Upload
others
View
13
Download
0
Embed Size (px)
Citation preview
TG 1196
APRIL 1972
Copy No. -?
Technical Memorandum
NASTRAN: USER EXPERIENCEWITH FOUR EXAMPLE PROBLEMSby R. M. RIVELLO
WITH FOUR EXAMPLE PROBLEMS 7. Rielo/(Applied Physics Lab.) ,pr. 1972 139 p
CSCL 20K Unclas
G3/32 3678. 8
' 'eii'oduced by NATIONAt TECHNICAL:
<:_iNFORMATION SERVICE:U S Department of Commerce. Springfield VA 22151 -
THE JOHNS HOPKINS UNIVERSITY * APPLIED PHYSICS LABORATORY
Approved for public release; distribution unlimited.
https://ntrs.nasa.gov/search.jsp?R=19720021257 2018-01-21T23:07:04+00:00Z
UNCLASSIFIEDSecurity Classification
DOCUMENT CONTROL DATA - R & DrSeccIrity classification of title, body of abstract and indexing annotation nlut be entered when tile overall report is classified)
I. ORIGINA TING ACTIVITY (Corporate author) 20. REPORT SECURITY CLASSIFICATION
The Johns Hopkins University Applied Physics Lab. Unclassified8621 Georgia Avenue 2b. GROUP
Silver Spring. Md. 20910 n. a.3. REPORT TITLE
NASTRAN: User Experience with Four Example Problems
4 DESCRIPTIVE NOTES (Type of report and inclusive dates)
Technical Memorandum5. AUTHOR(S) (First name, middle initial, last name)
Robert M. Rivello
6- REPORT DATE 7a. TOTAL NO. OF PAGES 7b. NO. OF REFS
April 1972 129 178a. CON TRAC T OR GRANT NO. 9a. ORIGINATOR'S REPORT NUMBER(S)
N00017-72-C-4401b. PROJECT NO. TG-1196
c. Sb. OTHER REPORT NO(S) (Any other numbers that may be assignedthis report)
d.
10. DISTRIBUTION STATEMENT .
Approved for public release; distribution unlimited
11. SUPPLEMENTARY NOTES i2. SPONSORING MILITARY ACTIVITY
n. a. Naval Ordnance Systems Command
1. AOSIL1. I
The NASTRAN computer program is used to solve four simple struc-tural problems. The problems are: (1) a simply-supported beam subjected tolateral loads, (2), a filamentary composite bar under the action of centrifugalforces, (3) a free beam subjected to lateral loads, and (4) the thermal bucklingof a simply-supported plate. Input and output data are given for each problem toassist the new NASTRAN user in preparing program input data. The results arecompared with solutions obtained by other methods. The example problems dis-closed errors in the plotting and thermal-buckling routines of the computer. Thesehave subsequently been corrected. The program was found to have broad capa-bilities and to offer many user conveniences.
I,
DD FNORV M 1473 UNCLASSIFIEDSecurity Classification
1 3. ABSTRACT
UNC LA SSIFIEDSecurity Classification
14.KEY WORDS
BucklingComputer plottingComputer programsFinite differences methodFinite element methodNASTRANStress analysisStress and deflectionStructural analysisSuperflywheelThermal stress analysis
UNC LA SSIFIEDSecurity Classification
[
TG 1196
APRIL 1972
Technical Memorandum
NASTRAN: USER EXPERIENCEWITH FOUR EXAMPLE PROBLEMSby R. M. RIVELLO
THE JOHNS HOPKINS UNIVERSITY *· APPLIED PHYSICS LABORATORY8621 Georgia Avenue o SilverSpring, Maryland o 20910Operating under Contract N00017-72-C-4401 with the Department of the Navy
Approved for public release; distribution unlimited.
_..,,,.
THE JOHNS HOPKINS UNIVERSITY PRECEDING PAGE BLANK NOT FILMEDAPPLIED PHYSICS LABORATORY
SILVER SPRING. MARYLAND
ABSTRACT
Four different structural problems are solved togain familiarity with the NASTRAN computer program.The problems are: (1) a simply-supported beam subjectedto lateral loads, (2) a rotating filamentary composite barunder the action of centrifugal forces, (3) a missile bodywith aerodynamic, gravitational, and inertial forces, and(4) a square simply-supported plate with in-plane tempera-ture changes capable of buckling the plate. Input and out-put data are given for each problem. These should be ofassistance to those who are using the program for thefirst time.
The results are compared with those obtained byother methods. However, except for the examples employingbeam elements in which the agreement is excellent, the ele-ment breakup chosen for convenience in obtaining programfamiliarity is too coarse to draw conclusions regarding theprogram accuracy. The example problems disclosed errorsin the plotting and thermal-buckling routines of the program.
The program was found to offer many user conveni-ences. Data preparation was straightforward once famil-iarity with the format appropriate to the problem was gained.The program documentation is complete for reference pur-poses, but is lacking in that it does not rapidly orient thenew user. The capabilities and conveniences of the programgreatly outweigh its inadequacies, and it is recommendedthat APL/JHU continue to update the program with eachnew release from NASA.
- iii -
TE OHNS HOPKINS UNv,,,,T PRECEDING PAGE BLANK NOT FILMAPPLIED PHYSICS LABORATORYSILVER SPRING. MARYLAND
CONTENTS
List of Illustrations vii
List of Tables xi
1 Introduction 1
2 Example Problems . 5Example Problem 1 . . 8Example Problem 2 .10Example Problem 3 . 15Example Problem 4 . . . 20
3. Discussion 29
Acknowledgment . . . . 31
References .33
Appendixes:
A. Example 1 - Simply-Supported Beam A-iB. Example 2 - Composite Flywheel B-1C. Example 3 - Missile Flight Loads C-1D. Example 4- Thermal Buckling D-1
-v
THE JOHNS HOPKINS UNIVERSITY PRECEDING PAGE BLANK NOT FITLMEDAPPLIED PHYSICS LABORATORY
SILVER SPRING. MARYLAND
ILLUSTRATIONS
1 Simply-Supported Beam, ExampleProblem 1. . 9
2 Finite-Element Idealizations, ExampleProblem 2 . 12
3 Comparison of Example Problem 2 Resultswith Results Given in Refs. 14 and 15 14
4 Example Problem 3 . 16
5 Finite-Element Breakup, ExampleProblem 3 . 16
6 Shear versus Body Station, ExampleProblem 3 . . . 17
7 Bending Moment versus Body Station,Example Problem 3 . . 17
8 Deflection versus Body Station, ExampleProblem 3 . . . 18
9 Example Problem 4 . 21
10 NASTRAN Idealization and TemperatureDistribution, Example Problem 4 21
11 Distribution of Prebuckling ThermalStresses axx' Example Problem 4 23
12 Distribution of Prebuckling ThermalStress a , Example Problem 4 . 24
- vii -
THE JOHNS HOPKINS UNIVERSITY
APPLIED PHYSICS LABORATORYSILV1ER SPRING. MARYLAND
13 Thermal-Buckling Mode Shape, ExampleProblem 4. 25
14 Finite Difference Mesh and TemperatureDistribution, Example Problem 4 26
A-1 Static Loading of Simply-Supported Beam;NASTRAN Example Problem 1: UndeformedShape . . . . A-19
A-2 Static Loading of Simply-Supported Beam,Concentrated Load at Center; NASTRANExample Problem 1: Static Deformation,Subcase 1, Load Set 1 . . . A-19
A-3 Static Loading of Simply-Supported Beam,Distributed Load; NASTRAN ExampleProblem 1: Static Deformation, Sub-case 2, Load Set 2 . . A-20
A-4 Static Loading of Simply-Supported Beam,Concentrated plus Distributed Load;NASTRAN Example Problem 1: StaticDeformation, Subcase 3, Load Set 3 A-20
B-1 Super Flywheel Stress Analysis, 1. 254cps; NASTRAN Example Problem 2:Undeformed Shape . . B-23
B-2 Super Flywheel Stress Analysis, 1. 254cps; NASTRAN Example Problem 2:Static Deformation, Subcase 1, LoadSet 1 . . . . B-24
B-3 Super Flywheel Stress Analysis, 1. 254cps; NASTRAN Example Problem 2:Static Deformation, Subcase 1, LoadSet 1 .. B-25
- viii -
THE JOHNS HOPKINS UNIVERSITY
APPLIED PHYSICS LABORATORYSILVER SPRING. MARYLAND
B-4 Super Flywheel Stress Analysis, 1. 254cps; NASTRAN Example Problem 2:Static Deformation, Subcase 1, LoadSet 1 . . . B-26
C-1 Flight Load Problem; NASTRAN ExampleProblem 3: Undeformed Shape C-17
C-2 Flight Load Problem; NASTRAN ExampleProblem 3: Static Deformation, Sub-case 1, Load Set 1 C-18
C-3 Flight Load Problem; NASTRAN ExampleProblem 3: Static Deformation, Sub-case 1, Load Set 1 . . C-19
D-1 Thermal Buckling of Square Plate;NASTRAN Example Problem 4: Unde-formed Shape . . . D-28
D-2 Thermal Buckling of Square Plate;NASTRAN Example Problem 4: StaticSolution, Static Deformation, Subcase1, Load Set 0 . . . . D-29
D-3 Thermal Buckling of Square Plate;NASTRAN Example Problem 4: BucklingSolution, Subcase 2, Mode 1, Eigen-value = 314.55923000 . . . D-30
- ix -
THE JOHNS HOPKINS UNIVERSITY
APPLIED PHYSICS LABORATORYSILVER SPRIWN. MARYLAND
PRECEDING PAGE BLANK NOT FILMED
TABLES
1 Program Options Used in ExampleProblems .
2 Example Problem 1: Comparison ofNASTRAN and Beam-Theory Results
- xi -
11
7
THE JOHNS HOPKINS UNIVERSITY
APPLIED PHYSICS LABORATORYSILVER SPRING. MARYLAND
1. INTRODUCTION
The advent of high-speed digital computers has hada revolutionary effect upon the analysis of stress and de-flection of structures. Prior to the availability of thesecomputers, it was necessary to use simplifying approxi-mations to analyze structural components. Although ap-proximate theories such as those for beams, plates, andshells frequently give satisfactory results for simple struc-tural components, they are generally unsuitable for the ac-curate analysis of complex structures.
Matrix methods of structural analysis in which thecomplex structure is considered to be an assemblage ofsimple finite-sized elements were introduced in the late1950's (Refs. 1 and 2). Most of the matrix methods thathave been developed since then have used either forces ordisplacements as the unknowns. Of the methods that havebeen proposed, the so called "direct-stiffness" displace-ment method introduced in Ref. 2 has proven to be rela-tively simple to program and has given well-conditionedsolutions. As a result, it has been widely used and under-gone extensive development. Today many programs areavailable that use the direct-stiffness method and it doesnot appear economical for organizations contemplating theneed for such a program to develop their own unless theyrequire small special-purpose programs that will be suffi-ciently used to merit the costs of program development.However, in some cases it may be justifiable to write sim-ple, efficient programs for special types of problems in-stead of using a large, complex, and inefficient all-purposeprogram.
Of the general-purpose programs, the NASA STRuc-tural ANalysis (NASTRAN) program is capable of handlingthe largest number of different types of structural prob-lems. Several million dollars have been invested in the
-1-
THE JOHNS HOPKINS UNIVERSITY
APPLIED PHYSICS LABORATORYSILVER SPRlNG. MARYLAND
development of this program and an annual expenditure ofapproximately one-half million dollars has been budgetedby NASA for its upkeep and improvement.
The diversity and complexity of structural problemsencountered by the Johns Hopkins University Applied Phys-ics Laboratory (APL) are such that the availability of ageneral-purpose program is a necessity. The capabilitiesof the nonproprietary NASTRAN program make it a naturalchoice. Furthermore, the Naval Ship Research and Devel-opment Center (NSRDC) had already installed Level 12. 0of the program on the IBM 360 computer at APL and, whenthe program was released by NASA to nongovernmentalagencies, the use of it was offered to APL.
Although the NASTRAN program had been installedon the APL computer, APL personnel had not been involvedand were, therefore, untrained in the use of the program.Self instruction in the use of the program is not a smallundertaking. The program has a total of twelve rigid for-mats to provide a general-purpose capability as follows:
1. Static Analysis
2. Static Analysis with Inertia Relief
3. Normal Modes Analysis
4. Differential Stiffness Analysis
5. Buckling Analysis
6. Piecewise Linear Analysis
7. Direct Complex Eigenvalue Analysis
8. Direct Frequency and Random Response
9. Direct Transient Response
10. Modal Complex Eigenvalue Analysis
-2-
THE JOHNS HOPKINS UNIVERSITY
APPLIED PHYSICS LABORATORYSILVER SPRING. MARYLAND
11. Modal Frequency and Random Response
12. Modal Transient Response
The program documentation that is available from theNASA COSMIC Office consists of a Theoretical Manual(Ref. 3), a'User's Manual (Ref. 4), a Programmer'sManual (Ref. 5), and a Demonstration Problem Manual(Ref. 6). The total number of pages in these documentsis roughly 3300. Unfortunately for the new user, themanuals are for reference rather than tutorial purposesand do not include indices.
The Demonstration Problem Manual gives a com-parison of NASTRAN results with solutions to the sameproblems obtained by other methods; however, this man-ual does not contain the input or output data for the NAS-TRAN solutions. As a result, it alone is of little valueas a learning aid. The NASTRAN tapes available fromCOSMIC contain a file of the bulk data card images for thedemonstration problems, but to obtain the full set of inputand output data it is necessary to prepare executive andcase control decks and run the problems. The NSRDCwas never successful in getting this portion of the tape torun on the APL computer. Furthermore, considerablecomputer expense would be entailed in running the 25demonstration problems.
After the four NASTRAN manuals were reviewed, itwas concluded that the only sensible way to become famil-iar with the program would be to prepare the data for sev-eral example problems and run them. The purpose of thisreport is to document the input and output data for the ex-ample problems, in the hope that the examples will behelpful to those who are learning to use the program.
Subsequent to running some of the example prob-lems, a set of the printouts of the demonstration problemsof Ref. 6 was obtained. These printouts (which were runwith NASTRAN Level 8. 1. 0) proved to be of considerablehelp, because there are several places where the User'sManual is unclear and some places where it is misleading.
-3-
THE JOHNS HOPKINS UNIVERSITY
APPLIED PHYSICS LABORATORYSILVER SPRING. MARYLAND
After the work documented in this report was com-pleted, a copy of a beginner's guide (Ref. 7) that is usedin the NASTRAN training courses taught by the MacNeal-Schwendler Corporation was obtained. The printouts forthe demonstration problems, the beginner's guide, andRefs. 8 through 12 should prove helpful to the new NASTRANuser. The BBE Project Office of APL has these refer-ences on file.
The job cards that are required to run NASTRANon the APL computer are described in Ref. 12. The newuser should also be aware of two newsletters that areperiodically published for NASTRAN users. One of these,the NASTRAN Newsletter, is published by NASA. Usersmay be placed on the distribution list for this newsletterby writing or phoning:
NASTRAN Systems Management OfficeMail Stop 188cNASA Langley Research CenterHampton, Va. 23365Telephone: (703) 827-2388
The other is the Navy Structures Computer Program NEWS-LETTER that is published by NSRDC and is available from:
NASTRAN Evaluation Project, Code 823Department of Applied Mathematics, NSRDCWashington, D. C. 20034
-4-
THE JOHNS HOPKINS UNIVERSITY
APPLIED PHYSICS LABORATORYSILVER SPRING. MARYLAND
2. EXAMPLE PROBLEMS
Example problems were chosen to exercise differ-ent rigid-format, structure-definition, loading, and out-put options of the program. The example problems are asfollows:
1. Static Deformations of a Simply-SupportedBeam
2. Static Deformation of a Composite Rectangular-Planform Flywheel
3. Static Deformation of a Missile Body Under theAction of Aerodynamic and Inertial Loads
4. Thermal Buckling of a Square Simply-SupportedPlate
The program features that are demonstrated by these prob-lems are:
1. Rigid Formats
a. Static Analysisb. Static Analysis, Inertia Reliefc. Buckling Analysis
2. Structure Definition Options
a. Single-Point Constraintsb. Free-Body Supportsc. Bar Elementsd. Quadrilateral Membrane Elementse. Quadrilateral Plate Elementsf. Thermally-Dependent Materialsg. Isotropic Materialsh. Anistropic Materials
-5-
THE JOHNS HOPKINS UNIVERSITY
APPLIED PHYSICS LABORATORYSlLVER SPRING. MARYLAND
3. Static Loading
a. Concentrated Loadsb. Gravity Loadsc. Inertial Loadsd. Centrifugal Field Loade. Thermal Loadsf. Combined Loads
4. Output Options
a. Shape Plot of Undeformed Structureb. Shape Plot of Deformed Structurec. Vector Plot of Structural Displacementsd. Point Output Selectionse. Element Output Selectionsf. Subcase Level Request Changesg. Modal Plot
The program options that are used for each of the exampleproblems are shown in Table 1.
The primary purpose of the example problems isto gain familiarity with the NASTRAN data format ratherthan to obtain high accuracy in the computed results. Be-cause of this, crude structural modeling with few gridpoints and elements is used to reduce the data preparationand computing times. Improved accuracy could be obtainedby using smaller elements, especially in the regions oflarge stress gradients.
In initial runs of the example problems, it wasfound that the program would not write a tape for the CAL-COMP plotter. This difficulty was reported to NSRDC whomade the necessary programming corrections to obtainCALCOMP Model 565 plots. It is still not possible to ob-tain plots with the CALCOMP Model 765, the default modelfor the program. It was also found that there was an errorin the thermal-buckling portion of the program (this typeof problem was not included in the demonstration problemsof Ref. 6). The difficulty was reported to the NASTRANSystems Management Office and to NSRDC. Correctionswere made by NSRDC to the APL copy of the program.
-6-
THE JOHNS HOPKINS UNIVERSITY
APPLIED PHYSICS LABORATORYSILVER SPRING. MARYLAND
Table 1
Program Options Used in Example Problems
Problem Proram OptionNo. lalb lc2a 2b2c2d2e2f2g2h 3a 3b3c3d3e3f 4aI4b 4c4d4e4f4g
1 X X X X XX XX X XXX
2 X X X X X XXXXX
3 XXX XX XX X X X XXX XX
4 X X X X X I X XI
-7-
THE JOHNS HOPKINS UNIVERSITY
APPLIED PHYSICS LABORATORYSILVER SPRING. MAIRYLAND
Detailed descriptions of the example problems aregiven in the following subsections in which the computed resultsare compared with the results obtained by other methods.The computer and plotter outputs for each of the exampleproblems is given in the appendixes at the end of the re-port. The output contains an echo of the executive, case,and bulk data decks that constitute the input to the program.This input should serve as a useful guide to the new userin preparing program data.
EXAMPLE PROBLEM 1
The first example problem is for a uniform, sim-ply-supported beam. The computer and CALCOMP outputsfor the problem are given in Appendix A. The geometry,method of support, and material properties of the beamare shown in Fig. 1. The finite-element idealization con-sisting of four BAR (beam) elements and 5 grid points isalso shown in this figure. The origin of the basic coordi-nate system is taken at grid point 1.
Three static-load subcases are used: Subcase 1consists of a concentrated 100-lb load applied upward atgrid point 3, Subcase 2 consists of a 100 lb/in uniformlydistributed upward loading, and Subcase 3 is the sum ofthe loadings from subcases 1 and 2. The NASTRAN pro-gram does not have a distributed load bulk data card forBAR elements. In this example problem, the gravity-loading card GRAV is used to provide the distributed load-ing. A gravitional acceleration (gravity vector scale fac-tor) of 3.86 x 104 in/s 2 is used to produce a loading of 10lb/in with a cross sectional area of 1. 0 in2 and a materialspecific weight of 0. 1 lb/in 3 .
Vertical displacements and rotations (slopes) arecomputed at all grid points. Reactions are determined atall single-point constraints. Bending stresses are foundat both ends of each element at the four cross-sectionalpoints shown in Fig. 1. CALCOMP plot requests are madeboth for the undeformed structure and for the deformed
-8-
THE JOHNS HOPKINS UNIVERSITY
APPLIED PHYSICS LABORATORYSILVER SPRING. MARYLAND
y
(t1 t - (2)
20 IN TYPICAL
F--(3) + (4) .X
_1IA = 1.0 IN 2
I = 0.1 IN 4
E = 10 7 PSI
w = 0.1 LB/IN 3
( ) ELEMENT NUMBERS
O GRID POINT NUMBERS
STRESS CALCULATIONPOINT NUMBERS
FIG. 1 SIMPLY-SUPPORTED BEAM, EXAMPLE PROBLEM 1
-9-
IN Ap
I
THE JOHNS HOPKINS UNIVERSITY
APPLIED PHYSICS LABORATORYSILVER SPRING. MARYLAND
structure for each of the three subcase loads. The result-ing CALCOMP plots are given at the end of Appendix A.
Bending deflection at the center of the beam andend slopes for subcases 1 and 2 were also computed.Stresses were calculated using bending-moment formulas fromRef. 13. The NASTRAN and beam-equation results arecompared in Table 2. It is seen that the NASTRAN resultsare in perfect agreement with those from beam theory forSubcase 1. This would be expected, since the BAR-ele-ment deflection function used in the program is a cubic, asis the actual deflection shape for a beam with concentratedloads. As a result, element size in this case does not af-fect accuracy. For Subcase 2 the stresses are in goodagreement, but the center deflection computed by NASTRANis 5% less than the exact solution given by beam theory.The deflection result is not surprising since, for a distrib-uted loading, the exact deflection curve for each elementis a quartic rather than a cubic as assumed in NASTRANand, in addition, the NASTRAN program uses lumped forcerather than consistent force matrices for distributedloads. Of course, accuracy could be improved by usingsmaller elements than those in the crude four-elementidealization used in the example.
EXAMPLE PROBLEM 2
In this second example problem the NASTRAN pro-gram is applied to a unidirectional graphite-epoxy com-posite bar rotating at a constant angular velocity about itscenter of gravity. Since the geometry, elastic properties,and loading are symmetric about both the longitudinal andlateral axes of the body, it is only necessary to model onequadrant of the bar. The finite-element idealization con-sists of 60 identical nonisotropic, quadrilateral, membrane(QDMEM) elements with 80 grid points as shown in Fig. 2a.The origin of the basic x-y coordinate system is taken atgrid point 1, the center of rotation. The angular velocityis 1. 264 rad/s.
