Implementation of SEREP Into LLNL Dyna3d for 

Global/Local Analysis 

by David A. Hopkins and Michael A. Minnicino II 

ARL-TR-3569 August 2005 

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Army Research Laboratory 

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ARL-TR-3569 August 2005 

Implementation of SEREP Into LLNL Dyna3d for 

Global/Local Analysis 

David A. Hopkins and Michael A. Minnicino II 

Weapons and Materials Research Directorate, ARL 

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Implementation of SEREP Into LLNL Dyna3d for Global/Local Analysis 

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14. ABSTRACT 

Reduction methods are used to reduce the number of degrees of freedom in a finite-element (FE) model at the expense of highfidelity solutions. The System Equivalent Reduction/Expansion Process (SEREP) is an attractive reduction technique since it 

can preserve the modal fidelity of the FE model up to a user-defined level. This capability allows for a more accurate 

representation of the physical structure. In this report, the feasibility of incorporating SEREP in the FE method for both discrete 

spring-mass-damper and distributed systems is explored. Modeling and numerical issues related to using SEREP as a 

superelement technique are examined and discussed. 

15. SUBJECT TERMS

local, global, finite element, LLNL Dyna3d 

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D. A. Hopkins 

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iii 

Contents 

List of Figures iv

1. Introduction 1

2. SEREP Implementation 3

3. Future Work 13

4. References 14

Distribution List 15 
iv 

List of Figures 

Figure 1. Baseline model with (a) standard FE mesh and (b) SEREP reduced model...................3 

Figure 2. SEREP as a multipoint constraint approach....................................................................4 

Figure 3. Simplified flow chart of SEREP implementation. ..........................................................6 

Figure 4. LLNL Dyna3d time step cycle. .......................................................................................7

Figure 5. Simple spring-mass model. .............................................................................................8 

Figure 6. Baseline and local results of the discrete spring-mass system ........................................9 

Figure 7. Y Stress results of 3D model. Baseline model results using only subset of interface 

nodes. .......................................................................................................................................10 

Figure 8. Y Stress results of 3D model. SEREP model results using subset of interface 

nodes. .......................................................................................................................................11 

Figure 9. Principal stress at interface—baseline model................................................................11 

Figure 10. Principal stress at interface—SEREP model...............................................................12 

Figure 11. Effective stress at interface using a tied interface. ......................................................13 
1 

1. Introduction 

Modern smart munitions rely upon electronic assemblies (1). These assemblies are often 

fabricated from commercial-off-the-shelf components that are not specifically designed to endure 

the harsh loading environment of a gun launch. One method of qualifying these assemblies and 

components is to build the projectile prototypes and conduct live-fire tests until all design issues 

are resolved. This approach is cost prohibitive. Another approach is to simulate the launch 

environment using air guns. While less costly, there are still drawbacks, including acquiring test 

units, simulating the combined loading environment of both setback and spin, and obtaining 

loading profiles that match both the gun launch peak load as well as load duration. Finally, the 

finite-element (FE) modeling approach can be used to construct numerical models of the 

components. 

While FE modeling allows numerous anticipated loading scenarios to be examined prior to 

actually testing hardware, issues related to the modeling process do arise. These issues include 

model fidelity, numerical accuracy, material properties, interface and other boundary conditions, 

and solution time. It would seem that in the design of smart munitions comprised of electronic 

components, we have simply traded cost issues associated with actual testing with numerical and 

other issues associated with the FE modeling process. To some extent, this view is correct, 

which is why any proposed design is rigorously tested in an actual gun launch environment prior 

to fielding. However, many of the modeling issues mentioned have been addressed by prior 

numerical studies such that, using reasonable engineering judgment, designs can be screened, 

thus reducing the required number of field tests. One issue that has not been addressed 

satisfactorily, though, is the time required to complete a numerical analysis of a highly detailed 

FE model. 

It is now possible to include more details in the FE analysis with the enhanced pre/postprocessing tools because of advances in FE modeling tools, analysis codes, and the increase in 

hardware computational capabilities. However, the inclusion of more details typically leads to 

longer analysis times. In fact, there is a continuing trend towards including as much of the “real” 

physics as possible in FE models. This conflicts with a designer’s need for quick analysis turnaround times so that designs can be evaluated and improved. 

