

 B JANZON 

 R HOLMLIN 

S 172 90 STOCKHOLM 

 SWEDEN

2 DEFENSE TECH & PROC 

 AGENCY GROUND

 I CREWTHER

GENERAL HERZOG HAUS 

 3602 THUN

 SWITZERLAND 

1 MINISTRY OF DEFENCE 

 RAFAEL 

 ARMAMENT DEVELOPMENT 

 AUTH 

 M MAYSELESS 

PO BOX 2250 

 HAIFA 31021 

 ISRAEL

 1 B HIRSCH

 TACHKEMONY ST 6 

 NETAMUA 42611

 ISRAEL

18
NO. OF 

COPIES ORGANIZATION

1 DEUTSCHE AEROSPACE AG 

 DYNAMICS SYSTEMS 

 M HELD

PO BOX 1340 

 D 86523 SCHROBENHAUSEN 

 GERMANY 

19