- 10 -
THE JOHNS HOPKINS UNIVERSITY
APPLIED PHYSICS LABORATORYSILVER SPRING. MARYLAND
Table 2
Example Problem 1:Comparison of NASTRAN and Beam-Theory Results
Center Deflection End Slope Center Bending StressLoading (inches) (10-2 radians) (psi)
NASTRAN Beam Theory NASTRAN Beam Theory NASTRAN Beam Theory
Subcase 1 0.1333 0,1333 0.9999 1.0000 + 4 999 + 5 000
Subcase 2 0.3167 0.3333 2.5003 2.6667 ±10 001 ±10 000
- 11 -
THE JOHNS HOPKINS UNIVERSITY
APPLIED PHYSICS LABORATORYSILVER SPRING. MARYLAND
0.625 IN TYPICAL(
f-F_
(a) 80-GRID POINT - 60 ELEMENT NASTRAN IDEALIZATION
(b) 80-GRID POINT - 120 ELEMENT (80/120) IDEALIZATION USED IN REF. 15
L
~flit OX
- 12 -
15 IN-
(c) 77-GRID POINT - 128 ELEMENT (77/128) IDEALIZATION USED IN REF. 15
FIG. 2 FINITE-ELEMENT IDEALIZATIONS, EXAMPLE PROBLEM 2
THE JOHNS HOPKINS UNIVERSITYAPPLIED PHYSICS LABORATORY
SILVIER SIING. MARYLAND
The symmetry conditions are imposed by applyingsingle-point constraints that prevent y-direction motion atgrid points on the x-axis and x-direction motion at gridpoints on the y-axis.
The computer printout and CALCOMP plots for theproblem are given in Appendix B. The centrifugal inertialforces are generated by using an RFORCE bulk-data card.Nondimensionalized values of the normal stresses axx andayy, and the shear stress Ux computed by the NASTRANprogram are given in Fig. 3 by the solid curves.
An exact solution to this problem does not exist.Weiss has obtained approximate solutions to the problem bythe collocation method (Ref. 14) and the finite-elementmethod (Ref. 15). These results are also shown in Fig. 3.Two different finite-element breakups were used in Ref. 15.In one of these (Fig. 2b) 80 grid points and 120 triangularmembrane elements (80/120) were used. In this case, thegrid points were chosen to coincide with those used in theNASTRAN solution. In the other idealization shown inFig. 2c, 77 grid points and 128 elements were used (77/128).
It is seen that the NASTRAN normal stresses are inexcellent agreement with the finite-element solutions ofRef. 15, but the agreement in the shearing stresses is notas good. There is considerable scatter in the shearingstresses computed by both the 80/120 and 77/128 idealiza-tions of Ref. 15. This scatter was not present in theNASTRAN results. Although they are not shown in Fig. 3,some of the values of the shear stress computed in Ref. 15were negative for x/a = 0. 6, and although the distributionshapes are similar, the collocation results do not agreewell with either the NASTRAN results or those of Ref. 15.This is especially true of the shear stress. The reasonsfor the lack of agreement are not apparent and the correctsolution is an open question. It appears, however, thatthe shear-stress calculations are very sensitive to theidealization.
- 13 -
02 0.4 0.6 0.8
xla
FIG. 3 COMPARISON OF EXAMPLE PROBLEM 2REFS. 14 AND 15
RESULTS WITH RESULTS GIVEN IN
- 14 -
THE JOHNS HOPKINS UNIVERSITY
APPLIED PHYSICS LABORATORYSILVER SPRING. MARYLAND
1.8
1.6
1.4
1.2
1.0
0.8
N,
C'
c:
C',
n-
-Jcu
zC,
0z
O
z
z
0.6
0.4
0.2
00 1.0
THE JOHNS HOPKINS UNIVERSITY
APPLIED PHYSICS LABORATORYSlLVER SPRING. MARYLAND
EXAMPLE PROBLEM 3
The third example problem illustrates the applica-bility of NASTRAN to the calculation of shear-force, bend-ing-moment, bending-stress, and deflection distributionsof a missile body under the combined action of aerodynamic,gravitational, and inertial loads. To reduce data preparation,the simplified model (Fig. 4), which has constant cross-sec-tional properties and a uniform weight per unit length, wasused to represent the missile. The NASTRAN program,of course, can handle the cross-sectional and weight dis-tributions of an actual missile with no difficulty.
The finite-element idealization of the body by beam(BAR) elements is shown in Fig. 5. The computer print-out and CALCOMP plots for the problems are given inAppendix C. Since the missile is a free body, it is neces-sary to use a SUPORT card in the bulk-data deck. Dis-placements are computed for a free-body support at gridpoint 6. The modulus of elasticity is made temperaturedependent by the use of MAT 1, MATT 1, TABLEM 1, andTEMPD cards. The aerodynamic forces, gravitationalforces, and inertial forces are applied by using FORCE,GRAV, and SUPORT cards, respectively.
The NASTRAN results for shear, bending moment,and total deflection are given in Figs. 6 through 8. Tocheck these results the shear, bending moment, and bend-ing deformations were computed by numerical integrationof the beam equations
dVP dx' (1)
dMV = (2)dx
and
d2Wb Mb M (3)
dx 2 E1
- 15-
THE JOHNS HOPKINS UNIVERSITY
APPLIED PHYSICS LABORATORYSILVER SPRING. MARYLAND
CROSS-SECTIONAL PROPERTIES: I = 100 IN4 , A = 4.4 IN 2
MATERIAL: STEEL, w= 0.3 LB/IN 3
NONSTRUCTURAL WEIGHT 8.68 LB/IN
FIG. 4 EXAMPLE PROBLEM 3
y
20 INTYPICAL
O GRID POINT NUMBERS( ) ELEMENT NUMBERS
FIG. 5 FINITE-ELEMENT BREAKUP, EXAMPLE PROBLEM 3
- 16 -
THE JOHNS HOPKINS UNIVERSITYAPPLIED PHYSICS LABORATORY
SILVER SPRING. MARYLAND
:
U,-i-
FIG. 6 SHEAR vs. BODY STATION, EXAMPLE PROBLEM 3
-12
-oC
1-zUJw
02
-8
-4
040 80 120 160 200
BODY STATION (inches)
FIG. 7 BENDING MOMENT vs. BODY STATION, EXAMPLE PROBLEM 3
- 17 -
40 80 120 160
BODY STATION (inches)
FIG. 8 DEFLECTION vs. BODY STATION, EXAMPLE PROBLEM 3
- 18 -
THE JOHNS HOPKINS UNIVERSITY
APPLIED PHYSICS LABORATORYSILVER SPRING. MARYLAND
-1.2
* -0.8UJ= -0,8C
z0
C-LUw
U-
-0.4
00 200
V = shear force (lb),
p = distributed load (lb/in),
M = bending moment (in-lb),
EI
Wb
bending rigidity (lb-in2),
bending deformation (in),
Shear deformations w were determined from a numericalintegration of the equation
dws
dxV
GKA '
where
G = shear modulus of elasticity (psi),
K = cross-sectional area factor for shear,(nondimensional),
and
A = cross-sectional area (in2 ).
(4)
The total deformation w was then computed from
W = Wb + w.bS (5)
Deformations were computed relative to a fictitious sup-port at grid point 6 as assumed in the NASTRAN computa-tion. The results of the laborious hand calculations usingEqs. 1 through 5 are also plotted in Figs. 6 through 8. Itis seen that the agreement in the two methods is very good.
- 19 -
THE JOHNS HOPKINS UNIVERSITY
APPLIED PHYSICS LABORATORY
SILV-R SPRING. MARYLAND
where
and
THE JOHNS HOPKINS UNIVERSITY
APPLIED PHYSICS LABORATORYSILVER SPRING. MARYLAND
EXAMPLE PROBLEM 4
Example problem 4 was chosen to illustrate the ap-plication of NASTRAN to thermal stress problems and,further, to demonstrate the method for computing thermalbuckling. The structure is a square, simply-supportedplate having uniform thickness. The geometry of the plateand the coordinate system are shown in Fig. 9. The plateis subjected to a temperature change T(x, y) that is sym-metric about both the x and y axes.
If the magnitude of the temperature change is greatenough, the thermal stresses induced in the plane of theplate will cause the plate to buckle. The mode shape ofthe buckle will be symmetric about the x and y axes.As a result of the above-noted symmetries, it is onlynecessary to model one quadrant of the plate if single-pointconstraints are used to prevent unsymmetrical deforma-tions along the x and y axes.
The idealization using quadrilateral plate (QUAD2)elements is shown in Fig. 10. This figure also shows thetemperature change at each of the grid points in terms ofT1, the temperature change at grid point 1. As shown,there is no temperature change at points on the simply-supported edges of the plate.
Difficulty was encountered in running the exampleproblem. The NASTRAN Demonstration Problem 5-1printout, run with NASTRAN Level 8. 1. 0, was used as aguide for preparation of the case control deck. In theLevel 8. 1. 0 printout the load card appears before Subcase1 (the statics solution). However, when the problem wasrun in this manner, there was a fatal-error message whichindicated that Subcase 2 (the buckling solution) containedboth a static load and a real eigenvalue method selection,and that one or the other must be removed. A check ofthe Level 12. 0 User's Manual (Ref. 4) indicated that theload (in this case TEMPERATURE(LOAD)) card must ap-pear in Subcase 1 rather than above the subcase level.
- 20 -
THE JOHNS HOPKINS UNIVERSITY
APPLIED PHYSICS LABORATORYSILVER SPRING. MARYLAND
E = 10 7 PSIv = 0.3a = 10 x 10-6 IN/IN OF
~I 4 4IN
I 1
~ -4 IN.- 4 IN -|1
'I _ i ~
0.1 IN
FIG. 9 EXAMPLE PROBLEM 4
OGRID POINTNUMBERS
() ELEMENTNUMBERS
FIG. 10 NASTRAN IDEALIZATION AND TEMPERATURE DISTRIBUTION, EXAMPLEPROBLEM 4
- 21 -
Y
SIMPLY-SUPPORTEDEDGES
THE JOHNS HOPKINS UNIVERSITY
APPLIED PHYSICS LABORATORYSILVER SPRING. MARYLAND
This change was made and the example problem wasrerun. The results contained only a static solution fol-lowed by "SYSTEM FATAL MESSAGE, 3001 ATTEMPT TOOPEN DATA SET **** IN SUBROUTINE DS1A, WHICH WASNOT DEFINED IN FIST." Since the cause appeared to be aNASTRAN program error, the difficulty was reported tothe NASTRAN System Management Office and NSRDC.Program corrections were made by NSRDC personnel whoreran the problem, using both the inverse and determinantmethods of eigenvalue extraction. The results of the twomethods did not agree. The NASA Goddard Space FlightCenter had experienced difficulty with the determinanteigenvalue method and had made corrections in their pro-gram for the IBM 360-95 computer. The problem was runat Goddard Space Flight Center and identical results wereobtained by both the inverse and determinant methods.NSRDC then made the necessary corrections to the programon the APL computer.
The NASTRAN results given in Figs. 11 to 13 andAppendix D were obtained after the corrections noted abovewere made. The problem was also solved by the finite-differences method. This method was first used to deter-mine the in-plane thermal stresses by obtaining an approxi-mate solution to the differential equation
V4 F = - EtV 2 T, (6)
subject to the boundary conditions F = aF/an = 0 alongthe boundary of the plate (Ref. 16), where F is the stressfunction defined by the equations
1 a2 F 1 2F 1 a2Fxx t 2 yy = and - . (7)xx t a2 2 xy t axay(ayxy t
The finite-difference mesh that was used in the solution isshown in Fig. 14. The normal stress axx and ayy deter-mined by the NASTRAN program and the finite-difference
- 22 -
THE JOHNS HOPKINS UNIVERSITY
APPLIED PHYSICS LABORATORYSILVER SPRING. MARYLAND
La.
-
tX
xx
FIG. 11 DISTRIBUTION OF PREBUCKLING THERMAL STRESSES ax, EXAMPLEPROBLEM 4
- 23 -
y (inches)
FIG. 12 DISTRIBUTION OF PREBUCKLING THERMAL STRESS yy EXAMPLEPROBLEM 4
- 24 -
THE JOHNS HOPKINS UNIVERSITY
APPLIED PHYSICS LABORATORYSILVER SPRING. MARYLAND
40
-
I-
oO.~·
5.0
THE JOHNS HOPKINS UNIVERSITY
APPLIED PHYSICS LABORATORYSILVER SPRING. MARYLAND
1.0 1
0.8
0,o
-
Z 0.6 E==
X.
I
O 0.4
Z
u.i
0.2
0
x (inches)
FIG. 13 THERMAL BUCKLING MODE SHAPE, EXAMPLE PROBLEM 4
- 25 -
SYM.-- _ _ -, X
FIG. 14 FINITE DIFFERENCE MESH AND TEMPERATURE DISTRIBUTION, EXAMPLEPROBLEM 4
- 26 -
THE JOHNS HOPKINS UNIVERSITY
APPLIED PHYSICS LABORATORYSILVER SPRING. MARYLAND
fySYM
I
4-
THE JOHNS HOPKINS UNIVERSITY
APPLIED PHYSICS LABORATORYSILVER SPRING. MARYLAND
method are compared-in Figs. 11 and 12. It is seen that,while the stress distributions computed by these twomethods are similar, the stresses computed by the finite-difference method are larger than those calculated byNASTRAN. It is not possible to say which method is moreaccurate as the grids that were used in both methodsare too coarse to expect accurate solutions. Whilethe grid that was used for the NASTRAN results istwice as fine as that used in the finite-difference solution,the NASTRAN program assumes that the temperaturewithin each quadrilateral, element is constant and equal tothe average of the temperatures at the grid points of theelement. As a result, a zero temperature change on theboundary is not attained. It is expected that this would re-duce the stresses computed by NASTRAN.
The finite-difference method was also used to solvefor the eigenvalue X and the mode shape w(x, y) of thedifferential equation
2F 2 a2F a 2 2F 2F w = 2 -2 + (8)
D 2 2 a x a y E _X-5-y 2 2V Da 22axa.y xay a ay
subject to the boundary conditions w = a2 w/an2 = 0 on theboundary (Ref. 16). In this equation X is a constant whichspecifies the magnitude of the temperature change accord-ing to the equation
T(x, y) = XT (x, y), (9)
where To(x, y) gives the spacial variation of the tempera-ture change normalized so that To(O, 0) = 1. The functionF o is related to F by
F(x, y) = XF (x, y). (10)0
- 27 -
THE JOHNS HOPKINS UNIVERSITY
APPLIED PHYSICS LABORATORYSILVER SPRING. MARYLAND
Physically, X is the temperature at the point (0, 0) at whichthermal buckling of the plate occurs when it is subjected tothe temperature change T(x,y) = XTo(x,y).
The NASTRAN solution predicts that buckling willoccur when the temperature change at the point (0, 0)reaches 314. 7°F, while the finite-difference solution indi-cates that buckling will occur when the temperature changereaches 168. 8°F. As expected, the finite-difference methodpredicts a lower buckling temperature because it predictsgreater thermal stresses per degree of temperature change.The buckling mode shapes predicted by the two methods areshown in Fig. 13. It is seen that the agreement in the modeshapes is excellent.
- 28 -
THE JOHNS HOPKINS UNIVERSITY
APPLIED PHYSICS LABORATORYSILVER SPRING. MARYLAND
3. DISCUSSION
The example problems demonstate only a few of themany capabilities of the NASTRAN program. Considerableeffort has gone into providing user convenience in the pro-gram. Once familiarity with a rigid format is gained, datapreparation is relatively simple and no programming skillsare required. The price of these user convenience featuresis, of course, increased computer run times. In largeproblems with many elements, bulk data preparation islaborious as there are no provisions for the automated gen-eration of grid point or element data.
Only the structural plot capabilities of the programwere used in the example problems. The case controlcards for these plots were found to be simple to prepare,since the program determines the appropriate scale, origin,and vantage point to be used for the plot. The x-y plot capa-bility extends the usefulness of the program; however, thereis no provision for stress-contour plots in two-dimensionalbodies such as those described in Ref. 17.
While the documentation is complete in the sensethat it provides a useful reference for those familiar with theprogram, it leaves something to be desired in aiding the newuser. A tutorial manual would be very helpful. The situa-tion for the new user is further aggravated by the lack of anindex for the NASTRAN manuals.
While the NASTRAN element library is extensive,there are programs with more and improved types of ele-ments. Fully compatible plate elements, consistent massand force matrices for all elements, and elements withvariable section properties and temperatures would allowadequate modeling with fewer elements.
- 29 -
THE JOHNS HOPKINS UNIVERSITY
APPLIED PHYSICS LABORATORYSILVER SPRING. MARYLAND
The inadequacies of the program that have beenpointed out have been noted by others and are well known toNASA. While these inadequacies are more than compen-sated for by the capability and convenience of the program,many of them are expected to be removed in later levels ofthe program. All indications are that the program will be-come more general, convenient, and accurate, while re-quiring less computer time. Use of the program is expectedto become widespread both in government and industry.Under these circumstances it appears advisable for APL/JHU to constantly maintain its NASTRAN capability at thelatest current level of release.
- 30 -
THE JOHNS HOPKINS UNIVERSITY
APPLIED PHYSICS LABORATORYSILVER SPRING. MARYLAND
ACKNOWLEDGMENT
The author is indebted to Messrs. James McKeeand Myles Hurwitz of NSRDC and to Mr. William Case andDr. James Mason of the NASA Goddard Space Flight Cen-ter for their assistance when troubles were encounteredin running the example problems described in this report.
- 31 -
PRECEDING PAGE BLANK NOT FTL,I TDTHE JOHNS HOPKINS UNIVERSITY
APPLIED PHYSICS LABORATORYSILVER SPRING. MAMYLAND
REFERENCES
1. J. H. Argyris and S. Kelsey, Energy Theoremsand Structural Analysis, Butterworth and Co. Ltd.,London, 1960.
2. M. J. Turner, R. W. Clough, H. C. Martin, andL. J. Topp, "Stiffness and Deflection Analysis ofComplex Structures, " J. Aeron. Sci., Vol. 23,No. 9, September 1956, pp. 805-824.
3. R. H. MacNeal (Ed.), The NASTRAN TheoreticalManual, NASA SP-221, National Aeronautics andSpace Administration, Washington, D. C., Octo-ber 1969.
4. C. W. McCormick (Ed.) The NASTRAN User'sManual, NASA SP-222, National Aeronautics andSpace Administration, Washington, D. C., Octo-ber 1969.
5. F. J. Douglas (Ed.), The NASTRAN Programmer'sManual, NASA SP-223, National Aeronautics andSpace Administration, Washington, D. C., Octo-ber, 1969.
6. NASTRAN Demonstration Problem Manual, NASASP-224, National Aeronautics and Space Adminis-tration, Washington, D. C., October 1969.
7. C. W. McCormick, NASTRAN Beginner's Guide,MS 139-1, MacNeal-Schwendler Corp., LosAngeles, May 10, 1971.
8. T. C. Butler and D. Michel, NASTRAN, A Summaryof the Function and Capabilities of the NASA Struc-tural Analysis Computer System, NASA SP-260,National Aeronautics and Space Administration,Washington, D. C., 1971.
- 33 -
THE JOHNS HOP'KINS UNIVERSITY
APPLIED PHYSICS LABORATORYSILVER SPRING. MARYLAND
9. E. Cuthill, et al., NASTRAN Evaluation Report,NSRDC Technical Note AML-49-70, Naval Ship Re-search and Development Center, Washington, D. C.,August 1970.
10. Proceedings of the Second Navv-NASTRAN Col-loquium, Naval Ship Research and DevelopmentCenter, Washington, D. C., December 1970.
11. NASTRAN: User's Experiences, NASA TM X-2378,National Aeronautics and Space Administration,Washington, D. C., September 13, 1971.
12. Navy Structures Computer Program NEWSLETTER,Vol. 1, No. 2, May 1970. (Pub. by Naval Ship Re-search and Development Center, Washington, D. C. ).
13. R. J. Roark, Formulas for Stress and Strain, 4thed., McGraw-Hill Book Co., New York, 1962.
14. R. O. Weiss, Elastic Analysis of a Rotating Aniso-tropic Bar Using the Method of Collocation, APL/JHU BFR-71-3, March 2, 1971.
15. R. O. Weiss, Analysis of Anistropic Flywheels byFinite Elements, APL/JHU BFR-71-09, September1, 1971.
16. R. M. Rivello, Theory and Analysis of FlightStructures, McGraw-Hill Book Co., New York,1969.
17. G. Dailey, A Computer Program to Plot ContourMaps of Stresses in Two-Dimensional StructuresAnalyzed by the Method of Finite Elements, APL/JHU TG 1128, July 1970.
- 34 -
THE JOHNS HOPKINS UNIVERSITY
APPLIED PHYSICS LABORATORYSILVER SPRING. MARYLAND
APPENDIX A
Example 1- Simply-Supported Beam
A-1
pN
G
PAGE BtL
At
NOT FrMm
TH
E
JO
HN
S
HO
PK
INS
U
NIV
ER
SIT
Y
AP
PL
IED
PH
YS
ICS
L
AB
OR
AT
OR
YSILV
ER
SPRING. M
ARYLAND
_. N
LU
C~
~~
~~
~~
~~
~~
~~
~
LU
.4
I- 4-
.0
W
0LN
4X
'
Da~
~~
~~
~~
tL
~~awU
LU
UU
WO
c
0.0
D
.
QV
uj
Z
-- a
W u
J.WO
c~
~~
~~
~~
~~
~~
~
c CO
cU
W
.J {
" a
O
C
' J
U
JU
W LU
0 )
uJ
O
CL .
..
0o ~
C
LU 0
lu
GU
°
W
C
WC
W-
CW
. Z
.
Z
Z
Z
>
X
u O
Z
4
s:
a 4
44
o C W
L
7 e
I W
U
U
O
,W
<
<
I W
U
J
_ O
-
X
<.
Z
t -
W
W[
a 7
-_
O
0 t C
-C
C
ua
L
a
ai U
a
u7 t
:7 *
`- u7
0J
C; IL
Z
W
J 1
--J
t .
W
CB
. W
4
-. X
U
n
.- -
I-- m
W
1 0
-4
0 W
1U
W
0 J
~~0 7~W
-- 0
t 0
-4
444t
U
LL
. 4
..