Techniques such as Guyan reduction have been used for static analysis to reduce the 

computational cost associated with the analysis of large, complex models (2). These techniques 

have also been applied to transient analysis problems where inertial effects are important even 

though the applicability of these reduction techniques for this class of problems is questionable. 

Direct solutions, whether by implicit or explicit solvers, of the full model are thus often 

employed to avoid the questionable application of these numerical approximations on the time 

dependent solution, even though computational analysis time for these models is substantial 
2 

(3, 4). The analysis time required for these models increases even more dramatically when the 

model length scales are highly disparate. For instance, a typical artillery round is on the order of 

one meter in length, while the capacitors used in the electronic components are on the order of 

millimeters or less in size. Inclusion of this small capacitor in the overall model is not feasible, 

since inclusion of these components in the model leads to excessive computational times, 

although it is the survivability of the electronic components that are of concern. 

A possible resolution to this issue is to develop a global/local modeling approach where the 

response of the small components, the local model, can be captured without necessarily 

including detailed FE models of these small components in the global FE model of the projectile. 

This approach would thus not incur the computational penalty due to the small time steps 

required if the detailed FE local models were included, as in a baseline FE model. There are 

several variations to this global/local modeling. One approach is to replace small components 

and intricate structures with generic coarsely-meshed representations that have material 

properties that approximate the response of the actual local structure and occupy the same 

volume (1). The boundary conditions in these coarse representations may have significant 

errors, as well as other issues such as appropriate stiffness properties, mass densities and 

rotational inertia properties. A second approach is to represent the local model as a rigid body. 

This approach for the overall model can solve some of the issues previously mentioned, but 

introduces concerns about the behavior of stress waves at the interface between the elastic and 

rigid parts of the FE model. Still another approach is to simply replace the small components 

with lumped masses and ignore stiffness effects completely. While this approach doesn’t 

preserve the volume requirements, it does work well for uniaxial response. Finally, 

superelement formulations and Guyan reduction, or similar techniques, can be used to convert a 

local model into an equivalent superelement. 

These techniques can be grouped into static and dynamic reduction techniques (5). The static 

reduction techniques, such as Guyan reduction, omit the inertial effect and focus on the system 

stiffness. Similarly, the dynamic reduction techniques primarily focus on the inertial aspect of 

the system, but can also account for both the inertial and stiffness effects for a range of 

frequencies. Among these dynamic techniques, the system equivalent reduction expansion 

process (SEREP) is a technique that can both reduce the number of degrees of freedom (DOF) 

and maintain the correct dynamic structural response for a user-selected frequency range. 

SEREP has traditionally been used to aid in correlating modal test data and modal numerical 

models for FE modeling validation. However, the approach appears to be a viable method for 

representing the response of complex structures without incurring some of the deficiencies noted 

for other techniques. Details of the theory behind SEREP can be found in several papers (6). In 

this report, we describe a method for implementing SEREP into the Lawrence Livermore 

National Laboratory (LLNL) Dyna3d FE modeling software (7) to allow global/local analysis. 
3 

2. SEREP Implementation 

The idea of the proposed approach is to replace portions of the global structure with their modal 

representations to achieve faster solution times by effectively increasing the characteristic time 

step. The difference between the SEREP approach and traditional modal analysis is that, while 

modal analysis solves the problem in terms of generalized modal DOF, SEREP reformulates the 

problem in terms of the physical DOF. Therefore, a FE model can be partitioned into sections 

represented as traditional FE meshes while other sections are represented by their SEREP 

approximations. Since both FE and SEREP formulations are in terms of the physical DOF, it is 

straightforward to relate the global and local DOF. To illustrate and clarify this distinction, 

consider the simple model shown in figure 1(a). This model was meshed traditionally, as seen in 

figure 1(a), and also using a mixed traditional-SEREP representation, seen in figure 1(b). 

Figure 1. Baseline model with (a) standard FE mesh and (b) SEREP reduced model. 

In the standard modeling approach, either mesh congruency can be maintained at the interface 

between the two components such that all DOF at the interface are merged, or an interface can be 

defined which relates the DOF of one component to the other, as seen in figure 1(a). In LSDyna, or LLNL Dyna3d, this type of interface is referred to as a tied interface. In general, it is a 

multipoint constraint equation. Our implementation of SEREP can be viewed, although the 

analogy is not exact, as an extension of the multipoint constraint formulation since the DOF of 
4 

the global model are related by the SEREP representation of the local model through the retained 

mode shapes. This is illustrated in figure 2 where node i and node j are related by the modal 

properties chosen for the representation of the local model. This modal representation usually 

results in a full mass matrix for the generic case. The mass matrix is not guaranteed to be full as 

some combinations of retained DOF and modes may lead to canceling of off-diagonal terms. 