U
.
~U ~
~ ~
~
r -O
D
0 4
O
O
-JJW
DE .l
0 .
Zu
Aa
l: '
-
avZ
LU
Z-
u
O
-a Il
v w
0
.- 4
n C
0
o w
u
LU 4
_ U
) D
z
NU
Z
r
U-
U
--
--
_ -
N
N
N
00
0
Z
Z
l Z
U
S
4-L
LL
j U
4
U
0 0
00
0
U
0. 4
-/ LU
Wu
1
N
4_
V
L)U
0
i
D_ -J 1
Z
a 0
0 tL
O
_ Z
L
A
_-
0lU
U
U
U
4
. 4
-..0----
' 0A
A
-3
7 J-
..J0
Z
w~
~n~
4u
TH
E J
OH
NS
H
OP
KIN
S
UN
IVE
RS
ITY
AP
PL
IED
P
HY
SIC
S
LA
BO
RA
TO
RY
SILVEIR SPRING.
MA
RY
LAN
D
0
0u
n .
.rr~
0o
40 4
-J
co08.O0
000U
N
IN
I0,0
000 0
O
0 *
00000
-† .
..
._N
*O
L-
0 in
.0
00000
_ .0
.N.t
..
..
.O
-t4N
~O
40
00
0
J U
4..
-000.
0 O
O
O
.. *O
N
.-NO ft
-''
-I
-
0
·0
._
_ _
O
_
c* -N -N
-
-N
-
..4 ~ ~
~ ~4
F ~~C.
_u
I: U
4
4c 00
8
51 tc
tt'
tC O' tr tY040t
f N
8.
Z.0
U!
U O
L
IL
In I5
In In
In t7
(N
IT r.
D_
~
In
I- * *
tt *
* *
* 4
* *
* *
* *
* *
* 4*
O
Z
_ N
0f a t
4 It
00 a. tt
.- N
0
.U
0
1t?
40U
i
A-4
w4a.N
0Oa.
C',t,NwIlmI-
'lw
U.
0O70
0
4I- C0LI
2, C
L
UJ-
IDO
-
uO4:
GZ
aleuOn, _
N
TH
E
JOH
NS
HO
PK
INS
U
NIV
ER
SIT
Y
AP
PL
IED
PH
YS
ICS
LA
BO
RA
TO
RY
SILV
ER
S
PR
ING
. M
AR
YLA
ND
U.
4a
zV,
-4vl
_. aM
)
IJ U,
LD a 0
M
U7
U
I .
r D
,
w
x
n o
o LU
07-
J L
, L~
Wu
a
C-4a. 'A
a. -
1:
1-
,,W-.
VI
_ 1-
Z
.
in
7 a.
-I- -
0
_ W
a.
a. In
W
r
(C -
->
Y4
N
Y
IC
>
-W
-
a. 4
I a.
M
-4 4
cccD
u.L D
1
U
(C U
a.
(o
a.
-N
'4
U
) .0
F W
(I
O
--
-
2 ZYCIA
O
0'-4
a W
-L-
D.
V) Z
7>L)
LL u
iLL
O
.)IA
OLL
o1 -
V)-
* -a
.
* a.Z
Li
t,
W
..
V)
Lli
CL
1-
U-
tLI
a. .U
aP
r Z
L
}
In
>
1A
)
W
_ U
J
Z
,-- V
->
Z
IJ
-.LU
L
I- C
I W
M
0.
UJ
-4 -4
F. W
Sa.
IL _L
-4 Va
5~ 14
aL a.
ts-
a *
a.
an _
r rs
>
a. *
IL 7
D. J
4 7
-4 c
1
a. U
. -,
a .-
I- >
I-
.I-
-4 .
-4 -
Ia.
-D.
a. a O
Z
--
4
a. >
7 W
U
In
W
C
1>
Z
04
0 -J
In U
L
.
N
Ii UD
.
NUZL D
Z
O
4
acrV
I I
>
i-
-a.
> (
--4CTC
N_ >
* 4
I 07Z
a.19Z
r ;
;W
Q
s
V)
7
UL
N
rD
r a
r o
YC
0 i V
C
Z
h X
IA
LU 0
1- -
n 7
a. .
L4
4 7
a. _-
, >
p -
-3
0
-, tL
a
e Z
-4.
c
>u I
4 a
In a.
(CIA
.
:Ic
V)
(C1
D
JW
'I.-
Lu
uj
1 Q
co
n >
IY
.Y
-4 a
4 4
D
I-
4 ( C
n
a .a .
L
9- (
-I
N
c C
--
-1 N
N
N
N
N
A-5
0·NaWNZL
i
--,I- a.Lia.z,I1.
a.
.I C
-J U
J7
-J 07
.4 L
D
.-a0U4aC3
a.znZ<OI.- 04 :
4zU
0Z
Uaz40
V)
-4MLIn wa-InVIc-4 Z441-,,l8z
iuYID.
0aC0
C I O
COT'
Z
(C-4
4'-
Z
'
TH
E
JOH
NS
HO
PK
INS
U
NIV
CR
SIT
Y
AP
PL
IED
P
HY
SIC
S L
AB
OR
AT
OR
YS
ILVE
R
SP
RIN
G.
MA
RY
LA
ND
U.U_
CD
O
OI
O
.Z
7
m
CU
r 3
7 -
VI
.a ,
LD
O
U
U
--
-LU
' CL
O
a
4- z
-"4C
7 7
_ D
0 G
' Y
C
-
a7
a -
7 4
-0
O
T
0 S
TU
a-
U
LU IA
-
C.
LD
z
Z
4 >
Y
O
r 4
IUI
In IA
UI
.13 a
I C
0
-N
M
4
IrN
N
N
CN
1 ) m
V)
43za0(.3LD
0 Z IA
c l
0 m
CD
CID
w
ED
aC 7C,
a4L)7 0-5Q. aLD
0
C.
0aOf
4U
'AW -47LD
zV "4
IY 10
_, X -5 L
D
-Y
-4
Lb
-i IA
°o
0 EL
" ,
O
0 m
U
4
4 C
yU
U
LI
V
0 O 1J
I0 I-
g 0
0 -
NE
n
In
Mt
1m
4 ,i
4
aIA0.JV-
zC
0 s
Z
XVI
L O
IA
L
L)
V
V)
M
I u4
.o r-
C
A-6
rI-UaUI
z.3UW
tZ.-J
0 z
ujIU
EULWZ
EL
-V
IZ
i E
n
t a
_ -
WN
70<r4-JaCd
xCU!
2:oZ
r
w 4aZIC
L
('IUa0 27crC
UI-14Ia
I7
I- - 447zI
a407ZC
aZ0zzZL Z
02
z z0 i
uJ
:
U
C
C_ Z
; Z
V)
_
O
Z
Z
Z
_~
ID.4100orr.
CL aaIn a
aCm
I
-
"40
74L.)24
i
4-
4-
UI
_J
44
-
Utj
Ci 0tZ
.
X"4
4V
W
. >
C
Z.4
4
41
V)
CL
L)
IA
TH
E JO
HN
S
HO
PK
INS
U
NIV
ER
mIT
Y
AP
PL
IED
PH
YS
ICS
L
AB
OR
AT
OR
YS
ILVE
II P
*IIN.
MA
RY
LA
ND
41
br.
L.
Lb Ir
cc
C[
4 c
o0L
) M
w4 0
o_q U
W_
C
2 Z
Z
rZ0
U.
_ C
%
_L
114*u .U
z
ICS
LU
-
J Y
cm
U, 1
72;Z'
O Z
Z
a. C
!
U
C-
004
o.
Z
J .
u V
N
., L.
o L
bZ
w~
n
-a-.
-.0
r -20N
z V
wrz
a
tD
I¢<
' .
4 aK
4
*N
1-
-4 %
-J
07I2
.J
S -
LU 4
L"
do
af
09 IC
I
4'IM aLb
0
4 &o
-0
Z
Z
0.0 a
0 .
zW
U
Ua
I-
UJ M
Y
Z
C
Z.C
3 X
LU Z
a-
a -
KL
b
0 ).
F
u
n ua
r, .
Ke
_ a
Z
Y e
U
L U
Lb
a a
.r
K
uj
4 0
4 in
a
0 0
N
M
.n
C
I-.
u%
tA
W% U%
in
VN rN
L-LinCCC a00
D
..
Z
ato
Y
i Y
O
a
W
U
4WC,
a-41-J,
-J 0
w
U.
a
.4
J J
-J
Lb
0z04V0
4aau
4 4
,U
Lb
.0
-J
J LU
427vube.L
bLbrb
e W
4 -U
,
L
0
U)
-LL
4 . eY
Y4
NZ
.4
2 U
2 m
7
Ube
-J
b
b
.J
Z
Z
.>
Z
0 s
W
W
U
0 -
N
a, (
-a
U
a 0 L
A
2 U W
U
be y
0 b e
u a
o 4
4 0
Lb 2J
Lb 2,
* 0
Lb b
0 U
,.4
b LbK
b
L L
D
Mo 0 o
-N
M
4
IA
4 ?
w
e
O
0 -
NIn
U
0
.4
4 4
4 4
4 4
4 I
r
A-7
TH
E
JO
HN
S
HO
PK
INS
U
NIV
ER
SIT
Y
AP
PL
IED
P
HY
SIC
S
LA
BO
RA
TO
RY
SIL
VIR
S
PR
ING
. M
AR
YLA
ND
.LCaa
CCtC44
a r!
F> F
C
a
J U
4
U-
Y U
.-
.In
-
C0o C3
C;
c4C3
0'are-J
a C
9-3 -J
M
Ce
Y4
a j W
<
-'A
z
Y-
Yo
-
-. 4a
*J *J
uwco
.4
-1
Mo t
-1 le
if -j
75
uD
<
z a
VZ
m
Y
Y
*
acea Y1tC -J~1Ce
-j
1- 1-
.,
--
> Z
Z
-
Z
-Z
w
-D
0
-_I
D
-M
D
O
O
to
C
y Z
Q
. le
M
M
Y
Z
w
Ye
4 a
s o
r F <
n
0o M
M
19- L.
LI) to
Li
-.1
w
Li
L M
Li
M
t l
t 0
-r-
r- r-
r I
I -
co co
Co CD
to CD
0 D
ara
a Y
-1 a
*J ,
J *
to
*. *
I- -
U
Y
-. .*
-a-.1
~v I
In
*J .j
co
*J-J
ic n
-i -.1
2C1UULI
a_o
0-C-J,
ICL) 7
It-.U-
.. I-.
-L
Oc
* ¢n,
1-C07
a c.
a
1- -1-
-J
N
Z
0 Z
Z
>
jw 1
D.
O
1 a
w
-a
-o
r z
r .i
e 0
1 e
-50
O
U
U
M
VW
D
0 0 _
N
Uo 0
Pan
a M 0
oa o, a
oa
o
A-8
z.-Clo.C4
c n a
7 IC
.
Z 0
0 0t
FC9-
aLt ra12
7i -.
_y J
LI_
U
C
XC
U
Cz W
L C
4- <
OZ
C
)
Z
V:
Ce
Li U
.V
:LI
U
7 Ym
1
W.
.h
-J
.LY
3
I-~
O
Z
-Z
V
N
..~
Y
'
20
-Y
K
-C
e0
Li
Z
U
t) L
I
THE
JO
HN
S H
OP
KIN
S
UN
IVE
RS
ITYA
PP
LIE
D
PH
YS
ICS
LA
BO
RA
TO
RY
SILV
ER
SPRIN*
.M
AIY
LA
ND
Ua.
C3c
a.
z
2- -faD
o
Z4 C
0 a
Ul
-a.
a D
* L
eZ
v
z0
Z
4C
-0
.£_
C
o
Zfl
w ~
~
-K 05-0a:O
ti a a'
I J
Vl
aa.
I 0
a.U
0
a,0
f"
I
a -
a'
O
0
I.,*L O
K
g
0 0
* U.
* a.
Y
0 I n
,Z
K
a.
* J
o ,
0 0
OW
A4 _
1- a.
-*
Ja I
0 0
e ,,
Z
Z
J
I O
I
I 4
InLI
I In
L
I .J
In
C
a'
0 _~
N
,1,
_ _
-_
a0a0
J o
Z
Z
2 2
U
U
M.
-_
ae J
0_0
0-J
I LU
I- 1-
a'
LU L
Iln In
C D
0*aJ'-~
(I
-
1- a'
ccZ
G.
G,
o -
o-
U
U1 z
3
azIna.l.
ItInU.IJa C A
0Jnl L
)
0-4
ID
0
aO t .4
0 0
UJ u
cm a.i- ,4
Z.
O
KU
. In
.0
0
I... L
LU
.. >
r
Ilu
XL
.
, .
C2
I,--
ZO
LIJL
WOa.
0 )J-
.-U
l>IV
n
* L.
O
I If2
J
0 K
&
. *
_ N
a *
1Z
O
Z
a
1- 1-
t..
rK
,,In-
.j ji
LU
-
a N
U
0
.- K
uJ
.U
c a
K
K
ao a.
>
z 0
I- r K
4
0 I
M
0 U
4
0 -
a:
4 M
4
J VI
U
0 O
II
Un
0 n
a.
a. -J
+
n .0
PF C
a
.O
I 0
P.
CD a'
0 -
N
fI z
A-9
TH
E J
OH
NI
HO
PK
INS
U
NIV
ER
SIT
Y
AP
PL
IED
P
HY
SIC
S
LA
BO
RA
TO
RY
SILV
ER
U
PR
lNO
. M
AR
YL
AN
D
LU
WI-,4a 0.
I%.r-a 31Ul
vpl
W'A
z0-J D.o
"Ji.-U
u
-1.VI
- ok a
r n
-I0.
C)
0
Z
4£2a
I I-
C
c
-- IC
I
-. -I
.,
Q.
___U
bU
A-1
0
I)0DC
I.4a 0,,IW
0IU3
oa0*
aU a uL.
.0.Z
U,
.w
_tJ
Z24
2 4
W
m
m-
*)
,el
-J4N
TH
I JO
HN
S
HO
PK
INS
U
NIV
RS
mlT
Y
AP
PL
IED
P
HY
SIC
S
LA
BO
RA
TO
RY
*ILVW
M
SPO
ING
. M
AR
YI"D
I,11V'LiX
V V1
ww
-
,4
2 CzD.L
o O U
.A.o IL
c
Y
U3 I
UJ
4
IL
U
-4
I _
UJ
W
Z
Z
U
WL
0L
i Z
2 2
L
a.
LU
-J
N4
t
C
_ N
-.
N
I
ILl
p.N
Li
7 WC -*1=
c
m
p.
4-w
ar
r)) UA
C
C
nC
o
uV
Z
N
Li
&,L
(Ca.0'Li
U 7w6U'A
LUI-JC0IILLi
17
4WoI.I-
Dju.J
C
CUVC
Z
LV)
VluU. CI
UZ' C
,i-
-$ I0C-
U. IUJ
CC
0 A.
A-11
TH
E
JO
HN
S
HO
IPK
INS
U
NIV
EIS
ITY
AP
PL
IED
PH
YS
ICS
L
AB
OR
AT
OR
YSILVlEtR
SP
RIN
. M
ARYLAN
D
uI(14WL77^ w 0^U. Wu.17uJ
"ImrUi 4 I- 00.UI
LuL7:
U7
U
L--
wUU.
Lu
2n0-Ja.
,0
o 0
L
C,
C) >
)
o4 (`j4
r
4
0 0
2: 2t
UJ
U
I) fJ
o o
IA
x 'A
N
7 w
L
'7 L
j Lu
* ..
*m
u7U
U.1
0U U
. (U
7IA
2:
at Ic
97 9a
Lu uj
uj
2r
* r.
IA
o0
ar
r r
r
o *
o o
U.
U.
U
L2
v7
n Y
7 )
o o
O
CI
IVS
IV I.
I. _u
--
_ LU
UJ
I w
I
, r
Lu
W
U
1
C)0
'
C) C
rn ~ ~ ~
uj u
J
uF
~~
~~
~~
u
o 9
N
4 4
JF 0'
N
2. 2.
A
_ U)
C. 'A
.L 0
' 2:
sIt
a' N
0 J
0 '
4 uJ ~
uj
4 U*
,IEU
\ A
' U'
A'
L1 L7
1- t-
A'. I
11 I
A' I
O) C
LU.
LU
Lu U
J U
. U
lU
l W
c
4 L
IA
IA
IA IA
IA
IA
UJ
LU
LUW L
u LU
7 2
J7
U
U7
U
7
7 U
U
l U
l
r zv
r z
r o 2
o Z
Z
) -
) -
--
_ U
7 -
U7
_ V
7 F
I.
4 Lu
4 Lu
4 Lu
2: 2r:
r r
K
L;
_ A
' N
A
' A
' O
O
o o
U.
LU.U
. U
. U
. 2
ZZ
Z
Z
-
_
_ _
_ C
a
* A
' *
A'
* A
' *
**
0 *
O
* O
*
*U
. *
U.
* U
*
*
A-12
LU U
.'A
V
)tA
IA
4 4
..
o C
z 2
_ _
UJ
.A-
* #
Lu LU
4 4
C
C7
O
Lr
r,a*,
C) ,
ro
2.J
*n W
'
LI*
-C
_
TH
E
JOA
4NU
H
OP
KIN
S
UN
IVE
RS
ITY
AP
PL
IED
P
HY
SIC
S LA
BO
RA
TO
RY
SILV
6I S
PR
ING
. M
AR
uYA
N
MUccU
,Li
.U 2ujtU-J
0-a aaLU
L-C,
a'Vl
.tCL
0I--
),. aLUUJ
0z
0000
I 0 II U
O. N
C
N
PD
0 O I
n 0
CY
L00000
eC
;: e
OO
C
00
00
0III
N
Z
0'LU
0'r0
O
0s a'
"'. K
. 0'
P. en
la
gC a
OI
0 I
I
o0 O
N
O
0' 0O
IC
0' 0'
0: 0cr
C0' a,
0' a
0 4 0oCaaa
a' a
, m
0
&
tt r-- 0
I- a,
Na C
00000
N
N
M
N
N00000
1 1
I I
I11111-
a
a -
C--
W, IN
O
N
P0
0-I0
0m*
I. a.-
Um 0
lf\ a.
in
I
N.-"-
-N
jI
I
NlyLUm
V
)_
<UC0U,
Lv0CL
4a'O00t2uja'uLui Ka'L
UU
,
ot
Cc
0O
0uJU
CO
000
00000
C
0 0
0
aemU cI- ujZL
LLI0V
I
C
N
0_
C
LU
LD
c-
40
UJo
attlul
v0 4
CC
O
)
00000O
O
0 f-u LiLU
L-zuKww LUaU,
I .J
N
-N
000
0 _
0
LU LU
LU
co C
Oo
m_ 1
10m
O
11, _!
IW' O
P .
0 C'O
P.'C
00'
"I0'
--
-000
tD
0 O
N
" ln
-1
NO
NV
I 0
0 N
_
N
0.
...
NO
O
N
tV4
C
oooo
C, O 0
0
xer 0a
YZ 0
LU -U.
aC
LI
Z U'-J
a'-
4L
U
00000
... ..~9
n0
0i 0
j
UO _
N C
(b
UE
j
0;
-N
P, .t
In
0a. ul_100l
5:
UU
0Ur
CL
ta
U, !o.
aE
I ILi
.2-l
4 I-4
.U
2LI
04C)
0C a'UJ
a- u,go rZ
UU
I.-O;
_ N
m
-* W
LU
I.z0a.
A-13
TH
E
JOH
NS
H
orPK
IN
UN
IVE
RS
ITY
AP
PL
IED
P
HY
SIC
S
LA
BO
RA
TO
RY
SIL
VE
R
SP
RIN
G.
MA
RY
LAN
O
Lu4U
caI--0v,
00
NLU
e in
u0'M4`
LLU(D0
ccNn
.-L
'
C
C
uI
0
04-J
74C 0IIrLI,-I-,C
u -n
c:
L
_a)
C·)Y
Z
U
_)U
cL
0-
00
ICz.40
ZC V4 L
ZV
I
uJLU
au-zU
M)0-O
q
0LOL0'0*O
M4LU
4c 0LUaQ.
i-n
a
cC
E0.
LU
OICY
ZU
-
-J
LU
L
in 4
cr-
v L
U
UC
zcn
-9
U
ulULM
L
I-zCa0.
LU,4
in
-.4
0
U-
4a
LU
-414
In
LL'
04aLU
aLU
in
a'
00o00000
I-V2
C
0r
74a
a0U01
0 C
o c.
o c
a..00o0C
n(-'
0c
zC-I-JZz
of o
0o o 00
0
0 00
00
o U
0
0 0
00
00
0
o00000
00000
00000
I- L0
_ 0
00000
00000
r. _0
0_ _
0 a00
c Z0OC-
I W'
0000000000,
.OO
000
0000
In
II
LU
U
_ -
00
_ N
NC
- n
L
U
00 C
C
00N
NV
) I
I
U
C
n
r4CDLU
DLU
C
I-O
U_
acr4eO
Ct
c0C:3 0 coccJ
CA
ULUaIn
co
0
0z-a-
LU LU
c 4.
ZiL
LUur1- zC4 04-uLU4U0
uuLUa .(0
(
O. g
-tn
09L
O0OC-
cr0
1-u
L.
A-14
TH
E
JOH
NS
HO
PK
INS
U
NIV
ER
SIT
Y
AP
PL
IED
P
HY
SIC
S L
AB
OR
AT
OR
YS
ILVE
R
SP
RA
IN.
MA
RY
LAN
D
-u
I I
U) 72
:
uI0
L)
O
Vi
N1
<)4
LiG
72
IL 4
40.
u.a eL
I- 0L
U1,A
V
-44
.I I
tL
xW
c, L
A-
D
71
NO
00I l
atO
40t N
N
Il44II
a 0
co I
to
rti
00000
s04oe.
oe0 (
N 4N '
In000000'
00'
00'
N
't
f ,
C,
N
IU
U
IU00
ONt 4
I I
II
Ce
e oe
.'N
NN°?' N
@'+
,tn
NIL-
V)
N
4LN
U)
LL
CWN
m
LU
w
C
0 O
0
o 0
n 0
L e
e 00
e eo 'C
L4
V)
It 0 04
e e
,U
U
'
o 0
0 @
0' 0
'
*4 n
*n D
_N
NI
I N
N
NG
II
II II
I
Yln in
L4~
NN
U
UI
I tDo 0ILa0
-. 0.~
~~
~-
c~
~~
~~
c
L)
00
LU
00 0.
2:V2
LA
L
O
UW
C1:
0
C
YZ
WO 4U
_ Z
c
(0.
C,
-I)C
O
2F
0. Z
L
)
7,Lu
Lt
oC9J
az IL0u LJ
Z
00
00
-w
w
WUU
U)U)U) '
o o0
0
L
0 O
0
V)
_N
N
C
V)
oo
U,
N
O
0 0 M
f t I
9- ±
-- 00
N N
N
°t
cO
O
0
00
00
L'
L 0
ui
_ N
N
't
co l
l
uJ^ 1t,
O
O
4
ILL C
-Iuw
r-0 "1
04
004
eN
NO
Nm
00
00
l W
LUW
oe oo
S.,t
tO'a
II I
00
ON
I
N
N0N
UI
WL
_ N
0n
I- L
I I
rrZZI
I
V) U)
V
44I I
aD r
rE
; J
1i £U
CUU
4
0 I-
0)DILo 0'
0
0 p
0locI
ICu
Lu
a'-O0
O0I
I
004 N
00CO.
0
't 1.
M N
C
0 00
WIL
W
W
NN
_P
-
OO
C)
C,
00
00n
.- L
. .
NN
r-.C
00
o00
EtCLP
0 0
0 0
o o
o
..
.
o 00
00
00
Lu U
w
u W
ILU
t '+
tin N
N
N
_I.
U)U
) 0
00
00
00n
O
Oo
o O
O
ca O
0 O
O
O
O
G
I I
I I I
I
GaW
0.n0.
LA
--j0.
J -r
co 4
D.0.
YZ
I
LO
4 L
io
-1
ZL
e)
() en
sm
-*
MZ
0
00
00
el 4 D
Lm N
N
N
0 00
00w
Q
0
0n o Ln
on
ftI-UI
0C-Joc-a k,I-I1
Jo0004pm
I
-- N L
m
a00Oo p.
luuLw-
Uw
00
C O
*nO
O
.. 4
.4
', -
a,
00
00
0C
00
"o on
40
04
_ N
G
ON
LUU
a,
OD
NeO
l
00OaD
O1N
00I N_-000O
0L
oON
I0000
0
A-15
0 uIo
V)
4a
w0.wr0,
ouu
0000O
t-2:h-ccz0tJ
0. 00
I-zZ0IQ.
-j
0.JZ
0 9
00JJ
-NNO
V)
IW
.LL
-N
N
a 00
U.aCLL
4-
LLCU.
I- IC0.U)
0. C
U
-
Z
LL
m0
40
-J
Z
)
CCr~Cl'JIm
cc 0cI- OLu
acczu)000
LN
TH
E JO
HN
S
HO
PK
INS
U
NIV
ER
SIT
Y
AP
PL
IED
P
HY
SIC
S
LA
BO
RA
TO
RY
SILV
ER
S
PR
ING
. M
AR
YLA
ND
1 u
I I
V)
.r
1 Z
ujUJ
N'
IAG
Z
0 Is XIIr
L 40
(1 nv
-O'
0'NI,'.LCa
LUL
L
"3>2
w0nILO.
a
wZ 0u1
IA
0 UUx 4
I- I
v0,1V
IA
X
IL
7r X:V
00-4C_JIL0.IL CLi
' ,d'
, d'C
00
00
O
0l1
IU
I4
o o
a o
0 0
10
O
II II
0 00
00
0 00
00O
00
C00
OI
-- C
t N
00 C
IWL0+O
NO
IL
I I
4N00I I
014
010'
O0
0..
O
n n
n
0 00
C
0 00
l O
O
o
v)I
O
00
0 0
ON
' O
O
Oi
0oo 0O
00
0 0
C) 0
4II
O
IL I
.. 4
..4I.
' W
I I
I II
4 44
44
4N
( C
C 0
, 0
NO
O
1
C C
°
0 00
00
00
J Ul U
l 1
Ul
U,
Ul
L C
O
O
C
0 t O
VI
Le)I
C,
4 IL
D
O
00
00
00IA
4(C
.-
OIL
.I
0.
IAIA
C
l 00
00
ON
o 00
00
o_4
00
0111 1
11
00 S
*.
......
O
___."I IL
IL
I IL
CZujuru .-
r
UJ
I
Uv)ILLA
00 64
1;
W en NI-,4ftILN
twL
LULA
-J0o-Jf-I0U.
14IA.sU
l
IUIL- CnV0'
_ J
:'
fL
Ul-
JIA
U .IA
0
'o0-4
z4CZI)
VUl
ILC0ZLU 0Il04-J UJJ-, 4r.
ftLU
w
IL
IL
VuI0 7FTI )ZOujC
)
Orn- I NN'a 4¢)
0IL4ILIL11'((z2'C
,0' 0
U,
,J 0.
J ZC JL
IL
LJU
O
VI
C
O
4 Z
U4 S
I 0
IY
O
U
l UU
l
Z
IL
4 IL
O.
I C
-I
L_
r 7 N
OU
OU
I
Z
I -
f LA
O
Ul
L
2vn
LU
O
U-4IU
IA-1
6
TH
E
JOH
NS
H
OP
KIN
S
UN
IVE
RS
ITY
AP
PL
IED
PH
YS
ICS
LA
BO
RA
TO
RY
SIL
VE
R
SP
RIN
O.
MA
RY
LAN
D
IC
1.1 t)a1-c2:
T-i
LUSyA
Itu >DdX
G
tOUlA
Tm)
_g of0
4 0
I
m
.
C
WN
a
--
_ O
C. 0
cN
.O
"W
I
4-4
Z'IVa
O
,' ;
= II
C
i
OW
O
.U
.2
I I,
_ 1
L O
_ .IU
J 0
LuC
D4aaO
'
Na. 42:U-
In
W
2t4O
ucaCD
.YZ aa- Inaa au
aoV
I
a.CD14
LD
.-.
m0
4e L
m .-
Un 4
4,-
Z
I
.4NInN
Lu
C,
4a
Lu11 La
aa,oU-
aUJ
wLu-SmaaauxD 1-:0 oca.La LL
4VW
InuJ2:
-w'Ain04
LJ J
-IO
.0
-O
_u
a C
4
.J
Wj
WU L
)
2:
4nI
1
atXLL ZIn
o
Ia
_Lu
C 0
Wj
LL
Lu I-
L
uaL)l'-411)0-0a
0ULuVI
UZ
C awa-C
In
OU
.a--
lu -
coL.)1-
VU;
Lu V).
UI
0z uJ
0. InU.
wIJL-
a:UU
C
Q.
aLUJa:-U
U
>
O
N
tu
In0.4
J U
J
W
O
1 -00 N
2 t Lu
a In
4
I 4
f- In
2:
'
0 I
a.Lu Z0
CD 4
4 2:
t6
wIn
0.L
. i
I1-
In .4LCJ-
0.
a.Lu0 z-J a
O.)
D.
_ Lu
I O
.I
-J u
Lu
1-
I Oo
Li
ZI L
uW
Z
4a 0
2 2:
L4
1 a
U4
LuJ
I-a.
')
0 I
0.z1 a
V4
-A-17I
TH
E
JOH
NS
H
OP
KIN
S U
NIV
ER
SIT
Y
AP
PL
IED
P
HY
SIC
S
LA
BO
RA
TO
RY
SIL
Vt
RI
rPIN
Go.
MA
RY
LA
ND
N
LAWXV)
IIU
J
U
C
WU3
a.LuOz -J au.
4 C
J -
I _
O
U.
4O _
Z
LuL _
U
K
0 9-
a
04
O
a W
J4 N
4 _N
.r- .
v 0
N
I
G1-
0N
Lu
4v co
C V
..
DC
-
OC"- X
4 LLof
;C' I
z -
A-1
8
NLua
CNG W p.-SLuLUU,
W LuI-.1C-J0-Lux9:0a. rV
)
Lu
c U,
'A 4t,UJ
Lu K
VC (1 au..CC
-Ja I-zuZuU4
CC
I: a.I-
W'AU,
a0W
-J
o L
I- V
_4cxC
.4 L
u
aCL
V)
4
I u
m
cl'-
nU,
xo4L z
U,
U,
IV
I 2
W
LuK
LuCLI40-U
,
a-LU
Na.WLU
WV)aJ C
L=
- ccW
I Lne
CU
-
Z
-LuC
14
14.L
4-ZIV
)
CLL 0u#
.4G Lua.a.V)
u-
rO
Lu
IC
L.
4 I-
ca-IL *"I
THE JOHNS HOPKINS UNIVERSITY
APPLIED PHYSICS LABORATORYSILVER SPRING. MARYLAND
ea IF
NA:STRAN EIEC£k PFROBLE1l I
TAT1IC LOADING OF !,FLY F TJFPcpOITED BEAM
UjNDtFORMED S9AH'
Fig. A-1 STATIC LOADING OF SIMPLY-SUPPORTED BEAM; NASTRAN EXAMPLE PROBLEM 1:UNDEFORMED SHAPE
-- pR
NAPTRAI CHECk PFROLEM I |
STATIC LOADINrG OF SIMrLY ,UrPOITEO RBEAM
CONCENTRATED LOAD AT CENTER
T.-TtC UEFVORMAT IOI - UCPCAY3E 1 L]AO 7:T 1
5
Fig. A-2 STATIC LOADING OF SIMPLY-SUPPORTED BEAM, CONCENTRATED LOAD AT CENTER;NASTRAN EXAMPLE PROBLEM 1: STATIC DEFORMATION-SUBCASE 1, LOAD SET 1
A-19
qIN
THE JOHNS HOPKINS UNIVERSITY
APPLIED PHYSICS LABORATORYSILVER SPRING. MARYLAND
INSTI~AN t'.'~JECtC F1 BL'1M I
NA3TIKAN F FROPLEM 1 I
'STATIC LOADING OF SINPLY 3UFBORTED BEAM IF
D IST.IleUTED LOAD
STArlC DEF'O\ATIwN - 3UPCIA3E Z LOAU SET Z15
Fig. A-3 STATIC LOADING OF SIMPLY-SUPPORTED BEAM, DISTRIBUTED LOAD; NASTRANEXAMPLE PROBLEM 1 :STATIC DEFORMATION-SUBCASE 2, LOAD SET 2
NASTRAN CI-JEC FIFROLEM I
TA.TIC LUADING OF 31SMLY 5UfFogrED BEAM R
CONEFNTItATED PLU7 D ITIBUTED LOJAD
YTATIC DEFOIRMATION - SUBLSF- 3 LOAD 3ET 3
Fig. A-4 STATIC LOADING AT SIMPLY-SUPPORTED BEAM, CONCENTRATED PLUS DISTRIBUTEDLOAD; NASTRAN EXAMPLE PROBLEM 1: STATIC DEFORMATION-SUBCASE 3,LOAD SET 3
A -20
THE JOHNS HOPKINS UNIVERSITY
APPLIED PHYSICS LABORATORYSILVER SPRING. MARYLAND
APPENDIX B
Example 2 - Composite Flywheel
B-1
TH
E
JOH
NS
H
OP
KIN
S
UN
IVI[E
IIT
AP
PLIE
D
PH
YS
ICS
LA
BO
RA
TO
RY
SILV
ER
S
PrIN
G.
MA
NY
LA
ND
PRE
CE
DIN
G
PAG
E B
LA
NK
N
OT FILM
ED
CU
LD4LU.
O.
CL
0tN
I KI-0rD.
U
V,
0.liU,
N.44
N
r-O',MNLU!'uJul(Al.J
Lu
U
u,Li
J1Z
r LgL
K -
i
wO
a C
L
O
LU
oLiLUU
; y,
W
W
L) S
cf. U
j~~~
O
c c
_ D
>
49
c
N'-4
~~I-
O
,, ,.
,- z
Xj
LU
LU
J C
)~~
~~
~~
*-
J
j W
e
J *i
@
_ i
U
%6
0W
4 40
z *
0 .-
,uj
Li &
uL
Li LflW
N
L
W6I
.U
' -
-
J O
,_ I-
s x
°z
n
4- _
,.,JU
w
O
., zou,
Zzz
w
r.
0 w
0
00
4 -W
4
uO
Z
K
KK
4 ~
0~
t O
00
~
L)
rU
\L
fU·L
LL
L~~~T
L) t
Lu -
S 0
'S
Li~
iO
~A
u
i L
0
U
a0
C
W
4- 0
O*
-uj
U
-J -J
J-
L T) -J
=-
J J
-. -j
VI
4 4164
I cn R
&
c)V
~c~
nX
m
maw
ZW
J 'A
O
-44
0
.jw0
o
.04
mr~
4-
P
~ r
CQ
IC0
bC
C~
Od00. ~
-~
Jl
Wd
If-IJJJ
o_-Y
C
) hV
eL
~L
Qb
o.
"
Ul
-J
U
OV
) I
C
VI Z
u I U
42. 0-9
I W
)
B-3
!,II.
TH
E
JO
HN
S H
OP
KIN
S
UN
IVE
RS
ITY
AP
PL
IED
P
HY
SIC
S L
AB
OR
AT
OR
YS
ILVE
R
SP
RIN
G.
MA
RY
LAN
D
NI
(104
-4
co 7'
u 0
IcO0oooooOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOaOOOOOO
LU L
l'- P-
m-
ul
44O
.0In
0~~~~~Nf',tI.
i '0N~l
4U~ rj
0' UN I'.I'0
.* .'j
, D 6't
ONr-O
0I. 4
(It (n
W
'
'' 4 -
M
C
0' 0 IN I,
co O,' a- e
* .-
1 I * I. "I-
I N
N
IN
N
N
I'II'I.
.rIn
mI e'.
mY -t
.4 m
4
4 .4
. .
4 .
U. It,
U.' U
In
In .
In ,
0 In
'0
'0 '0
L
0
CD
* ---
-- -
-- -4--
4---~
---- --
--
-N
N4-4
-4m
nm
t-
r4tI
tInI
n -I
~ nu~
4-4
0
=~
4
4 L
.JCX I
hin
It 9 r-
a 0 -
--
--
--
fI Nh
IN N
N
('I l I m
m m
m m
Inm rrt s
* 4 *
\uu m
0 v
u U
-1 m
In .tm
f
N
O-4N.0.06'O-4Nm46'0N.00I-06'C-Ner.'~t.,O?-~6'
-~~W
UJUJLU~WW
WW
LUUJWW
~W~W
W
LU
LW
LL
W
W~
WW
WW
WL
WW
WL
WJW
UL
UW
WL
e00OOOO
n00
0000
~ On0060
00000000000b0
O~.O
4 *I3
Li~
~i~
i~iL
)()Li~
~i~
i~i~
imi4
In
4 P
- w
m
L0
i L
IN
P- w
a,
0 ~ij
m
i4 m
4
p- w
a,
LiN
imi4
iIn
L0
I`- w
C
'
4 (S
-
U' LU
I 0-I
N
N
N
N
N
N~~~eNNjtNjN4mmm m
m
m.~
*4
Ig.
L 40
=U LU
I Y
I
U-
Z4
Inl cc
a &
)
3 4
U,
Z
B-4
TH
E
JOH
NS
HO
PK
INS
U
NIV
ERSrITY
AP
PL
IED
PH
YS
ICS
LA
BO
RA
TO
RY
SILV
ER
S
PR
ING
. M
AR
YL
AN
D
0a,
0xLLU
0
o°~
oo00o0ou
ee eee
·I 9T
9
*-
4. LA
P.. al
00
N
m~
.4' In
I- a
* o
0 0
--I '-
4
a,
0 N
M1
4. lr.
-a,0
0
-I1
0r 0'.-
N- 49 .-
CP- P, P
0
L -D
o
000000000000000000000000000000000000000
I IA
I IA
IA
IA
WA
LA
NN
U
: N
N
~ UN
I C
CI
N
N
In
NN
aIA
M
NN
In
NN
CY
N
%
N
0'oe ...
0o.. .o
... o..o
O
. o..0 ..
..0
O
...0 ..
o .
.o .oo
-`--N
* * C
N
C
*.4
n on
* N
*
*.4N
% N
N
U
*r'a
.4N
00
00
00
00
00
00
00
00
00
0
00
00
00
00
00
00
00
000000
.·················*
* *
*~..N
~d
NN
I m
1' m
flfl+',
4.4
.4.IIA
AIA
A.0
Q
.OO
*-*
-I p
* -
--- --
-- --
-- --
-- --
-- --
-- --
--N
S-
LA
L
--J~
~~
~~
~~
~B
5
000000IL
~00000…
00P
PO
PP
OO
P0
0000~
00
60000~
~ 4
4 4
c 4
~
&4
44
4
4 4
44
4
4
4 4
4
44
44
* L U
L
i U
U
U
L
I U
U
U
? 0~ 0~
0 0?
0 (N
) ~ 0~ (N
0D
0 0
0
0 0)
IN
0 0
0~
0 0
) 0~
0~ 0~ 0
0 03 0~
(N 0~
0 0
0~ 0 0
I 00
0
em N-.J 0
4P ~
I A
'O
'0m
bO
9c~
o4
4 It-f-I-
m~
9m
~O
a'o
mo
004
40
LU4.
4
B-5.
LU4toP.0G"
NccLUmrLU
1- Q.
LL
'A.'
4.'0N-I 4A.4'A,Aw-
LULUIll
LUwIll
TH
E
JOH
NS
HO
PK
INS
U
NIV
ER
SIT
Y
AP
PL
IED
P
HY
SIC
S LA
BO
RA
TO
RY
SIL
VE
R
SP
RIN
G.
MA
RY
LA
ND
r Z
U
4
-X
X
or
~~
~U
~~
~~
~~
~~
~
0
.-
0'A
-J0 r
NN
0
NN
4
NN
r
NN
l4
NN
tO
N
ND
r
NN
tr N
N f4U
N
N
* .
_ _
N
.*
_ _
N
..
_r _
N
.. * -
_N
.
* _
_ N
* *
_ _
N
..
_ -
.4 .
-_
N
._ -N
44
0 4
1_
00000000000..
0.00
000-rrr
0°°°
4
NN
N~
t8N
§N
nIlm
f1)
..4-.44'4
* -
o 4
CL 44
N
* *
4. 4.4
. 4.r
.4.
4. 4.
4
44r U
' r. r.
in .
u r m
r0
4
D
4
4
0 44
4 444444
r- I-
r- 1-
f-- r-1 r-
-t
_ _
_ -
P-
-I ....
W4
.-.-
MM
V)
O~
O) O)
O?) O? O
O
) O~
O
O~
O
OQ
C,
Oll O
~ O
O
O
~ O
O
O
O
O
O
O
L
) CD C
()
CD
O
to
Q
O
L
CD
O
LO 0
O
(O
O
N
5 tr
_ O
3E
OL
z4 N
V)
:LU
u
-0
I w
x I
U
Z
a a
a 4
CL 4
z
B-6
THE
JOH
NS
H
OP
KIN
S
UN
IVE
IRS
TYA
PP
LIE
D
PH
YS
ICS
LA
BO
RA
TO
RY
SILVER
lPRIN
O.
MAR
YLAND
WI
4a.NWto wU'
0
U
UI-4.J-3L3
r
.0 N
&.
a_f
L
_I
b W
V)
us
IL
I
WI 0
I
'4 4
2>
IJ
2
c 0
UL Z
IZ
a.
v D
..:
4 40
0
LIZ.J
.J-J -'L 0 a1
.J
-W
-
I Z
-a X
4 W
4 J
0 -a
LI
N S
I- 00
0 4
.0
0 -I
W.
2 -J
I!1
.
u2IL
2-a-I'4V,
22
J
-a'4 ZWW
o ~~~
V-
w
(A
4
.IL
t
'4 ' x
-J
M
Ul~
~~
~~
'
a.
-I 4
'4a
,L W
r U
! I -
U
I0 a.
a. -IL
2 '4p.-
CU
U
Z
LI
X
.
-I-
X
a 'a
W
Il*
o -
-
I W
N
G O
PwU
.r
mb
0 J
a w
os
I a
W
U
Q
.J
-0
1W 0-2
J -
>
y-L
a. 4
2L
( '
LI
N
4 Ifl
.0
O- p..
2 W
(L U
.
r C
0
0-
._
a. -.
o _
2 a.
._I
ILL'4
.o
O
LUW
,.
WI
J .
Q,
.,
-0 >
'
";,
I L
.
.J Z
J
IL
G-
LI
-
J
Y
-a.
>
U
IL
N
M-
ap
WI
0 1-
4 0
J4
U
0.
4 0
_ _
WL-J
LL
Coa.
IL
Q.- -
a. p.2
' al
0
I M
2. I-.
r e
4 a
V- Q
-a
4oa .
2 Z
Z
o;
a
N
a_
>a
-2
.
LI
-. 0
U
Yr
a.
U)
'4
a 2
O
Z
Y
-
1 4
2 0
(9
o9 2
U
2 W
o
s o
J
B-7
TH
E JO
HN
S
HO
PK
INS
U
NIV
ER
SIT
Y
AP
PL
IED
P
HY
SIC
S
LA
BO
RA
TO
RY
SIL
VE
R
SP
RIN
G.
MA
RY
LA
ND
0La..-I-Nrw
u
LU
2
z
.J0
uutJ
2wz
_ 0
LZ
U
...zl'-
z c
4d
0 I
Z4
O
1,
N
t tL
4U
.J2
WU,
_.
Z
Z
tl I W
4 N
0
t O
01
.7
0
V
W
Z
t a2
a D
-
.r
v)
a Z
LI V
II' V
U.
0 L
UN
0
I WU
Z
Vl
Z
Z
N
N0
*4a.0ZZZ 1.z5Z-4x-4 ;2:w0 225
0101U)0
4*
7
LD
0Zn
LO
o 0
Z
O-
ZZ
Z
i
LLI
2O
0O
Z
_ 44
-4 2
>
-r
IL
F01
00
0.
.L
) (
2 -
uj Z:~~~~2
* ,~
~~
~~
~~
U
I- L
L
-
U,
3
W
(L
C
Z
01
LL
D_ V
t7
e0 Y
c
0 0
O
_*~
11
-PI
2 A
I 0
-·r 4
L
r
W
D,
O
U,
,L a
a
V)
W
trL
DO
4*
a. 01
U) 01.-.