Figure 2. SEREP as a multipoint constraint approach. 

Implementation of the SEREP representation of the local model requires the construction of the 

global mass and stiffness matrices. From Hopkins and Minnicino (5), the SEREP reduced mass 

matrix Ms, where the subscript s denotes SEREP reduced, is given by 

M T MlT T

s = , (1) 

where Ml is the local mass matrix and the transformation matrix T is given by 

−1

⎥Φ

⎦

⎤ ⎢

⎣

⎡

Φ

Φ = rm

tm

rm T , (2) 

where the subscript r denotes the retained DOF, m denotes the retained modes, and t denotes the 

truncated DOF. When r = m, the inverse required in equation 2 is the usual matrix inverse. For 

the general case when r ≠ m, the inverse in equation 2 is the generalized matrix inverse (6). 

Substituting equation 2 into equation 1 allows the global mass matrix to be expressed as 
5 

11 1

1 1 ,

T T

rm rm rm rm T

s rm l rm rm l rm

tm tm tm tm

T T

rm rm rm rm

MM M

I

− −− −

− − −−

Φ Φ ΦΦ ⎡ ⎤ ⎡ ⎤⎡ ⎤ ⎡ ⎤ ⎡⎤ ⎡⎤ ⎡⎤ ⎡⎤ = Φ Φ =Φ Φ ⎢ ⎥ ⎢ ⎥⎢ ⎥ ⎢ ⎥ ⎢⎥ ⎢⎥ ⎢⎥ ⎢⎥ ⎣ ⎦⎣ ⎦ ⎣ ⎦ ⎣⎦ ⎣⎦ ⎣⎦ ⎣⎦ Φ Φ ΦΦ ⎢⎣ ⎥⎦

=Φ Φ =Φ Φ

 , (3) 

where the orthogonality of the mass-normalized eigenvectors has been utilized. This resultant 

matrix is singular if the number of retained DOF, r, is greater than the number of retained modes, 

m (6). The meaning of the inverse shown in equation 3 depends on the dimensionality of −1 Φrm . 

The superscript –T denotes the inverse of the matrix transpose, i.e., A-T

 = (AT)

-1. 

This SEREP reduced local mass matrix is used to construct the global mass matrix 

M = M d + M s

~ , (4) 

where Md is the diagonal mass matrix obtained from the elements in the global model (the d

subscript denotes diagonal). M

~ is subsequently used to solve for the nodal accelerations of the 

global model 

a M F ~ −1 = . (5) 

M

~ may be singular because Ms is singular, in which case, the normal inverse does not exist. 

The solution of equation 5 can still be determined using singular value decomposition (SVD) (8), 

but this approach is not discussed in this report. In addition to being singular because of rank 

deficiency, the reduced mass matrix can also be ill-conditioned. This can also lead to numerical 

problems with the SVD approach for solving for the response. The results presented in this 

report are for SEREP models that have been constructed such that M

~ is nonsingular and wellconditioned. This was accomplished by selecting local model DOF which were on the boundary 

of the local model and had corresponding global model DOF associated with the local model 

DOF. 

Proper selection of the retained DOF depends upon the actual boundary conditions between the 

global and local models as well as consideration of the desired frequency response present in the 

local model’s SEREP representation. As a rule of thumb, all local modes below or near the 

highest frequency of interest should be selected. Also, only selecting nodes on the interface 

between the global and local models typically leads to acceptable results. Research is currently 

being conducted to develop more precise guidelines based on the modal characteristics of the 

local and global models. 

The previous formulation of the reduced mass matrix was implemented in LLNL Dyna3d. A 

simple flowchart of the implementation is shown in figure 3. 
6 

Dyna3d 

input

Initialize Serep 

data arrays

Dyna3d 

solver 

Compute 

Serep loads

Initialize Dyna3d 

 data arrays 

Set up Serep

storage 

arrays

Figure 3. Simplified flow chart of SEREP implementation. 

It is seen that implementation in LLNL Dyna3d was fairly straightforward. Routines were added 

to allocate storage arrays for the SEREP variables, initialize these arrays, and then calculate 

effective forces acting upon the nodes associated with the SEREP nodes. Initialization of the 

reduced mass matrix, and the computation of its inverse, are done once during the initialization 

phase. This information is saved so that computation of the nodal acceleration during the 

solution phase is efficient. The only values that must be recomputed at every time step are the 

effective internal nodal-loads due to the SEREP effective stiffness. These internal forces are 

computed using 

rm r n

T Fr n rm X ,1

, 1

− −

+ = Φ ΛΦ , (6)

where Λ is a diagonal matrix of the system’s eigenvalues and Xr,n are the nodal displacements at 

time tn of the retained nodal DOF. 

The time step cycle (9) that the solver uses to advance from tn to tn+1 is shown in figure 4, 

together with the modifications to the Dyna3d logic required to include SEREP loading. 

A time step in Dyna3d starts with the determination of the loads acting on the nodes. First, we 

discuss the normal time step cycle for Dyna3d. This cycle will be assumed to start at time t0 with 

all nodal displacements, velocities, accelerations, and applied forces known. The nodal 

accelerations are very simple to compute because the Dyna3d formulation results in a diagonal 

mass matrix. Thus, the nodal accelerations are given by 

n M Fn a

1

1

−

+ = . (7) 

The nodal velocities and displacements are subsequently computed using a central difference 

update scheme. Technically, Dyna3d uses a strain and stress rate formulation. However, for the 

sake of brevity, the cycle simply indicates that the strains are computed after the displacement. 
7 

Then, depending on the constitutive model, the element stresses are computed. Finally, the 

gradient of the stress provides the internal forces. This internal force is subtracted from the 

external applied forces on a nodal basis. Finally, the cycle completes with the accelerations 

again being computed. 

Implementing SEREP involves introducing two changes into this time step cycle. The first 

change, labeled “1” in figure 4, requires updating the nodal internal forces using equation 6. 

Entries in the force vector that are associated with SEREP DOF are temporarily saved for later 

use. Dyna3d then computes the nodal accelerations via the normal update method, equation 7. 

However, this computation assumes that the mass matrix is diagonal, which for SEREP-related 

DOFs is not necessarily true. Consequently, as indicated at “3” of figure 4, the actual nodal 

accelerations are computed using the previously stored force vector and the inverse of the mass 

submatrix that is associated with SEREP DOFs. These accelerations are then used to replace the 

erroneous values, and the normal time step cycle continues. This implementation thus requires 

minimal changes to the Dyna3d time step cycle, as seen in figure 4. The most difficult aspect of 

the implementation was, in fact, determining how to setup the appropriate storage requirements 

for the implementation to ensure that Dyna3d storage requirements were not adversely affected. 

C

a

f v

a=m-1 f

σ

ε

f=f+fs

f=ma

σ=σ(ε)

f=f(dσ/dx)

ε=ε(v,d)

1

2

3

4

B

A

E

D

F

d

C

a

f v

a=m-1 f

σ

ε

f=f+fs

f=ma

σ=σ(ε)

f=f(dσ/dx)

ε=ε(v,d)

1

2

3

4

B

A

E

D

F

d

Figure 4. LLNL Dyna3d time step cycle. 

This implementation was initially tested using the simple 1-D discrete spring-mass model shown 

in figure 5. This model was used to validate the implementation. The local model consisted of 

the DOF associated with masses 1–4, while the global model consisted of the DOF associated 
8 

1 2 3 4

K1 K1 K1 K1 K1

Global

model

Local

model F

1 2 3 4

K1 K1 K1 K1 K1

Global

model

Local

model F

Figure 5. Simple spring-mass model. 