I- ,
, , I
r: 5
LI
4 tL
*
D
LU)->
tL
tL
t
LI
4*
01 L
UD
w
r: v1
r w
01
W4
o _
.( _
: .
x r
Z
Vl
I U
) I.
01
D_ Ia
D*
O
D_ 0
tL t01
Ye D
4 7
LI
z r:
X
U'
r:oG
' s
W..
..
.LI'
o I.
._
: r
-' -
r a:
U, 1-
J I-
U, .J
l_
>
WU 01
W
J. VI
01 .J
LI,:
I.-a w
z
0 0
a. 0
4-
49 0
MI
2 0
2:C
. U
0
. LI
LI L
5 O
V
D
L O
c o
ot
o t
L tL
L
J
L
-a) N
0
N
N
N
en)
ICLI
u
i.l)4-u0.001
--4 00x
2 L
I
4*
01 LU
-
z r
z G
V
LI
LI 0
0 -
g O,
0 -I
NM
en
em
m
4 4
4
t000Z
0 N
lJ
Z
4 >
_ N
m
D
U
NY
e
m,
en I
e
-4wIL0m20
-(3
: o
I J Y
'AaD.
U)
x02:i 5-4zLi00z
.4 2: 75U
11
V)
0 54
1 L
DtO
Y07
)(Z
X
0 4 v
01 _)
y 01
t0
o -
t0Y
e J
0 be
J >
Z
Z
WL -
(L
0 Im
D
.
J W
L
LI
Ln
U
e 4?
UI
'0
1-
U)
4 4
4 4
.4
B-8
TH
E
JOH
NS
HO
PK
INS
U
NIV
ER
SIT
Y
AP
PLIE
D
PH
YS
ICS
LA
BO
RA
TO
RY
SILV
ER
S
PR
ING
. M
AR
YLA
ND
WQu
IDQ.Ue
LU
0.V)
QC
Ui
bJ
0CZ
0. :L3
_..
C
0
C
N
4
V)
W
ZW
-
z I
J *tC Q
4
U
K
0
4 4
3 a
LU I-0
-S--W
rcl
LZ
Cf
ZZ
Q.
W U
-S. Ct
· -Z
JY
.LZ
1; 3
°W .4..
L
LU
* cy
-Z
r
-C
.._
U
V)
.Z
D.
Zu
Z-
-WLU
J L
J V
)KZ
* U
, U
, U
,
O
Z
04
O
A
O0
0
Z
Z
0
W
L2 o
U
U,
c U
J
0 J,
U,
Y
~ 0
(ZLUS 4
U, _
K
a .
z Z
4 0
IL.
* *
O
' C
2
IN
0 .9
- -
D.
.cc 4
zK
U
'
A
e0
9
r o
C
O
.0.
4 U
, 0
r-n
z%
n i
v\ ~'r
uU,
0VI
0VI
C0 0 O,
CC0
1£
0..
Cf
>
Y! 0
D
9t
v,
OZo
IO
a
J z
_ £
9- >
m
Z
jLUW t
2! D
. *
O
coJ .J
C
C4
CD
0.
4
N
L
U .
4 K
o
N
1-
.J
-J
W
Z zU
£10
If
4LU-J(05
t,IL.4A
U.
_ 4
N
Z
u_j
U
U.
_ .0
C.
W
W
L 0
N
D_ L
O
2 Z G.
>
C L
Z
W
CU
O
o
x o
CL w
4
4 D
0
I or
a z
UW U
L
( O
V
J
L L
Z
L
U
J W
U
D0
0 O N
m
4
U,
9 o-
C
0 0
NU
U
, D
C
D
'0
D
D
D
D
'
0 9
r9
B-9
TH
E
JOH
NS
HO
PK
INS
U
NIV
ER
SIT
Y
AP
PL
IED
PH
YS
ICS
LA
BO
RA
TO
RY
SLV
1ER
S
PR
ING
. M
AR
YL
AN
D
t!4r-I-UA
w'A
z0--Jo.O
or C Li
a <
-
aT
0._L L
L¢.--JLUJ
J Lo
CL
-
w
Z
L Z
4 4
VA
LAU.
U.
Z
Z
-h
U
LU o
LA L:
0 -
0z
Lu9
a L
l
U
ZIU
C-
JA
U
-J S
-J >
Ul
-
4
J U
.
ujco
=
4 O
f-j
U
000.J
40U.
L J
Al
m3
I-zIU
o oAo 0o
30
V
CD .-
i
O
4J
O
LUY
-
4 Y
e J
C
J
--J
4 Y
4
LA
) .Iif
-I
a Y
4 4
LA5 a.J aTaT-i-j-J
A
,.4
aT
.J ¢-
L ..
'A
.1 _j1
t _j
.I .
-
J _J
-J
J -J
-J Y
D
-J
-j
7C-I~UU
J'A4LiC U 01-a.
S.
I-_ALU-_1LAS
_;1- 'A
LA
0
Z.>
Z
K
w4 J
I tn
r C
-j
-1 'A
J
I-LA-J
(C
(ba.
D.
z J
> z
-Z
J
N
Z
I Z
J
Z
>O
-
0 L
-a
C0 D
. LU
(! a
. a
0 .
U
-.
Z
IL
Y
w
m
Y
Z
K
Y
m
r !
7z K
,
G, 0
C
nC
K
x
4 a
2 0
M
x 4-
M
I 0
ED S
4
'A
I a
L)
L V
-J
1 V
I c
u -V
J
i C
L
I V
aT
, V
L
V
Ul
o 0
0 -O
_
N
r9 U
4 '0
-
M
0' 0
-N
M
\-
P-
0l
o CD
C C)
'D
G
CD co
CD 0
a,
a 0
e o,
ac ,
B-10
THE
JOH
N$
HO
PK
INS
U
NIV
ER
SITY
AP
PL
IED
P
HY
SIC
S
LA
BO
RA
TO
RY
SILVIER
SP
RIN
G.
MA
RY
LA
ND
0aU.
IL
C
lh
cc
L Lc.-
_ L
a z 0
U:
4 N
NJ
IL¢
Z
W
Z
LU L
) Z
C
J 0
DI
L
0
.e C
O
L0
.'
.a
U,
0 O
a
-J
0 0
J <
>
U,
g a
J;
a- .4
~ 0
c
z J
G.
a N
.
Wy
Z
t! Y
s
x O
O
) I
<Q
0
V,
Q
J
0o .4
at
0.
VO
0e
>
J.O
_j
-.1-0
IO
o Y
Z
tD0
0 -O
N
M
I
0 0
0 0
0 0
0 0
0 0
0 .,4
F'
-4.4
'
Ci
V)
accVI >K . (5aa
LL
-i (5S.
J O
a U ,
Uv,
0 VN
J L
W
L
co
o
0 U
-J
0
J 5
-I -t
U ,.
-I 0
a4A(t9t
C.
lJ
Z
acm
i
r O
-,
c .4
4 4
0 K
K
z -*
U
U.
C.
U,
).aa
-C
D
, z
-- 0
.cr
-e
>
o -
D.
NY
-
D
LVl a
0 0
0 0
.da
a a
^ _c
_
r-
No-aJa J
U.,
Z
o
' U
a
U,
LI eU>
U -
LUW
00
*a
V>
a J
0 -
a-,
o a
a-K
4,N4-
A
0-i N
0 -J
LU C
) It
U>
Z
O
I-
.-
0 -J
CZ
4
* 0
0 _
N
-) _ -
-_ f
N l
N
B-ll
N'A
L
·- O
Z
w-
oLL
,
.-
N
NC4
TH
E JO
HN
S
HO
PK
INS
U
NIV
ER
SIT
Y
AP
PL
IED
P
HY
SIC
S
LA
BO
RA
TO
RY
SILV
ER
S
PR
ING
. M
AR
YL
AN
D
LU
41-Ue U7:In ruPU
J
LU
I-C2-rUet0
_ tI
tU4 &
V)
t
<
I'-
J 0
V)
Z
:C
0)
L)
I_
4
L,
c U
Z
Z*
U
L;
* r)
-
.Z
a
Z
O
-0
LU
C
LU
-
_ .
_ _
4024aU,
xCY
u- LuCz
VI
U''A4I-U,
7Li
NI2:wa .4C.
aNr
0Lu
z'UwU.
Lu
*0
NLU7-4
V)2-
z wS:
azZ
4
Lu
W4
* n-
-uiLL
-J LN
4NIq
B-12
THI JO
HN
S
HO
PK
INS
U
NIV
ER
SIT
Y
AP
PLIE
D
PH
YS
ICS
LA
BO
RA
TO
RY
SILV
ER
S
PR
ING
M
AR
YLA
ND
VLU
W
_W
4 L
iW
C
f
W,
W
9I I
C
K
I-0N Z0
If' r
' X
0u, ~ I
C
U
..,o
sU.
oW
L
4
vr uu
a t
u
I T
J
CD
I
4 -
go
0 c)
0
KL
~ ~
Q
II 0
O
W
W
J N
I
I- I
o ,
W.
, W
o-
K
a z
lJ Z
C
Z
uL
C
' Z
N
r
O
, r
0I
.
3~ C
V
I
cc .
W
-°
I 0
r
<W
W
"
X
0 , c
, I
8.
C
Z
, Z
N
O
WC
tU
.° 1
V
N
I 0
-8
. a
1
CL W
-W:
2W
.4
C1
B
I -
2 1
TH
E
JOH
NS
HO
PK
INS
U
NIV
ER
SIT
Y
AP
PL
IED
P
HY
SIC
S L
AB
OR
AT
OR
YS
lLV
ER
S
PR
ING
. M
AR
YL
AN
D
WD
V)
Q.
Q.
o o
Z
Z_:
2
0 0
o c
1 2
D
I
w
4
N
N
0 0
O
O
U, N
N
W
WW
W
-u
4 _ 4
.C
V
)LA
VL
I _
A
Z
tf O
2 c
2 0
0O
-a
0 -4
U
LL -
Z
Z
D
-U( 5
AA
W
W
D,
V7 V
lV
) V
, :
0
* U
*
U
* *
* *
* *
* .4
* O
*
*
U
W
VR V
"
D- -,
.4 .4
o 0
;: 2:
* IC
C
Q
M
0 0
.4
l o
o
W
zN
z
N
o -
£ W
r
r
Z-Y
2: 2L
o z
z
U'
J J
=)
4 LU
*
· U
.· Z
* 2.L
B-1
4
h-CI
U,
W0Cz
ICU,
D'
W w2: r
W VI
D. U,
It-tNU,
In-U-a.47.4U,
LU
V)Uw w Of
1-22:-JLL -4n: a.W D_
U.
LLJ
II.
Za
I-CaD_
-J0I.--j r0.ICu.V:
Wr
t-Uo
0.Wttz.1
TH
E JO
HN
$
HO
PK
INS
U
NIV
ER
SIT
Y
AP
PL
IED
P
HY
SIC
S
LA
BO
RA
TO
RY
*ILV
ER
S
PR
I4O.
MA
RY
LA
ND
4 D,
-40.000
0O
0 0 000
0. 0
0 0 0
0 00
0 0 00
0000
0 000
O0
00
0 00C
0 O
O
0
0 0
00000
OO
OO
OO
OO
oO
OO
OO
OO
oO
OO
OO
OO
OO
OO
OcoO
OO
OC
OO
OcO
OO
O
e 0
0 0'0
D_0
· 09e00e
00e00
0 00000000000000000000000000000
O
OO
O
OO
O
OO
O
OO
O
Oo
OO
O
OC
O
OO
O
nO
R
oO
O
O
..O
.O
O
-
.@
e *@
s
|. @
@
*
*@
**
.*
.. **
* @
. *
.v
000000000000000000000000000000000000000000000000
zC "a
0N£4
-00 'O
a'O
O
'''' 606'O
' O
'6O
'O
O~
O'O
6
'00
6
6'0
00
o
~0
oo
a
'00
6'0
o0
0000
0000
000
0
00
00
0
00
0
00
00
0
00
0
00
00
0
00
0
0000
G;
l ii
i l
l il
l 1
11
,1
lii g
il g
ll 1
11
III
|§@
@
@0
"a W
U/W
W
UlW
WW
W
WU
J W
UlW
W W
U W
WW U
l U
W
W W
LJW
41Ul
W W
W W
LJaU
. WL
U
W
W
UlW
in
0'r
00N
0
-r- IO
(aIN
0
O'N
O
00
.11
N
llO0
N
I IO
I.I .6
0.
ON
.C,A1
0 f-
fl _
CD
O
C
Y
in
_-
P.-
U 00
DN
a,
CD
m
1
6 1
\ 1m D
1o In
P
- W
%
O
N1
f
D0
m
u
a Fl
D
INN
It
NN
O
N
aO
_
UN
4
N
TO
.
0-
CN
6-
t M
.
WG'0 0
LA 0
U_
.. N
ONOc
N.p-
N
-O
1
- IO
O
' -
4 1-
1-
N
1'U
Dr0
a,
o ' _
O
C
t LI
4 N
ItlIN
t- O
D 4'
rn N
U
to In
In
V
D
0.
In
0.
I- It
NIa
OG
IS
rO_
1 i<
P
D+
1
_U
9
ND
U
-0 '
-PN
mO
m
N
10
1D
it N
O
O
0s _ U
O
N0c
_ O
ON
N
_
1S
NO
40'Y
0
N'O
NO
N
.0'O
U
'iC
dm
m
iti-cN
O
NO
~
0-i0
N
-.U'
~N.,.0
1-t6
N
- 0
10 NcO
0
N'
1 0
0
4 N
O
N
0O
G-
0 a
'00
0
0 _'
0..I n
0 0.P
4
0 00
o0
-N
N- O
-
0D
4
NO
CO
iT
0 4
O
4 C
O
O
0 G
_
O
_C
O
' 0
D6
_
_o
__A
0;
__
CD CD CID
c0
CD
cr
CD
CC
CD P- IF
.-t r-
P- rF I- F. r- F.
I_ -
r. P- P- r. I-
P_ P- P
. p- 1_
P. -
t- 1-F 1-~ P-_
Fl 1,_ I_
000
000000000
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
c0
OO
OO
OO
OO
OO
a
tA
`0
m
tOO
U
O nO
O4uO
nO
fO
min
uC
ao
ii I
llllllllllllllll il
II 1
1
1 1
1 ill
lii ii
i li
ii il
l i i
U 0
-N
N
~ 0 N
0
a' 0
.6
in
N
an in
N
40
0 IV
1-
0 0
00
IN
0
-P-
0' N
4 O,
m
0 0
' rI
C D el; --
O
OS~N N
O
4'0
00
*N
N~
0Q
-NN
NN
~m
~S
mD
~N
C~
m+
N
b~o00 6~
~n~
~~
~~
nm
mnhC
~C
~~
NN
"m
m
I, z~
_ 0
0 0
0 0
N
0- -
-0
-N
IV
- U
N
_ 0
U
0 0
60
_ N
N
0No
6'
0' 0D
1-0
0
L
0 0
.) .0
'0
00
0
' 6
' 0
0 O
0 -
-0
3
C
0 _
_0
0
_ -
_0 _
_ A
A
C
P
0 N
00000'0
r' m
a
O
O
O
D
U
-r
_ _ _ _ _ r
.r
N
N
N
N
N
l D
0
' D
G' G
' 0 O
0
D
0 D
00
00
O
O
4 .1
4 (.
G6 0'
6'
0'
_ _
_ _-_
___-
_ _
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
0 000
00
0 0
0
"ao
B-1
5
NI- UJ
Du
UJ'A
i-zu'31
-JU.
NUj
co0cc0.UW4 UzCan.42
w
TH
E
JOH
NS
H
OP
KIN
S
UN
IVE
RS
ITY
AP
PL
IED
P
HY
SIC
S
LA
BO
RA
TO
RY
SILV
ER
SPRING
C. M
AY
LA
ND
00000000
000
000000000000000
00
00000000000
00
00
00
00
00
00
00
00
00
0
0 0
00000
0
0I I
0 000000r4p-
w
N
00
00
0
0
0 P
n 0
000000000000000000000000000000
000000000000000000000000000000
OC
o
o0 ooU
oo0en0000
00
0in
0
00000000000
00
00
00
00
00
00
00
00
00
0
00000
0
P00000000
00
00
0
00
m ~ ~ ~
~ ~
~ ~
Url'
C.N
a
O
In~%. 0
UH
N
''~
~~
~Il
l,111~'C
'C
0Il
I N
, II.ll,
I II
IulII
' I1I4N
I
IU
cla. 0
L
O0
0
0 0''0
L)
0 0 V00000000
0 I
0'C
00
H.~
0H
. a
'N
In
, P.-
w-' o
.o
0 U
L
U
0 I)
UN
.
.N
NN
0
.. N
N
N
O...
r- N
N
- (a
00
mU
90
009~
00
m~
00
09
0~
00
00
00
00
00
0
II I
I 1
11
11
11
II Ils
II
11
1
11
11
,L,
U
,
L U
U
,
LLL
, , LL-L
U
L
L
°L U
44m44JNjJJJJJ;JJJJ9JJJ0jjJ0j~j
-104
' 0
'CN
lm
C
I
V0
''C
m
-.'C
N
0 N
H.0
C
'
' H
'
-.. C
N
C
4 '
O4
'C-
' '
'CC
~'lfN
0'.-l.1
0
' C
C
N
I
H.
4 H
. 'C
n
H.
0 4
'C 'C
0'
¶0N
.N
N
'0
..
.'' C
IfIH
.40H
. -.
04.-
'CIn
IN
N04N
..
0'
'sN
H
'
'C0
0'4
46
0
~~6~~N
N-4
10'
' '
P
44
~N C
C
H.H
.'C.)
C
0'C
4
' "0''C
H
0'
' '
' 0
----4
P
I; P
C
; 4
44
4'C
4L
'C
C
C
C '
' '
'
P1 P
I'
P1P
1 4
44
4
44
1
'4
44
4
4 4
4 4
44
4
LU0.
I. ~
m
O~
nC
O
IA
m
~90 00000
00
00
00
04
) A
00
00
0
00.
B-16
LU04-1
H.
0'9UC
cc NI-w0.wD.
L)
4I'ANU,
-J4z4LU
'CL,
1II3-IU-
0.Z'C
r.,
00L.)zLuWL..
0 ,q4-J 0.(L0
NLU
-I00.LUx0z.4 VIz'C4)2
THI JO
HN
S
HO
PK
INS
U
NIV
IRS
ITY
AP
PL
IED
P
HY
SIC
S
LA
BO
RA
TO
RY
SltV
ER
S
PIN
G.
IMARYLAND
LC
0.~
~ C
O
'O00000000
C0C
. 00000O
000Q
O000000O
00000000000000
0 C
) 000
00
0'
0 C
C
0 0
0
0 0 0
0 0
, -00
0 .
0 0
0 0 C
) C
) 0
0 0
o 0
0 c
C) 0
C
.a
0 C
C. C
cd 0 0
CD C
C.0
~4NOC
OD
O
OO
c,
OO
OO
OO
tOO
OO
O6
O
OO
O0
OQ
o0
oO
O0
oO
o
O0
oo
00
00
0·
·*~ ~
~ c
;c
!8c
;c
c -c
;;
c ;c
, ;c
;8c
;8~
98~
1
;81
F1
cC
1 T
~c
0000000
0oc00000000000
0000000
00000000000000000000
U-
o
00000000000000000000000000000000000000000000000000
4
OO0O00Oddd000000000~o00o0o0d0o0ooo0000o000000o~
-J M
m
M
'
n in
'l'4N)
In CY
(In M
ONl' f
lnMn
m nIN
mmI n I'
M
NIO
mm
NM
!e
Nm
0000
0000
0000
00
00
0
00
0
00
0
0 0
00
0
00
00
o
00
00
''Ii I'll
I'll I'll
I'll I'll
I'llg
''I
tI l
I I'll
I .
" .U
, 1
I .I
I III
1.
LIII
"I
I I
11
1 "I I
.1
I I
I I
LUIniY
n
LWW
LU
Y
WWU)YW
WU JWU
W
WUJUWCI
WWUJWII WWIUJW
UL
Y~
WiniU)
u
WLAJWWW
to In
1.0
0.IC
Itm
0 .0
.t0
CsIt 'fl
N4
.ift 0
Na
tlI'0
N
4 Ifb
N0tm
l0 N
4a
.r,0
Na
.U'C
eq -r ~~~~~'o 't
wIco
r DmO It(ma,
4 t(, M
, It
, m
N
N
4.0
4
.0O
'M
O
.00 l00
.00
M
0 .0
o
M O
U
'o M
o IIo
M
o
i lI
' 0
.O
m
O
.0
0
0 0
N
4.0
4
t311mm
4m31
*4w
0
4.m
mm
4
Om
m
.*0
mm
4
m
0' 4.0
o0' a
~m
mm
mm
NN
~~
~N
~m
~N
NN
NN
NN
NN
NN
r4NN
NN
NN
C)O
OO
OO
O
C)O
00
00
00
00
000
00
0O
Y0
00
00
0
C)
0 0
0 0
0 0
0 0
C111
1
l
i
I
i ii
111111111 11
1 II II
II lIII
11,11
III
iII
in IW In
II
.in
I
in U
,i
LU I
i
in Lu
i
w U)
in a UI
I in
UI WI L
I n
W
L
Ui I I
i U, UI
1 u Lu L
u UI
LU in
LU 11I
Ia,
0
.0 m
0'.))
.t M
m
.0
0 N~ .0
-t 4 0
'o
w3 4.
0 .-
0 0
.0 m
m
. m
-
NI N 4.
4. fn
31 W
1 3
0 J.
0. C
, 0.
z -
..
0-I N
N
..
3 1 0
0 0
3 1
N
4 4
4N
1 0 .
.3
0 N
N
0
3 1
1 1
'.W
40
o ~
, .
~- --
U,'..
N N
N
-0
00. 0 N
.t 4.
PtN LIN II) 0
P- .0~
.0
31 P.
P- N- 3
4.M
I 31
1 4.
0 00
0.0
.0 -
--
I)' ..
0 00
-a .
II .
.0 0
0 0
00 o N P
un
..In 1-
U '
00 0.0
N
Uf'
Uf, iUN
0 0
0
3,0 .0.l3
...
0 0 0 0
.P- .0 0U N
mI -
--
.0 1 .
..
3 .
-m
p. -
L .
.0.I
-0 0 0 .
4
.4
..
.
c. 0n L!)
0 0
0D 0! 0
05 0 0 L5 C. 0 CD
0 05 0
5 LI
Lo 5 CD
0 v)
0 0
) L0 C.
0 0
0) 0 01
0 0)
0 0 0
C
0 C.
0. 0D
1I 0
0 n
LI
-N
~~
~~
ln~o
~N
N
N
N
N
N
N
N
N
0
.4.
4.
4.
4.
UN
I-
~ ~ ~
~ ~
·
N
m
0 L
4 U'%
1 0
C
O
I a,
0 f
U
M
LA
w
M
I U
N
0 r0
M
0
0I1 C
)
0 m
t In
0
f C
0
0 0
m It
00
P co
0.
B-1
7
0.mUejr'A-J .07 .0-.4
in 3 <f
U-
0.
T U,-1
IM
Nx3100.wo CL
2z-9U,
42
TH
E JO
HN
S
HO
PK
INS
U
NIV
ER
SIT
Y
AP
PL
IED
P
HY
SIC
S
LA
BO
RA
TO
RY
SIL
VE
R
SPRIIN
G.
IMARYLAND
000
00
C
0 O
0
O
O
00
00O
O
O
OO
O
C
OO
000000000'0
00
00
00
00
00
C0
00
00
00
00
000
000
0000000 00
0000000000O
000
000
0 , 0
U0
00a 0
C
I000o 0
0
00e 0
0 0
0
0a
I (0
0 0
C
.0
0 0 I
0a
0
00
0
0 0
00
0t
eJ00C
U00O
0Q
00000000000000000
0000000C
JC
0000000000000000000
II
II IIIll
11i1
gIUI,
III II
IO
G
U
O
NO
O O
O
tOOO
NIt
O
O
O O
N4lI O
00
.0
.0 0
L .0
'0
0
fL5 .0
N- .0
0 I.5
0
LL
b
N
0 I V
5
0 .( r0
E
. I
N
N
N
NA
N
N
t U
O
N
N
t UO
N
N
ON
N
N
N
t N
O
N
N
N N
0
O0m
0000000
0C
0
00
00
0u
s0
00
00
0
000
V W
. 0
WN
u -N
U
N
N
Z-0
+
0 Z
.0 N
4
-P
P.
P rI rL
P0
N
fL
,. k
B-1
8
-O
' V
O
O
O
O
L
0 .
C
..0
.0
P.
P
P
P.
P
P. P
. P
. P
. O
OO
I.- UJz U
JU
LU
JU
U
U
J
UU
rUJW
U
U0N
r1
n
N
I I
01
U
N
_
N.N
N
4 _
rrZ mr0
__
_
NN
N_
0
rr0N
.
N
000-18 1
_ /%
_NrJN
_90r O
O
N
+
>
~~
mc
Cm
~~q NP \1
-r O
y
_ _1E -N 0
d m
9
m
c~
~~
~~
~N
0C
IO__
O0
00___1 0
r r1
U
U
EF
OO
OO
Oe@
n
OnU
!0
F
u 0t
O~~U
a ~
c0 N
nes
r oC
0 rM
rEr
FK
F
r r
w@ t
OL o
t9o
do
d o
(bn
9 oe
Xd
dX
d
X
o t
O
~~
N
.t Ita 4 F
0 >
O
~
N
o1
U 0100
Nt0
000
_ 1
C
|JI
EU
E
s
Om
s1
r
DL
B -1
8
0,U.a0'
flrLU
UJ
LU
040-I
.'
L.
,.-3 zu.Ia.
In
Nuiacc0L)u I7:Cz a:4A
TH
E JO
HN
S
HO
PK
INS
U
NIV
ER
SIT
Y
AP
PL
IED
P
HY
SIC
S
LA
BO
RA
TO
RY
SILV
ER
S
PIN
G,.
MA
RY
LAN
D
WI 1 .0 U
J INU W
W
0
0 4
Nj 01
0
IfW 0
1 a 0
0 ID
W
0 UW .W-
4 I0
4 in 41 .IW
N
N
W
1
0' N
N
In
W W
W
1-1 W
. W4
W4 N
X
10
mI N
4
0a N
-
-_ O 1-
0
la -
m
_
nIa C01D 1
\ In
IIN .
,D N
:2
4-
-'
0 O
0 0A
00 ¢
0 -_-
P-
I
M
N` 0
10
1
N rI
'0 10
( 01
c L O
01 C
-.:1
N'O
'
W. IA
.0
.0
4
WA
VW
N
0
t-' W (I
W
IA
N W
0 4 N
0
.0 P-
W
a 4
A 0
1 N
t _
' a P-
m
-0 4 N _
4o
4
W,
-.- U
, n
O
.- P .N I-
O- _W
0 M
I00 AO 4IN
in
N N
C
1 0o
0 .Cmov.. N N N
Z01
4
eD
C
D
01 0.
4
O0
I
IL IL IL
IL UU
W
L' IL ~L
W
L IL
IL IL
IL IL
W
L ILW
UI
IL IL W
W
W
I I
W
WL
U I
UII
UI IL
IL IL IL
W
UIL UI
.I
UI
IL
II IJ
L. W
I
0
0 F~
Cy, W
I_ 0,
m
W
e~4
-IL
-
C4D °
W
4 0
It Dn
e N.-
I D
W
N-
_ t -_
UN O
....W
.. O- I
l N
n r-
P.- I
* .m
N
EC 0
00
00
00
00
000
00
000000000000000000000000000000000
DE
O
N N
_ ^L
IN In
N
N
_
' N
I uN
_
_ UN
N N
_ a
N N
_l N
N
I t
N N
_ r0
N
N
- _
*c
Nl N
_ .o
N
N
_ 4
N
N
.-
o o
0 t -
0 1
D e
I D
o O
9
o N
4
0
-N
0
40N
o P
.'o o
N
O
I N
-
W0
I' 0 0n 0
o 0
n
0
-_
0 .
n
I
.CA
r eV
, o
IA
N
D
104
N
r P.
1 0 0 01
e0 V '
0 P
r,
NN
I In
_ I N.
N
4 .F
0r D
000
0 0D
0000
00 o
0000o00o00h
r 0aDN
eD o00
-_N
N
-
I -
o N
o _
e fIA
_ I
CD N
0
_- CI
0
UU r
U1
I Ir
I I
I I
_ I
I r
I I
o I
I o
N
eDI
I I
I I
I o
e D
_ e
I I
o I
I I
IOI_
I eD
I _ I
I r
W_
00
W 0
-, m
IL D!
t1JNNN
'
0N
.N.NN-'NN0tNNNN.i
NN.
ONN.
0NN.
'N..NN.
0NN.
NN,
0NN
0 000000000000000000000000000000000000000000000000000
Al Z
O
I
IL I
I I
IL I
I I
I I
I
J tI
7- U
e
0 On
1q
N0O
IA4IA
0010.0
00N
I_4LA
O0
OO
0..4
NIA
ONIA
00
0
00010NIA
4IA'0P
.-O0
LN 10
.-..IUrO0rhV
N
NO N-NNO
-O^N
^O
NN
NtN
NIIII-A
0II_
0t
4.
0
IL
N
mN
mN
m
N~
N~
N~
N~
N
N
N~
N~
oo, ooooo~c~ooooo~~~~o13-19oo
~
TH
E JO
HN
S
HO
PK
INS
U
NIV
ER
SIT
Y
AP
PL
IED
PH
YS
ICS
L
AB
OR
AT
OR
YS
ILVE
R
SP
RIN
G.
MA
RY
LAN
O
--
N
N
N
N
N N
N
N
0000000000
W
In
In
W
II
W
W
aL
W
0.4
IA
r.
(I .0
N
Il C
D
N
OX
C
4
N
4 G
N
N
.0 m
\ N
4 w
N
'0
.0
N
Wt i rA
q 40o
IA m
P.f
-, N
1
- 00
0 In
4.-fL
0.....4
............
V
_- _ G
t 0
eN
NN
N
S~
~~
~
77 I
I I
I I
I I
I IN
Iw
W
W
L
W
W
W
W
W
Wli
0 N
N
N
_ N
0
U
iiaaiir
iiLN
(i
N
Nm
NN
4N
N.1
0.0
000000000
of II F-
a,
III IN
I i
LU70 N
N
0
-I* f
-0G
'
7 IA
Z
N
G
0
N
r- )
_. r 0 .11 N
C7
No 0'
U
N
tn
4 4N
6000'IA
4N
C4In
%
Cy, w~
~m
9
tl .
.-
..
4.0
4 .
7W.
A0N
.44c If LA
0' .0
1-
-( 0
N.- N
- C) U
N '
N _
C'.
0.Z
-In
U'.
4 C'
C
0
V)J
-1
7a
0000
00
0000
-In
_ _
t- U
N
N
N
N
Lu
UJ
a)
W-
WC
U
W
lU
LE
I--
U
W- Z
w
1 E
N
_
V
_~~
~~~
O ~
G
t,4
N__
IA
Z'
N
N
Oi
mr
tNerr_
.
-0
000000000c,
aC a
0_ N
Ne
0 U
. G
4 V
N
U
S
N
OO
0
U
44
N
0
L
....N
.
..W
0 00N
000000
'a00
I- .. A
.
-....I
.. I
0 0
m
-VR
J O
OO
OO
O
OO
OA
X
7 UN 0I
UN O
N
I) UN
N
IA 7. N
N
NW
0f'
ff 04.0G
O
0 N
G
0
' N 1-. N
W
4 C'
G
N
w
.-"O
NN
.*A
.....0
IWA
7
IAJ- ul0A
0000000000
LU 0.
IAI
WW
U
JLU
WU
WU
WW
U_'U
_4 IA
INIIIC
Y_
0V
O
._
ItANG 4
0 0.0
V
u'
N
h 4 aIO
N
0.S
IN
NC
NIN
m
o
I'.0o
NW
20
000'0
' A
IA40
4 I
IV
LI I-IA
-
-_
_ _
_ A
N
N
N
N
4 ZX
I A
IA I A
I
m
gCD N
4
Q
Clla
oso
0N
0w
eV
z w
ZW
-JU)
0NUu
ar- CC
.00.N
a'
GE
N
0.IAW
0
N0.
us
z 'A
co w
cr
WW N
I
U
0
W-JGO
0.usI'
0 11
u u
ww
u C
aU
U
tL
Li '
o,
aV
\ Z
UIAIAI
-4
.0
N
u .4
N)
0
VIU V)Zu0LI 0.-o..
'oI-aLUa.-JLr0uI.rILL-J4'
N
(J -JU.
0.
,. N7i.IA 111I.x Itx V
I
'Aa.00 r n
az I2J
_
tu
0a -4
a J olL I
OL.
N
0 aI
-z4
N
N
4 0
LU N
I 0e
N
-4 0
IAo
_-
-U
I0U
. 0.0
Z
U-
a..0
07
7
-r
0
U.
N0
IAI
00i
-
ILU
W2
I.0
v V(AWUIz7hA00
a oW
N
o
0 C.0o I
Wu 0
U
4 U
LA
G
. co
,M
0 zI. 0'
4V
G
WZ
N
SI
oN
0Z
1
W
0 L)W
N-
4-0
Y
0.0
If
O 1o
'U
B-2
0
a,W(C.0(Lr-VNLU
NWWW0.L
UIA0.-4'.INIJV
-
IV-4U-
VIA
TH
E
JOH
NS
H
OP
KIN
S
UN
IVE
RS
ITY
AP
PL
IED
P
HY
SIC
S
LA
BO
RA
TO
RY
SILV
ER
SRIN
Ga.
MA
RY
LA
ND
NCy
IAI-4C,J XliO
ccU,
z
O
0J
Z
U
1-4
4-
o _r
-J
U
i -4J
-J W O
U
CI
aZle
Li
VI
9- JJ
I I
<
n D
r zr
_ oL
W
I _
-4 -4
0
S
n L
KJ
K
Z
4 E
<I
K
-.
VLaiIALizZD
O
C4
0I
c o
4 L
U0
4v
,I
r-. -
NO
¢l
,- CD be Z
C -
I -0
4 LiV
.J
0
Z
2 -,
zU
UJ
tc8I.D
4I-If'NCl'I-IA
-4.11o
-J
-4
-o.
_
I M
o I0 1
r -4
1-=
44
o
J IJ1-
-J0IC0LI
-4K
p- I..If`N-8.cw ,A=a ItI~
.0IA-J7I-2'A-JU
-
U.,
el-
VIIUI -t~I-Ccc'aLA
Ll4 4CI
aJU.
v-
.I-
I-
I-a
..
D_
-J
8.
InCL Q.6,A D- 4-d
K4 N
rl-4
D.
-J a
-4
F
j QI
-J cc at
w
K
-4
4A
M
4In
K
N-4rWI D¢LD afMUz4QCIA
4K
B-21
TH
E
JOH
NS
H
OP
KIN
S
UN
IVE
RS
ITY
AP
PL
IED
P
HY
SIC
S L
AB
OR
AT
OR
YS
ILV
tR
SP
RIN
G.
MA
RY
LA
ND
It
o OVI40O
-J L
.nnno U
lCL
2a 4
L
ZoiL
z
in
0c
rLi
r <
U
LI
W40 w9
tMI-0.rtIVI
I--
WC,
0VC, w-i0Li1-r0Ua LiV)
U,
4ininLi
a
4 0
-L
U,
n I
-J
I 4
L In
iz
I a
I
Ul
V)
W
2 L
i 2
J W
J
tL
C
U
UU Y
aZ
U
a
-Li
4-
a)
a a
4 0
42
in
2
VLu
1- UC7uL ccUi
QL
0 -J0. .J4zI--U 0.aU
Ou
:
J0.
I..
ujr7I/I
inItLi It.4 C
,
0i
UzJ.
J.zLi
U.
2:
z
a 0
U
0
IJ
JZ
I I
0 Li
i U
IL
1
Z
-_
z U
2 v 2
L4
9- 0
vIz60
a0
4 0
0 Li
G
UU
-J
D0
4 4aco
a
C0
9-0
wt
.
L r
o a
- >
a o
W
I0
tDW °,Q
N
O
L
CC
r I-
40
.0
I. 9L.
LD
U
0 U
'
" 'o
z W
a-
O
Li
T
O
4I-
a tJ
J
ow
W
cc
c
0 x
WW
O0.1
1
t-
2 S
7,
-4
70
tU 0b
Li
Ul_
U
JU
U
z'a
*
0
22 uu
rCO
t
B-2
2
I.t.
wl-,
W r-0'oJ
i-4VI -ruavi0.
in Ul
o
0W
-
oI
0G.
VI
W
U
r cI7
V)
I
L -a4J
7-Li J0.Li
IAJ
in0.-vl.el
NL,.
C.. a,X)
U4 It-i4-.
'A Li
I of3I-JLiCL WxIt-J
0./11U
.,
ILM
tD 0ULi0cz1W
*
1-M.
7xLi-2
co0Cc
U0.IUz4-ain42
rnts,
TH
E
JOH
NS
H
OP
KIN
S
UN
IVE
RS
ITY
AP
PL
IED
P
HY
SIC
S
LA
BO
RA
TO
RY
SILV
ER
S
PR
ING
. M
AR
YL
AN
D
A
u~
/ L
I- gIDD
0~~
0N W0C
L
LU
z 0.
r) cli~~~~~
LU U,
Li~
~~
~~
~~
~~
~~
:
h UJI~~~
t,~~o r
UL,
w
W CL~
U,
>-<
~~
~~
~-J
J c
h k
_j 09-
IS LL0
n I
B~~~~~~~~~c
WD
-
L
tkw
0
r v\~
~~
~~
~~
r
LW
IL
I. W
PI, z~
cr //
~ ~
~ V
' ~~~~~~~IS :d L
•~~~~~~~~~~o/~
~~
~~
~~
~~
~~
~~
l Id
/~
I .
I.p~
L W
I (0A
td
r~
~~
~:Z
B-23
5
TH
E JO
HN
S
HO
PK
INS
U
NIV
ER
SIT
Y
AP
PL
IED
P
HY
SIC
S
LA
BO
RA
TO
RY
D
SIL
VE
R
SP
RIN
G.
MA
RY
LAN
D
D
DI-j
h
LuUw-J tih-JzJ3J LLIL6)
uLI
U It
I D
z C
Y. U
Z
FI
B-2
4
cN
-J0 a-O-J.1-
z Xc/N<~
z
LI
U)-
_--
Z
U)
Cm
Ul-
oLuO
en
mch
izv
Id0-J 1(0i
THE
JO
HN
S H
OP
KIN
S U
NIV
ER
SITY
AP
PLIE
D
PH
YS
ICS
LA
BO
RA
TO
RY
SILV
ER
S
PR
ING
. M
AR
YL
AN
D
wozwo
<XU tQ
ZU
O
Zcn
r
-
<o I
US
Yi U
)o
Lu
I
Fw
-O
n0 0
ii
l-h0DJ-
ha_toIN LLi
IDIA -J4.AALiwMhI-JIL
i-Jti.tL uLj'
Un
J I h
DZaD
U
A
uI L D
7-tvy
Z
:L)
Z
F1
Vk
tL
L
B-25
TH
E JO
HN
S
HO
PK
INS
U
NIV
ER
SIT
Y
AP
PL
IED
P
HY
SIC
S L
AB
OR
AT
OR
YS
ILVE
R
SP
RIN
G.
MA
RYLA
ND
/
5'~
~~
~~
L
/
/,
-J0o0X-- a-;,r
tLL
<0
xe
-iW
U
C
4:>
Z,._
'-O
-o
LU
U)
<4
:
'I ~zo
t. A
~~
~~
~~
L~
~~
~~
~~
~~
LL
aZ
{
u'/
j L
Li~
~~
~>
-L
u co"v
4 w
~~
~-~
cr¶
v,,;
'°A
u
-I If /
Q-
U
LL
J Li
~ m
~~~~~~~~
~~~~L) ~
t
-D I'-
I~~
~~
~~
~~
~~
~~
u
-4.
Li I--
a II
IL L
<
>-
At-
U L
Ow(L
z 0
ff C
L
3 44
A
Z~
-V\
B-2
6
THE JOHNS HOPKINS UNIVERSITY
APPLIED PHYSICS LABORATORYSILVER SPRING. MARYLAND
APPENDIX C
Example 3 - Missile Flight Loads
C-1
PRE
CE
DIN
G
PAG
E B
LA
NK
N
OT FILM
ED
TH
E
JOH
N!S
H
OP
KIP
U
. mt[0
PIIT
Y
Ap
PL
IED
P
HY
SIC
S L
AB
OR
AT
OR
YS
ILVIR
ISriN
. ARYLANl D
0 0D
oa
DI
O~00m060,[.u1In
0U
Uu
U
D3
D1
HUDo 4.41 4O
0H
1C
% 0 ..
4 t
,Oa C
.(n
-4 I.,"
AlA0
0 DI
0 H
W
H
c tn
4 V
)
Uu
0m
Qomn
0n _
e1 X
d
oi4 0
VD
P
acC
a
0C
A
o u
t n'
V
I1
DI
3~l 01
004
00
w
00
E* .
1 4
.1
01. 4
d r.4
40pdb
aP
.1 .3 a.00
P
·2 9
M,
0c
l r
ra rO
C
a 0
H
i
1..O
C-3:
TH
E JO
HN
S
HO
PK
INS
U
NIV
ER
SIT
Y
AP
PL
IED
PH
YS
ICS
LA
BO
RA
TO
RY
SILV
ER
S
PR
ING
. M
ARYLAND
eaC4
a'
O
.000
t.
.m
4 0
4
0
0 0
a0000
0
..
I
00e0
_.
.0,fi,
~ C
~
1¢ t
·v a
O___
:t .
0 0
_ tNH
t4
vD
eD
r
P
_o 0m
I
o Nu
r ~
C0I010'aN0N
l
No-
000000
00000
.
0
... .0
000000
O
N
O
O
N
C a0
a0
.4.2
"
Ma!0
!-----t !
:M
--
0 000O
m
* O
:
er .4 c
0
0·
0 .
.0 (on
,"
* O-
0trO
o IO~O _ 00
N0
en
N- In
I' .
0O
-~ ~ ~
~ ~
~ ~ cm
r o
w
--^
->
-S
1
hN
^e
_N
t
D
0e
-_
----
* vD
N 1 ,
UO
0 C
0
NO
* N
f'~*In
~r-0
Ol.N
C,*
-N
tfm)*
InD
~r*
.0…
'0
*'0N
I~I-0
U--
N
0 S
c -
N t
1 0
0u O _
N
U
u 2
0 0 0
0 O
_ 0
0 0
0 0
0 -O
_ 4 4
0 .
0 0
0~4~4~~4 4
4444440040H
HH
HH
HH
H1
-44
HH
00
0.4
4E
.mU
UU
UU
UU
UU
a
~ ~
OO
UO
U31O
m0.1
0
0,~
...31
F.
0 D
_-
N
_. _1 _- 0
_-
0_
_
N
Nn N
0 N
N
N
0 N
N
' N
In
'0t1
--1
0 0'
0'
Nf2
*I0
0
UU
N
NN
NN
NN
NN
NM
ME
mm
M
UU
C-4
-N
as. I..
10to 210t
0Q
r1a 0.D4
U,
*
%0
r
212.30m0Dpqtrt
En
wD1
w
-300
eo0
tn.020.
w
a4 O
USc
O(
PI
F H
H
In-3
49
P1. m
THI JO
HN
S H
OP
KIN
S
UN
IVE
RS
ITY
AP
PL
IED
P
HY
SIC
S
LA
BO
RA
TO
RY
SILV
ER
S
PR
ING
. M
AR
YLA
ND
0140ea0D.
acn
0o.Ca.U Ha
0 0 0 u
M
0
el
0 o
m
a 2U
0 0m
o Ua w
n 0
a..
.4 B
- 0
o. 0
0C
:lpt
a:
4U14H
PH541.
NUC43CI
11F
%.
.40114
a*a.OI
A1
0ILU'S.~
.4aa. CD
540 0
0 0
a I
0 t
0i
0 54
0 0
* U
0 .1
0 a.
0.4
D
C
tO
U
tJ
Cl
Y
111 l0
nr.1,, 0 0U
· I
IS 510 a
o 10
CD
Cn. I
P
a54
co a
54V}
.4
0 h
, a.