with masses 1 and 4. Thus, the DOF of masses 1 and 4 constitute the interface between the 

global and local models. The local model’s equations of motion are given by 

⎪

⎪

⎭

⎪

⎪

⎬

⎫

⎪

⎪

⎩

⎪

⎪

⎨

⎧

=

⎪

⎪

⎭

⎪

⎪

⎬

⎫

⎪

⎪

⎩

⎪

⎪

⎨

⎧

⎥

⎥

⎥

⎥

⎦

⎤

⎢

⎢

⎢

⎢

⎣

⎡

−

−

− −

−

+

⎪

⎪

⎭

⎪

⎪

⎬

⎫

⎪

⎪

⎩

⎪

⎪

⎨

⎧

⎥

⎥

⎥

⎥

⎥

⎥

⎦

⎤

⎢

⎢

⎢

⎢

⎢

⎢

⎣

⎡

0

0

0

0

0 0

0 2 0

2 0

0 0

2

0 0 0

0 0 0

0 0 0

0 0 0

2

4

3

2

1

1 1

1 1

1 1 1

1 1

4

3

2

1

x

x

x

x

K K

K K

K K K

K K

x

x

x

x

M

M

M

M









, (8) 

where the full mass of DOF 2 and 3, and half of mass associated with DOF 1 and 4 and the 

springs connecting these DOF, are considered to comprise the local model. The global model’s 

equations of motion, based on the DOF associated with masses 1 and 4, together with the springs 

connected to the rigid walls, are given by 

⎭

⎬

⎫

⎩

⎨

⎧ − =

⎭

⎬

⎫

⎩

⎨

⎧

⎥

⎦

⎤ ⎢

⎣

⎡

+

⎪⎭

⎪

⎬

⎫

⎪⎩

⎪

⎨

⎧

⎥

⎥

⎥

⎥

⎦

⎤

⎢

⎢

⎢

⎢

⎣

⎡

-f (t)

F f (t)

x

x

K

K

x

x

M

M

..

..

2

1

2

1

4

1

0

0

2

0

0

2 , (9) 

where a step load, F, was applied to mass 1. The forces, f1(t) and f2(t), in equation 9 are the 

effective forces at the global/local interface. The eigenvalues and eigenvectors for the local 

model were computed using equation 8 for free-free boundary conditions. These 

eigenvalues/eigenvector pairs were used to construct the SEREP representation of the local 

model. The numerical results for the complete spring-mass system were computed as the 

baseline response. Two SEREP cases were then analyzed. First, all modes for the local model 

were retained. For this condition, the resultant equations of motion are identical to the baseline 

system. In the second SEREP case, the highest eigenvalue was omitted, so only three modes 
9 

were retained for the local model: the rigid body motion and the first two elastic modes. Results 

for the response at masses 2 and 4 for all three cases are shown in figure 6. Both SEREP 

solutions are in excellent agreement with the baseline model. The effect of neglecting the 

highest eigenvalue shows up as a slight difference in the response for this case as compared to 

the baseline case. This simple spring-mass model verified that the implementation into Dyna3d 

was correct. Comparison of the baseline and SEREP results indicates that this approach 

represents a reasonable method of solving the global/local modeling problem. It is important to 

realize that the current implementation of SEREP assumes that all modes below a given upper 

frequency are retained. If the system shown in figure 5 was driven at a frequency higher than 

that of the greatest retained system natural frequency, then the error between the baseline 

solution and SEREP solution would increase. 

Figure 6. Baseline and local results of the discrete spring-mass system. 

Next, the acceleration response of the model shown in figure 1(a) to a unit step load was 

computed. Baseline results for the full model where all common interface nodes have been 

merged are shown in figure 7. As seen previously in figure 1(b), 15 local model nodes at the 

global/local interface are merged because the meshes between the local and global models are 

non-congruent. Therefore, these merged nodes are a subset of the complete set of interface 
10 

nodes. The Y-direction stress results for the SEREP model, using these merged nodes at the 

interface, are shown in figure 8. It is seen that the results at the interface are different, which is 

to be expected. However, the contour levels are very similar a short distance away from the 

interface. Also note that this test case does not represent the best correlation that can be expected 

from this technique since not all interface nodes were used. Regardless, the results are 

encouraging. Using only the common interface nodes, the mass matrix that is inverted to solve 

for the nodal accelerations, step “A” of figure 4, is rendered nonsingular. This is because the 

equation to be solved is given by 

F Ma ([M ] [M ])a = = d + s

~ , (10) 

where [ ] M d is a diagonal mass matrix obtained from the single-point integration formulation of 

the FE elements at the global/local interface and the [ ] M s is the potentially singular SEREPderived reduced mass matrix. The addition of these two matrices, for this case, results in a 

nonsingular matrix that is invertible. This is an empirical observation, since mathematically the 

resultant matrix could be singular for arbitrary matrices [ ] M d and [ ] M s . If internal DOF were 

selected from the local model for this case, then the resultant mass matrix is guaranteed to be 

singular. 