54 54
a. a.
oItII
e W
~
C;4
a0: D
0' C
I
;4a.
U
M
54 .
a.',.0
t.',
CD 0.
0! Ih
A
CD 5
.4
D.
U
54 M
-F
M.
a_
N
01
_ _
#
.H 0.4 .4aro
·'0m0
.4
054
UO
.CCD. I0
5
0.
a .\ .0
' a
4
a.
a a
w
-F
F
00.4a.
0U
rs t
., .In It
a ~..
A t
C04
.
U
tm)
* 0.
5 0
tD
.0
.C
0
a'
0.
N
cl 0O
CD In
.
5e
0 .
e
9-
0 .)
.N
0
aD .
1 U
_ -
N
N
5 M
4 4
P V
)
N
,N
N
C-5
TH
E
JOH
NS
HO
PK
INS
U
NIV
ER
SIT
Y
AP
PL
IED
P
HY
SIC
S L
AB
OR
AT
OR
YS
ILVE
R
SP
RIN
O.
MA
RY
LAN
D
aA.
r0'P
0cou4¢3
O aC03uM E
na,-
,4z0
*0 0
3 0
O
U
.IO
3 4
,.In000
40CD
bl U1M.
a u CD
u3 a,
E
a
00
A
U
t!
3 .
.-
3 H
H
C
CD A.
.
H
a D
A
.
0 0
3LI
A. E
J
H_
a4
Ae
U
DIn
LI
CD
a0o tt4-4
tD Ua
0
'U
C
~I
vJ .M
U EJ
34·
4 F4
ED H
-
0 0n
3 _M
M
CD 0
31
0 Al
CD C
M
3 3
.4
4IC1: I43aH'S Hto a.0Al
0 CD HH5'
CDUco E.
0 C4
0In 03
zN
3
O
A
0 U
4 t
a Y
Zo
aI
4 u
u u
o.In
In LI
tI EJ
(A
t In
0
! 0
0M 0
-N
MY
ecN
N
N
N
N
N
0
M
M-
en
M
0au0ad4INa
0 U
3 0
C
40
u
4A.
UHInM0aaHo 5'
MI
aUU
00a3D-H.
41na
Z4 4
3 H
l 4
\4 4
I
0 C
M
0 N
g
C
3E
D C
D
Z
ED E
D
4 A
l O
C
3 .-
0 M
N
A.
CD CD
.4
H
CD
CD CD
CD 3
3Z C
4 Yl
Yl .
CD Y
H
H
A
3 H
A. a
a M
.
M.
H
3 0
Al M
4
Al
P.
4 4
C.c
0 3
IC3o
In .1
.a L
0 In
u
u 4
0 .3
u A
l
S.-.
HA
.u
3'-
4 .
.~
InA
OHu E
lA
*1 ICN,
o
\' uD
E
Z;
-U
u
c
H H
zo
u i
I *z
.4
4la ~
0 >( A
c o M
cI
_
* F0
3 .4
.4z
* _-1
30
LI
In z
:
In
u CD'S:
* 3H
31 D
I n
I0
D
I- C
0'
0 _
N
M
-'
r0P1
M
n M
M
*
* e
* *
*
C-6
44o3UInV-
4D34DAl
1-4UNa4 V
]
TH
E JO
HN
S
HO
PK
INS
U
NIV
IRS
ITY
AP
PL
IED
P
HY
SIC
S L
AB
OR
AT
OR
YSIL
VE
R
SP
RIN
G.
MA
RY
LA
ND
40
Ii-
eo0
C
t)D.
a
cc: t, ~
In
m
n
e O
a.
, 04
40b.
"rim
0.
VIn
In=.
o71 0H0 o L0
0 1 -k
o 0%
rr O
0%
P
0% tO
llO
0%
I] 0%
0
's
0%
H4
*) H
00100.InIn00 mo 0Io o 0oGac
0-I
0I
i0- 4
4
Nl tO
a a
U
H l
a 0 a0
UI
U
0 U
U
W
I
0 0
N
2 0,
0e In
0% in
In In
In
Sn In
0%00%0alU.4 uL0%'NInA.
C3
0
000.4U
o In
e lN 0
H
10
0% a
H
a. 0
M
Um In
U
'a
trM
0% C
-0
in
n M
MO
w
V
0
0%\1
M
0%ale
e
M
Hw
d .I H
tN
a
10 '
m
e m
0.InH0%P.
o D
0 1 00
N
lz
It
64
0%HK PkPkHItInVi
InHk0%
0eI4
.-4
IC
N
D
a,
H
0 M
a
-N
H
0
0 ,
.4
C
I0 U
K
m
I A
e% Ui
,. 0.
U
o In
U
m
=
{_ U
0 V '
r rD
%D
%
-V
C-7
TH
E
JOH
NS
HO
PK
INS
U
NIV
ER
SIT
Y
AP
PL
IED
P
HY
SIC
S L
AB
OR
AT
OR
YS
ILVE
R
SP
RIN
G.
MA
RY
LA
ND
I.-I-~r,r a,03n-IC/U
)
0
aH.4HF
.
2 0
In U
a O
02 F
c
U
V
,C
tH
F
:0i
0
No
00000 00.40 0 00 o0i o
.4
Y
_i D
0d0000a
0200I.0 000
0$'ar: cm002 _iW .40l.4.4020coIt0.4It.4.4'.5
02-CC
In
I
.4 P
2W
i W
.4
D
D,
W 'IIM020020.402WIt.4 i.4.4 W ;a_i a.4.4 02
a 4M,
W0wIt w.
00.4
.4
.4.4
.4_i
DL
.4
03
.4 .4
0P
.
n.JF-EH
F0la
in ID
Q
ir
tn .w
ID PV
F..A
; 1
a0.s
l_
F-4o
0:oF
o
C
I
2 0
a.a,g H
0
a. It
e112
c H
co
0 I.
o 0
0.
.C
0iaa
a
a 0
a
o 02 .4
0
I W
P H
0
t
I .4
0 .4
V.
0o
C
E
a,
o
:,C *
H
.H
N
c:. 0
eI
0i
0.
.4N
.X
D
i
1 v
_ D
'A
0
0 O
2.
C-
.4
0 O
D
D3
.4
.4
Fi
VH "
"
.4
D
D
Am
ffi
D4 m
i a
In -
0 04
-N
0
m
0.
1 0
a 0 au
W
0i
Ca Ca
Ca Ca
0 a
1 Ca
in
Ca Ca
pn
Ca D
02
U
tn
i .4
W
U
W
U
O
U
W
u
vW u
V
u V
u
C)
U
U
t
en a1
11 10
ID
CD a
0 N
m
i -
H
H
rH
rH
rH
H
H
co
CD CD
CD
V. D
D 1-
W
0 _
N
12 :r
u1 ID
c a0 0
02 02
a,
0m 0a
, o0
C-8
TH
E
JOH
NS
HO
PK
INS
U
NIV
ER
SIT
Y
AP
PLIE
D
PH
YS
ICS
LA
BO
RA
TO
RY
SILV
ER
S
PR
ING
,. M
AR
YLA
ND
WLI,MIr
'i
a ,-
0 HtC '4EO 1 2
U4
aV
o U2
40
CJ '
=
O.-
In
0.
-o4
4
Ul::a I.U.
C-CInVl
0.00 '400tnInOa. In 0. I,Q7U C-,
0edC.b1
000
*U.4
0D
1"
.H
'I
E-
('4 0.1
4
' .
IU
En.
r0, ·In
'4r
65
'S0D-
a
U~
I0 CD
C-x
mU
0 h¢
aO
o
64W
U
-. .O
0 0
0
C
.
..
In .4
W
U
4.
_0
00
0
z F
.0
U
E)
C,
N'a-I
0
c.
e4
.;
0
4
U'Im
In
C,
HI
FU1
V.1
.0C
0
.
u W
a 2 '
'Shi
H
N4
H0.
Pk
4 1
H
I
N
NU
U
_ H
-.
S
0. 2
D
U
0.0
0
IN2
's N
U
.
e U
a P
.C
:
C-C I-
0N
Q
.U
N
P
l N
0
N
0D
. '4
, 0
U1
0. '4
0. '4
N
4 .3
0. 4
0 4
0. 4
0 In
11 0.
[ 1
.i
0 .4
.
Cf VD
1 0D
' 0
_ N
f\
VD 1-
O
O
a a
c -M
_ r
_ _
_ r
r r
r r
r
Dn
C"
a je 00.0.
U,
~~~N U <
4 0
I M
:r .
* £
C~
~~
~~
~E
c11
Cl
ZQ
to
P
: v)_
'4
H IC
C
0. 0
. 0
U
I O
z < z
FE
=
:
H
N
2Po
3
0 D
U~
~~
l
tC
_ S
_
N0
V
_l
_ _c
-E
D
ru a
a as
a~~~~~0U
C
-C
N
a
.4
0. .
N
2.4
r r r
r p~
~~
.0
C-9
TH
E
JOH
NS
H
OP
KIN
S
UN
IVrR
SIT
Y
AP
PL
IED
P
HY
SIC
S
LA
BO
RA
TO
RY
SILV
OR
S
PR
ING
. M
AR
YL
AN
D
VHnI
in
RN
O 0
O4~
~
rnU~~~
rv U
rm
ao I ob
DI
10
~~
a ~~~
~~
~~
=
r e
1
O
14
[U*-
11OO
.I
~ H
U
~q
H
t~U
-
Enr
e r
N
0
rn
W
-1 0
CA no
I
F c
a4 L
a 1 I
e IJ
-
O
-
rn
1 a c
.4
P r
0 W
cn M
l r
-O
N
.J N
.I
a n 4
Da
I
N4 W
A
1
o e
O
.O I
0C
.U
eN
0
1. 4
1 N
Dr )
W
A.
Vn
IL
i .=
0
D.0
W
.
D
0 -
O
IC
Oa e
w
F4 C
. N
tntn
I
e e
V
I
a O
rc
~ sa
0 o aC
cl e
X
e eL
i F
4 rI
I H
o
.L uiV
O
ffi e
rH
Dz IJ
N
H
I
W
e 0 O
a N
aa
.N
IN
U
I
H
U
a 2
0 H
N
D4
r
U
N
TH
E
JOH
NS
H
OP
KIN
S
UN
IVE
RIIT
Y
AP
PL
IED
P
HY
SIC
S
LA
BO
RA
TO
RY
SILV
ER
S
PR
ING
. M
AR
YL
AN
D
0
LI
4
0Eh I
a 0
O
0A
. 0
_ *
* *
* _
=
a -
--
I -
-
n In
4
e e
( C
I
Io
DI
Inc
V
n In
o o
0In
`I
I 0
0 0
0 0
I
PQ
t In
n w
.
0 q
PQ
M
9o 0
0 _
0 0
0
.0
0 0
0 u
IC
IC
I. I.
IM C
a M
N
I
N
CZ
0
19 0
0 0
0 0
0 N
N
a aN
oa
a
a a
10 0 11
In N
N
N
N
M
N
C
M
e eM
C
C
Oa
IC0a
I I
M
0 I
I in
I In
a
h 0In In
H
M
I
j a
i In
In
S *
O*
ooo
o*O
W
N
e O
hiO
h
iC
N
4 N
O
O
V
n 1H
0
* n
UH
I
O
0hiU
U
U
U
l
UV
U
U
C
_C
V
l C
U
V
) V
l DJ
l l
7 C
0
0 V
l C
14 H
0
V
H
U
I H
In
14 14
1 141
14 14
HV V
0 H
4 K
O
4
14 U
4
h U
U
U
°
U
° O
4 IC
O
U
U
° U
0
0 0
0 0
0 d
d
o u
e e
; e
e00 0
0 0
0 0
0 0 e
:C
0 a
0 0
5. 0
5. 1.
5.
1. 5
O
.0
0
0 0
U
U
5 1
H
I H
H
H
H
H
H
U
U
U
14
H
I1
V
1 aI
a 0
U
0 0
0 1
Inj
d 01
a 0
1I
4 h
i bl
hi
hi
hi
i 0
0I 0
I In
t a
In l 0
D
O
0 a
0 0
r In
U
a U
0
5 *
Sa
5 C
5
0 5
1 5
* *
* *
* 5
* G
4*
0
C-ll
TH
E
JOH
NS
H
OP
KIN
S
UN
IVE
RS
ITY
AP
PL
IED
P
HY
SIC
S LA
BO
RA
TO
RY
SILV
ER
S
PR
ING
. M
AR
YLA
ND
CIN
NIC
M
MC
MIe
CIM
00000
00000
_ oU
(su
I U
n U
0 m0N
Cy m
Dom
-O
P11110
CY, O
jm *
s P1
mO
Cn
D
1N
--1- S
t I
I C
1
ID I
KDs tlc
e
D D
1-
I 1
r-0Grr.I,uV
P
N'a
00000000000
00000000000
00UU0.
00000000000
00000000000
II
Vl
VI
a 07
In
VI
o4 D
=
O
_ 0
O
0O
OIc I
I I 0
0a 0
a 0 4
-4
o P
·
D .
U
14
1U" m
U
..i 0
0
Oa
0 -
-
V)
UI
5 0
* *
4
go o
m
0
O
U0
D00
U
0 U
.4-40 0
Hk U
U
oooooooo
00
00
00
00
00
0
In 1i
11
11
1
a et
-c
,n
c O
a
N- T
0U
9.
..
.1..
.
H I
I H
I
I r 1
O
I I
CN
m N
11 I
1 D
I-
W C
o
IH
_
t4H0
C-12
Ca
I.L
01VU
U,
41, f
U)
W7 M
VU V
I V
l
0. .
0.
o 0
0
C
En
U_
_ _
cn n
,II
II
0 0
0
IC IC
H
HH
..P
.4
H
6 4
la
Ca
We
VI
ZI
Z
U
U
UE
U
U
c U
U
H
o H
.4f .4
SU
U
m
0 a0
H
H
U
U
UH
H
0 0
0U
U
U
, ,
U0
0
.4U
co
.4
00
o
o 0.
0. 1
U
O
U
-4
U
0H
V
U
TH
E
JOH
NS
H
OP
KIN
S
UN
IVE
RS
ITY
AP
PLIE
D
PH
YS
ICS
LA
BO
RA
TO
RY
SILV
ER
S
PR
No.
MtY
LA
ND
010?o
0000000000
ooooooooo00000000000oo
00000000000
00000000000
00000000000
u U0
00000000000
000
0 0
00
0 0 0
0000a0000
0
o o
o -o
oo
oes
O
OO
O
Ch
O
O
b
C D
NO
W
-t
0 0
0 0
0 i
0 0
0000
000000
D. I
I I
I I
I I
I I
I
_ N
0a V
c
-a
O O
m
I0000000000
W
I00000000
r 0
aIU n
53 I
twa
O
11 0
00
00
00
00
0
D.
Cl
O 0
U)O
W. 530
D1
- 0'*
0 O
tD
vw
~~
~~
~c
Oa
-1U
5 In
r :r
o D
0
tD
_
f f
i~f~d
1n
0
_ 0
0 _N
0 0_
CD
-
a. 0
D
X
F n
Wl rz
m
t X
W
y:
I I
1 11
PI-N
. 8
-I-1
02 0
1--e
n0
N_
-4~
0t0
00
00
00
00
sa .
5D O
O3_0%
x
1 0000 0
00
0
D-
2KK
00
00
00
00
00
0
H 0
0
N 0
0 V
) 10
N ID
0
2 0
0 P ~ r '1l
' .
P l
tl 0
* 53
0 ,fl
a'
K~o '
.0
10 9F
0
a.H
1
0 N
U
~O
c1 0
N
I I
I I
I I
I I
I
U
N
_0
0 C
OO
O
00
00
00
0
IC
a W
W
D
.4
i
.
=1'
00 0
0 0
00
W0
0
cu· 6
4···
000000000I00000000000
0
YO
1
It cc0010,
.--.D
a W
a
e-s
0 C
, 0
F. Ia
0 1 N
fP
l f
0 .1
o U U
I
II
iH
-H
H
I 0
0 J
C^ 0
J C
W
H
-. m
a.
W.
aa a~
~~
~~
~~
~~
~~
~~
~~
~r
C-13
a. blt!:.EI.a.
TH
E
JOH
NS
HO
PK
INS
U
NIV
ER
SIT
Y
AP
PL
IED
P
HY
SIC
S LA
BO
RA
TO
RY
SIL
VIR
S
PR
INO
. M
AR
YL
AN
D
I I
I .iee
oo
o o0o
o0 0
oo0
0o
o O
o
oo
oo
oo
0a,
00
o
o 0
00
00
o0
0o
o
o!
v
0 00
00
0
0
00
00
00
00
00
0c
C
r. te
e e,
fr m
0m
0C
o
co i
Om
oo
co oo
a o
o ,o
o o
o oC
o 0
0 o
O
W
m
e- r
N
l ed
r 0
btm
t
m-
-_
_ ol
4 aI
la
ip -,
ei
o-
_~
1
S re
o
o m
r rr
r l o
io o
a
meaelU
=V
=
UW
00
o no
oo
oo
on
oo
oo
0 o
o O
IC
.. ..
..C
Q
(0 o
Co
QC
o o 00
CC
00
CD
C
00
H
: m
lY
D,Ir.
N
Ntn
U
,In
E
n
00
00
00
0
0
O0
00
o0
O0
00
00
O0
00
00
00
00
00
00
00
00
00
oo
oo
oo
00
oo
0o
m
MI
a0
00
W4
Po
P4
fD fto
--
t CD It
a:m
m
$
tVU
U)
U)
0t0
0OC
..
.1.
o 1
cr
Oft
*-
a-ae
oA
l--3Po
00
00
00
00
00
00
0 0O
0
00
00
oo
oo
00
00
ftft *
* *
* fc
.t *a
* 0
0 0 a
00
0
0
00
0
0
00
0
0
00
00
Al
AW
W
IA
D
I A
.
C.
M
Ib m
f mf
mo-
NO
o
r- -t
o 1-
o0-0
%N
00
CD
o
O
e t
tOfN
O% V
IOD
r~
t %
r
ot
tftN
NeN
N
O O
%
O
ft-
.0
03D
3eo
o O
t VD
D
me
*o
o
m
ftN
NO
0
0
OU
t U
_ -1V
D
V
1 S
N
(N
e
eO
e It
IC
r- fc
CY a
C-1
4
ml
I I
0')
f,,
W
o u
m
WO
D
.
.e
a A
r,
O
In
P3
o m
m
Ft
a.
0 A
,
0r 0
TH
E
JOH
NS
HO
PK
INS
U
NIV
LR
SIT
Y
AP
PLIE
D
PH
YS
ICS
LA
BO
RA
TO
RY
SILV
ER
S
PR
ING
. M
AR
YL
AN
D
~~~~~rD
rn~
~~
~~
~~
~~
~~
~~
~
Io
e
Gh
CI
tr~r~
tIna a
z
o
o N
W
i n
I{
0I
-J~
<~4
.u
0
0 U
o I
on
0 0
cc
n4
O
0
V)
c o
C-
wb
4
4 C
- aN
I P
In 0
n e
0 4
O
U
e 0
InI
(I
InW
H
° C
W
v I
D 0:X
a o
00ra
0 In
I D
Oq
.4
P 0
0
O
r
C
-15
4. P
;C
0U
a -0
CZ I
*.3 0
ILD 4
0A
C-.
0A
M
b W
E
01 0 0
c0
0 0
I C
0
C
0I
H
.4 0
0 r vnC
000
L
0 0-
0 0
tnH
0
TH
E
JOH
NS
HO
PK
INS
U
NIV
ER
SIT
Y
AP
PL
IED
PH
YS
ICS
LA
BO
RA
TO
RY
SILV
ER
S
PR
ING
. M
AR
YL
AN
D
r 0
e -
,,rsPo-0
W1
00
W0
0F4
O
4.
0
4 u
O
_
o - 14
al .4
0n' U
a m
4 W.4
4 W
0 0
to
0UW
aW
4F
401
4 .4
; o3
a P
0
04 .4
C
U
1 W
0.
0
.4CD
D0
Ir C4
.4 00r-0(rIC
Ar
40I
.4
r c0
c
oo
m0
a4U0
r;4
0 U
Iz F
4
4 .4
V04F4C.4UUUoU ue40r U ,tcuDI
O,,..4Ca
1O adI-0I OU0u
0 14
U1E4
14 HIC
VI
O
W
o0
0no 00U0014
IC0F
4
0=
14
O
0.4
0S
DI
04 H
14 14
d 0Ic 0
; U
14 F
4
F4 ;
U2 D
0 0
0 U
0 40
U
a:
;cl
amd 0
; s:
0 U
*-
.4
F4
0 0
I 0
I0
H0
14 C
o
.C, r-
_9 4
.
CD
a
.4r "
.4 I
Is
:s
44 o
m4.0
u0
.4N
_
00
0
0 0
Ca
0-4
O
u
0
14
0
05
0 1
H
01
0
0 ..
4 1
C-1
6
0.CMr=P
0, 00U0I-DiH
0 11-D
,
-0,Ca
MpaW V1 04m0l
14H0WQ,-C 0
a
.4
C,
F4
; r
.4
0d
04 t
W
MJ
F
t.O
0
J'4 F
4C
I
005 00
D0 O a
0r
1.4a
4 IC
I 0HE
4-C FV
10-
*I)4F
e 40
;
.
Ua
Ca
c
O
.40
0l
.4
00C
00
040;
¢U0
0a
.-4 01
0 U.0
A1. 0
0
H
0)
-
TH
E
JOH
NS
H
OP
KIN
S
UN
IVE
RS
ITY
AP
PLIE
D P
HY
SIC
S
LA
BO
RA
TO
RY
SILV
ER
S
PR
ING
. M
AR
YLA
ND
L
/ e
Qri
uiU.
oZoKi
IL b
/ k 0
, a 7a-
w'/
./
Xz
W
lZ
" o.
7. .
D
-
i 4 I 1
og ~ ~
~ .u
FiI
C-
.0
IhS ~
~ ~
--
C-1
7.~
L
C-1
7
TH
E JO
HN
S
HO
PK
INS
U
NIV
ER
SIT
Y
AP
PL
IED
P
HY
SIC
S
LA
BO
RA
TO
RY
SIL
VE
R
SP
RIN
O.
MA
RY
LA
ND
0
Zr
or-
,(/ OLLI
0
r/A/
~ ~
~ ~
~~
r Q
w
/ _
h /
lu/i n
A
QQQ.