Figure 7. Y Stress results of 3D model. Baseline model results 

using only subset of interface nodes. 
11 

Figure 8. Y Stress results of 3D model. SEREP model results using 

subset of interface nodes. 

As was observed from the Y-direction stress global results, examining the principal stresses 

shows that the results are different near the interface but similar away from the interface, as seen 

in figures 9 and 10. 

Figure 9. Principal stress at interface—baseline 

model. 
12 

Figure 10. Principal stress at interface—SEREP 

model. 

This observation allows for the efficient computation of the high-fidelity local solution by 

applying the global solution as local model boundary conditions where the full and global 

solutions appear equivalent. In a real structural analysis, the full system solution is not known 

and the correct global boundary condition is an engineering judgment based on the physics of the 

problem. The appropriate boundary conditions to apply to the local model are the time 

dependent displacements. Stress/time histories could also be used, but are more likely to 

introduce errors since stresses depend upon the displacement gradients. While the displacements 

of the interface nodes themselves could be used, because of St. Venant’s Principle, the localized 

stresses, strains, and thus displacements of these nodal displacements are not representative of 

the actual system. However, the use of nodes located away from the actual interface would 

provide a better local response where the new, high-fidelity local model now includes the 

original local model and a part of the original global model, the size of which is dictated by St. 

Venant’s Principle. 

For comparison with the previous models, results for a more representative model using a tied 

interface are presented in figure 11. Unlike the SEREP or merged results presented previously, it 

is seen that the actual response at the interface is smooth. Again, this difference is to be expected 

for the sample problem since not all of the interface nodes were used in either the SEREP or 

baseline models. It is hypothesized that if the local model mesh is constructed such that all of 

the global model’s interface nodes have corresponding nodes in the local model, then a more 

accurate response can be obtained for both the global and local models. This is inferred because 

the effect of point loading on the global model will be reduced if the global and local models are 

meshed such that the above mesh congruency is true. 
13 

Figure 11. Effective stress at interface using a tied interface. 

3. Future Work 

Based on these preliminary results, the SEREP approach for global/local modeling presents a 

promising method for reducing a FE model’s complexity while retaining correct mass and 

stiffness effects. Remaining issues which must be addressed include implementing a more 

robust SVD solver for finding solutions when the mass matrix is singular, automating the task of 

relating global and local DOF, and automating the selection of a proper set of local DOF so as to 

maintain accuracy in the global response calculation. None of these issues are intractable. They 

simply require diligence in formulating a reasonable modeling methodology such that this 

technique can be a useful tool for quickly analyzing proposed designs involving electronic 

components. Future research will examine SEREP’s ability to use actual modal test data to 

generate the SEREP superelement for inclusion in the FE model. This would be useful when 

construction of a representative FE model for a complex part cannot be obtained in a timely 

manner, but modal data either already exists or can be obtained. 
14 

4. References 

1. Wilkerson, S.; Hopkins, D.; Gazonas, G.; Berman, M. Developing a Transient Finite Element 

Model to Simulate the Launch Environment of the 155-mm SADARM Projectile. 

ADA388168. 

2. Guyan, R. J. Reduction of Stiffness and Mass Matrices. AIAA Journal 1965, 3. 

3. Newill, J. F.; Burns, B. P.; Wilkerson, S. A. Overview of Gun Dynamics Numerical 

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 R MARTIN 

 MERL 

 TAMWORTH RD 

 HERTFORD SG13 7DG 

 UK 

 1 SMC SCOTLAND 

 P W LAY 

 DERA ROSYTH 

 ROSYTH ROYAL DOCKYARD 

 DUNFERMLINE FIFE KY 2XR 

 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 

 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 
NO. OF 

COPIES ORGANIZATION 

27

 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 

 1 TNO DEFENSE RESEARCH 

 I H PASMAN 

 POSTBUS 6006 

 2600 JA DELFT 

 THE NETHERLANDS 

 1 DEUTSCHE AEROSPACE AG 

 DYNAMICS SYSTEMS 

 M HELD 

 PO BOX 1340 

 D 86523 SCHROBENHAUSEN 

 GERMANY
28

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