ZLLJ
a/
w
cci
E
n CDo
Ijr I
_/
C
-18,D
u u.
_ ::
I I l
Lp
r LE
L
L
C-18
TH
E
JOH
NS
H
OP
KIN
S U
NIV
ER
SIT
Y
AP
PLIE
D
PH
YS
ICS
LA
BO
RA
TO
RY
SILV
ER
S
PR
ING
. M
AR
YLA
ND
rr
0-z
00
IL
LI
iC)
LmOa-iii
7 R
x
/0Xiu
v _
<
u ou
I r~
~~
~~
~~
~~
i u
<J
0-
F i
<
Id F
-0
4 h
C
U-
.J .
.E 0
c-19
THE JOHNS HOPKINS UNIVERSITY
APPLIED PHYSICS LABORATORYSILVER SPRING. MARYLAND
APPENDIX D
Example 4 - Thermal Buckling
D-1
T'?PT
.TT
N(C
PAG
TE BL
AN
K
NO
T FM
ED
TH
E JO
HN
S
HO
PK
INS
U
NIV
ER
SIT
Y
AP
PLIE
D
PH
YS
ICS
LA
BO
RA
TO
RY
SILV
ER
S
PR
ING
. M
AR
YL
AN
D
LU4Q0.
LU4ft
Nr-U'
crIUX
Nr-crIU4:
Li
004-0Ui
L.) WW,
0zx
-4X
_
U
Li4-Jz
43 .~<
M
I.
Li) Z
Ili L4:
I Wui
-4 -r44
WO
.
LU
U
(A
J <
-i _J
W
-4 L
L ft
L -
C4
VA I-LitW
UJ
_ <
.)
1- U
IU-I
4
U-) ft
0
04c
ZO
.
.42-JZ
W V
)
U!
wft4IV'
0V)
LU
'A
~~~~~~~~~~~~~~~~~~~U
-4O
O
I :
I:
0
w
V)
-J D
.~~
~~
~~
~~
~~
~~
~~
~~
~~
-
at ~ ~
~ ~
~ a W
.C W
u ~~~~~~~44
Li~
~~
~~
~~
~~
~~
~~
~~
~~
~~
LC
I J
W
vU
0.
Oi V
, 4..o
U. D
E
z~
U.
4
WU
5),
~J WU
4- z°
VI
et
U
.
0 4 -) 4
0. x
U
D
ft t
~J
W.
W
WA
.4-
W4
ftKC
C
0:
CD
v
<,
ft -4
44
Z
4* J
cx~
~~
~~
~~
~~
~c
U
a} v,
o
L -i fU
' 0-
U
0 .
L O
U
.' v
Z
2~q z
q a
M
cU
M
w
U. Cf
Z
O
.-
O Z
Oa.
Z
V
Lu'a L
W
-U
Li)Y
-
U
z v
, ,
-U
) Z
U
-
1 0 *
21-
V
U.
-,r .4
.4 4L
*.-.
ftU
1
U
..J L w
UW
J J
M
f _
cr M
vm
J I
V)
_ U
Y Y
-w
Q
C
cY
M
J o
L
) M
i
L U
) Z
I
O4
L .
V)I :1
O
Z
-IW
U
.~L
4 4 m
L
iL)Iu
4-L
]Lu
m4
rn
I C
O~
)
J1)
OW
Li
44
U
) V
Z
Cft-_
-L O
0
z v
J M
u
-J
r suI
Jt F
j J iL
J
-<t
J J
<
LO
J
UC
M
.W
IJ 0
J M
4
Vt
Q
J I
UL
-
-4
-4
4 -
f --
l -.
ft .
I40ftZ
W
~
4-
F w
-4
_W
O
O
J I0
OW
4c410
W
Y
w
vlAW
CO
I J
U<
.
J4U
') n
I z W
W
cr U
) r
f W
C
W
J
Y
WI L
Y
cr V
) S
FD
1L
Q
W
v
1F J
OcrW
~~
V
)l V
tOcfW
J Y~
OU
Z O
J
c~.J
~WJ~iftW
.J~fW.J
3 t0
r
0-1
.44
C-4
-fU.0
Vftt4
l/WIO
WO
CW
I
O.J
ftftW
Ov>
OU
rc
nw
~v>
C
ol ,w
FF
U:Z
c
Z-J
-
Ct
-ft
J4 i
4S ft
D
J L
i 4
UJ) 4-
D
4- WU
f__
1 Co
W
CJ
W cO
J
OO
O
)OxL
0
_ D
r
D
IU
J J
4 u
IV)-O
iA
1
V1
tL ft
m
4
OZ
4 O
i _.
N
mt
41 U
) 1
- i'.
U'
0 _
N
(' '3
UA '0
1-
CC cr 0
-~
N
m
4 A
5
Vi
O
-4-4
_
_ -_
-_
--
N
)IN N
N C
N
D-3
TN
E
JOH
NS
H
OP
KIN
S
UN
IVE
RS
ITY
AP
PL
IED
P
HY
SIC
S L
AB
OR
AT
OR
YS
ILV
R
SP
RIN
G.
MA
RY
LA
ND
D
o
Co
<
_ o
r,
_
LU
.0
4e
e
a
U
0 I
-O
LU
Cf
t r
o
D
' cr
U.0
'0 .·
· 0
1 '0
IrI'-
4 O
U
0
.m4 N
f '
0 O
w
LU
_ I
_ _ Nal
P-
C
r _ -N 'LUrlU.LrULULULU..
Nm
N.
-r
=
0
co 0
00
00
00
00
00
00
00
00
00
00
rl (I~ ~f
Nn
Ix cu
tp
NN
u
l ¢
*Nrq
~In
-Wu
.4L
UIU
)¢--
-4N
.
LU
LU
-
N-N
N
N
-
--
--
--
O
0 0
00
0
00
00
0
00
0
00
00
0
00
0
0 'U
IX ..
4 N 1
.I~'0
I W
W L
UoooooooooL Uoooo,-I.
Cf
N ~ t
*L U
I'JI K
.
Ict m
m
fl
t C f
C
Y
It -T
I IT
It cr c
c
4 N
NN
NN
NrN
NN
NN
NrN
N
L N
D
L 0
30 0001J0000000
3
0
AZ
W
W
D-4
-Jz1~
,9+
,,~C
,~*t~
~+
~+
**44
O~
m~
~~
~m
~gm
ON
~S
~O
Nm
~~
~~
m~
C~
9-
~3~
~~
~~
~~
NN
~m
mm
mm
b~
g**
-ly 40 ~
~ ~
~ D
-
TH
E JO
HN
S H
OP
KIN
S
UN
IVE
RS
ITY
AP
PLIE
D
PH
YS
ICS
LA
BO
RA
TO
RY
SIL
VR
S
PR
lING
. M
AR
YLA
ND
Lu4aLD
o-r"r-U`
O
0 m
0
I c
I N
rG C
:
U
L *
.
srC
U
J~
~1
:,4
031-IrL)
-. _ -
_-I N
N
10
UN
UN
U'
.1
%,
, )
_- N
N
4:-
--
-
'i U
' N
IA
'_
l _
N
N
N
_ __
G.
0.
..
C.
U
LJ
WU U
J Z
I- I--
-I-
u-
0 Z
-
N
m
I,
-) U
In In) U
'L
'C[ULI-5
D-5
-J w°-
-1'3ul
w
uJ
Z 0YC
D
2 x
Ul V
,
D
.
(
TH
E
JOH
NS
HO
PK
INS
U
NIV
ER
SIT
Y
AP
PL
IED
P
HY
SIC
S L
AB
OR
AT
OR
YSIL
VE
R
PRINGla.
MA
RY
LAN
D
LULD
4a.NI-0'Ox
z0U -2. LUIJ
Cl
C
1)
4a. Li
C
CL
0- O
UJC Z
U
ZO
CD
OY C
U1L
Z
O
Z
L
C
44a.-
wvr
V
4U
ct i
Z 0
,ia
Z
xi
LU
-JIv}4-JzLi
C)ZuJ
NLI
UJ. Li
LZ-I0L-
UJ
00CV)
-Z
_ It00
--J
O
Z
-J U
J;
Z-IV)
ZZ
.V)
UJ
V)LUI.-
J j U
L
_ -t
ZO
L
X
X-
FUJ
0 t.
a.
U
O
OJ
I- U
J I-
X
-L
U
V
W
O
F O
i
-. 7
.L
a.,
4DL
CL U-VL z a.-J
U,z
z
LLi
-JV) Z
Lf
C
>L
_ J
ILX0
LU I-L
O
'>
Z
OQ
.
V o
z02
LL
U
A
40 ;
-c
-JLU
.-4 IU
Z
LA.
UJ
-V
) I
'A
Li
-I-I.,_
-W
L
0- LL
i--U
i--(I
-. .4
D.
W! i A
It ID
`
'C
-.
a. L
a. -
Li
2. a.
-
UJ
_4 Z
IJ L
4.
aU
7
.. * a.
* (
a.J
.,
.-
JU
=
a. a
.a
a a
-,
V)
O
r LI.
-V
) U
J
U
C
C
UJ
F V
)
llJ
X
X
F J
D
w
-L 2
4-Z
.e
W
V)
Z
4rWU
LU
L
U
V,
LU
2. a,
,4
_ >
Y
N
Y
1
I -Y
. .-
-a.
4 1
a m
4
a.
J.L L
U
LL
L
U
) U
L
L
i a.
al D
. U
V
)
-rA)1
- X
S
(U
(rl U
O
0
U·
u 0
I- L
<
U
_J <
V)
U
a.
VA
N
m
Un
U)
4X 'CI--Ja.
4V1)
m EnoN
z LiS. 0. CCEn
UJ
z(VI-ItInU 7LL
-
LU
G U Ci
LU
a. L
I-zC.
Li UC
LUa.>Li
Li zCL
II
CD
:
VR
Li
2.t L
'
~U,
>
.Y
N
-.
L _
L
U
i -
Z
2 S -
4 4
.4
-,U
a
4 7
U,
La.
--.
L
-U
, -4
IU
J
Z
a.
4 <
4
.4
CL
J L
VA
a. L
i
CO
U'
_'
_ N
E
n-
-_ N
-
V
IV
N
D-6
TH
E
JOH
NS
H
OP
KIN
S
UN
IVE
RS
ITY
AP
PLIE
D
PH
YS
ICS
L
AB
OR
AT
OR
YS
ILVE
R
SP
RIN
G.
MA
RY
LA
ND
Li
U.,
4a041-IOL
a~
~~
~
42
UJ-J
zZ
D
I-.
_ V
I
wt
z n
Li
-z
I I-
4 L aU
l Z
LW
<
Li
UV
z
Z
W
c z
LZ
C
N
h.~
~~
~~
~2
Li^ A
Z<
I a_(2
0
CaU
': O
:
Li
i-"4
02
a a-z
cr
n:
o _
D 1
2!
V-
LA
U
u'
UJ
Z
LN
I
-a
-Ia
--~U
C
V)
O, L
_ ,
OC C
1
Li
ar
m
v
1 ~
<
l: F
s Y
U
T
rr
oL
tY
O
A
"4 z -L
Li
L-J
a
Lu
U1
Z
_
w
-w
4 C
C)
z 2
W
4-UU
* L
a2:
a I-
"
-V
) U/
-
Z
Z. C
"4
_ O
vr
"41 z
Z
w
W
u L
C
C
Li
a .
4/ N
a
Ni
LA C
4.
a,
4'10zL-JLi
UwuC.
VI
c. I- LDUCI-LI Li
aoz2!zc.o.;II
L)
z -
>L
a ¢
vl
Li
.4
4.z
p-
Cr
Y
Z
N
n)
*,
04-4I' v2
}
N
4'Li(Dxuz
Y 1-
4 I
rn" -
Li
CI-CZ
L
x U
;1 --
_ co
OL
2: a
o a
I-
* a J
I
Li
LI
LL
i .L
a
aLU
U
L
uLLA
0
N
aU
-I-O
" v
In
M
D-7
7-J-J.
dcUzZN
.L
Oi X
0 )
Z
~ 4 JI
-Li
i az
uW L
Y
Y
Y
Z
C?
Y
Y
1. U
V
IL
i ,.
LA Li
N*~ 9'L
.J Lfl
or '4*
'T
oLza
-a
-S
wo0YZ
(3
a tz
-4-
of
-J
Y
<
a)
oQ
-J
we
er
" '
D C)~
I C
<
43LvrI
2! -"
C) -
4
al
._
L
C· a
, Li
TH
E
JOH
NS
HO
PK
INS
U
NIV
ER
SIT
Y
AP
PL
IED
PH
YS
ICS
L
AB
OR
AT
OR
YS
ILVE
R
SP
RIN
G.
MA
RY
LA
ND
r-W4NVF
I4 uw
Z 'A4 0z -JI04 I-'A02: wtIc 0zW)
1-40.w ItI-Li0.I-0 LiwL x 0.4LLLi
II
I W
>
Z
UW O
( 4
(2 -
a>
Z
o:
a:
J y
4 U
L 4
U
( I
V)
U
I C
L LU
u
-UJ
zu.
VI
V)
V)IL-0
Z
LL
C
Z
Z. 0'
-0
z C
>
~LO0.
A
0
>Z O
CZ
0
0.
4 0.0
Ul
-
'Azz(2wV)
LI
1l0 U,u VU
_ an
0.uuuO
0L Y
Li~
~~
~~
~L
Z:
.C
W
Z
L .
N
iY
o
O
z
t:4 .4
z -4
.
i 0
I- =
In
w
Y
LU
J
r*
4 W
~-
0 e
(2 0.
..4
4 *
N
(2I
.4.4I-
vr
U0
Z
13O
U
z_
0Li
ccN
4
In
I -I
U) N C
U,
N
0. (2 I
.. J 0.
0.
(
( c
'40zL)Li
N
IIL
(2
It N
I-
-J .J
Z
)
-1 4.1
IVa]
I IX
_j
j :
zzbe .40
NY wWJ
0 Z
1M
--
JC
z
.II
y VI
(2N
Z
4 a.
( .
IL
V)
* ye
I .4
N
, .4
,I
.4 W
Z
J4
Z
IL J4
4 In
Z
0 Z
a.
0(2
b Y
J
Y
Y
J
U
u '
) n
u .u
n
n u
u i
' l"
I O
'
' .
.'
.0 Q
'
v0 -
r-
D-8
1-
4- -
i -iJ
z z
J -
ZLi
a W
U
0
. w
w
Li
_ IN
v
w
-W
U
z -
aM
z In
0. m
a
z w
YI
w
Y
04 y Y
zO
4
4 0
0 IL
424
(2 O u
Li I
4 u
LUU
-
L)
( 0
JI
_J Li
O
a L
4 W
J
LU
wr--J 0.0.
CZ(2U
)
tuo
cUa.Z
0.
-1Y
YU
L)
I
Uj
zLi a
a I-
-Z
-s
.to
Z0
1)
0.
-Li
uC
L -4
'O.
I-L c,
>Z
w
-
.J (2 U
02
W
N
(2
zo-LL)u0.
z
cY nw
:2
0.I-
CU
TH
E
JOH
NS
H
OP
KIN
S
UN
IVE
RS
ITY
AP
PLIE
D
PH
YS
ICS
LA
BO
RA
TO
RY
ILIE
R
SP
RIN
G.
MA
RY
lAN
D
C,
4'lf-U42:
ZU'U,.La
, a
Co a
-Y
C.
Vb
aLL
aY
' -
heb
: -
Z
CZY
'/)
W
v,
ur
y
1-=)
x
C
C
L
;N
m1'P
70x O
4C
. 4
.J
U.
Ga U
-1
Y
J4 >
UJ
-
4 en
J U
J
UUUU-J
OY
C-w
a2:
U-
<
en
Vi
y -J
:3
cIx'o
UUUUwU0 C.a
Li0 .4 CA
Lienbe
~(Ct _
IZ CA
-Ib
ZC-
UJ
UV)
Vl
1J
V) C'
-.1
aa tLa itDVIt
aItY
3 ,_
Sz o
r c ;
W
L.
CA
J en
-
-. .
C.,
I/33.4
0
"-
I'-
*. .0
L
U
5,
.4
CA J .,
a LI
aJ .
,(L
L
L
-1
_ C
J4 N
Z
Z
>
4 m
I
vA L
r co
J c
u vl
U
wu
G
_ N
O
¢
U)
, W
) W
) 0)
WY
2eL) ru,
UUL
U
0.
aV)
aena
ULi
-JD aU-J.JU0
-S -J
.
Li.-I
aULi
-1 Z,
J U
t
It tU
.4
Li
-Uz
e:
e
J I
U
.4 .,
0'cc~
C.4
.4
.-a
a. -)
co J
in-
CD
C
Z
..Z
a
aV
l 1
i .,
a i,
<t
'I
VC L
iU
U
U!
U
L 2
I
I O
._
N
C
IC
CA
WA V
' V
' V
V
' V
' U
'
D-9
TH
E
JOH
NS
H
OP
KIN
S U
NIV
I[SIT
Y
AP
PL
IED
P
HY
SIC
S
LA
BO
RA
TO
RY
SILV
ER
S
PR
ING
. M
AR
YLA
ND
Ca
rir
Z
.=L
L
U*
0wL
JU
a
C
C
O a L
Li
CL
I :L
* V
_ w
V )
11 --
v m-
w.U
J4 C
Z
_-
Z4
c c L.
Si Y
G
. Ca
LIcu
0. Y
a
Y
0 i .
YJ
C
.O
1
a 4
VI .
-J V
. U
V
I L
U
V
0 .
V'
V'
V'
V.
La
.z C
Z~
~Yy _
Ca
~ ~
YU
N
V
Oa
--
UU '
I
Z
UY
U
. Z
n
Z
C aU
Z
U
O
t E
2 m
3
CD V
O
Yc Y
Y
J
e J
Y
Y
-J Y
1.-zZC
-a
ci I
L x
LU
V
L'
-N
('I
.4 U
U
L
' )
C- L
i_(
_ _(
_ _
_
U L
U
O
-U
L ) a
Z
-4
a I
LV L
i U
J
LU
U
, r.-,
, 0v
-v. -
--
_ _
_ _
-04
0 Ou
-L
L(n
oY
-
L-
L
C a
0Y
.4
U
_ (L
V
-
a L
aZ
LU
Y
2
_J
Y
ZO
U
I
<
O
I L
U
)L
1J J
L
U
LJ
_ N
(,J
4 It
V
la
1-
V)
'
--
--
-:4
-.
.4 .4-
__________P
_ _
_ _
_ _
_ _
__I~L(
D-10
zUzLi3 C!CL
C)
o.r.V-JO0
J4 I
n
_J 004
LUU
Ca,CaU Q.
-.t
-ZXu
LC
U
L0. ._
urO
0>
..
C
400
LaO
Z09-UCL
U 0LaC--
rn - Z
G
ZI4
U
(L4CY
In
2
U1
o 7- Li w
a J
2.II
U
L
mu
Z
cr
c Y
-J z
4 4
-U
_J
Z
CL Iu
v
TH
E
JOH
NS
H
OP
KIN
S
UN
IVE
RS
ITY
AP
PLIE
D
PH
YS
ICS
LA
BO
RA
TO
RY
SILV
ER
S
PR
ING
. M
AR
YLA
ND
C0aNP-v·
IX:
zo.CD
UU -J2Li
00>0 o
LU
CL
~
C
er
C)
M
0U
l z
0 '
-Cl:
D0
zac
-d
O4
L)U O
w LM
0-
ZI
6 V
V
L/ a
)if <
4:1 t
2w11
vaot0:
0i
zZ
ZZ-
f0
.
LU
O
0O
.U
0u
au
.Z
0 O
-O
N_
,-i
J Li
W
Vl
.
NY I
C
,-
4c '
-0-J
a Z
Z
i-
a- 0
-l A
O
.
u.
.v.
Z
0 U
2
I aL .
U
0 NY
Y
>a >
Y
-0
-2
-U.
0 x a
I 4
Il 4
4 4
W
J W
0
U
4 J'
4 4
Z
V)
Z
W
Dvn
0 62
0 0a
M 0
0 a
D
Y
Y
Y
0 JZ
Z
U
Z
-Z
z
IN
.-
a u
Ua
X
LU 0
0Z
he
UI -
0; t
U
O
IVi
0 .
q 0
0 v)i
0
4 _-
M
4 I.-.
N
MN N
N
N
N
______l
10 N-
L U
''N
Nv
*N
N_
_ _
6 0Z.J0zLU
0L.
LJ W24-400 a-
.0
W
4W
W
Z
LU
-1u
uj 0
CD
I- U,W
J a
>
C
'A
LL
0 4I--
I
Z
0 0.~
0
ID
c -
u.
L
CD
Ce .
* J.
0Z
r
NY c
., n
_
aW -i.
-
-Y
-
a 0J
C3 L
I
a _n w.
0 LU
W
LU
z .
cL
0
a .
x .
li
Lf -
0m
I-U
L
cK
vo
UU
_
0 Y
W
W
0
-.
..0
0) (
ZU
-
-F-
U
0 .
v -
20
--
4 -
4 NY
I- 0
4 2
UJ
-,I
a
_ t
.4 -
a a
-0
0a
-0
* -
2 0
v- in
2
Z
I -
0V 0
--
O
at LU
-Z
la
LU 4
LU a
o n
I
46
2
au
-w
0
rL
fi r
a .
0Z
>
O
a
W
D
a Q
o
O
U
az>
YLU
Ica
V=
-Q
U
) _-
a Z
Z
a
LU 4
00
V)
0
0 N
" M
w
I',
1') *
II M -
-4 -4
-4 -4
-4 -
AC
I0
LU
Ir.
qc >
0J
a -
.i>
ina
v)
Z
..
ZIn
V)
>
0.4'n
w
-
)- >W
L 2)>
I _
Z
N
U
-.
a -
Ca
,.c>
4 N
X
Q
o a
Ca
N
Ul
-a
a >
Z
O
0 U.
4 0 w
I) U
V
i
a
.4
r iL
*
r U
_
e nl
I ~l
s i
D-1
1
XM-
I.J
av,3iaN.-
TH
E JO
HN
S
HO
PK
INS
U
NIV
ER
SIT
Y
AP
PLIE
D P
HY
SIC
S
LAB
OR
ATO
RY
SIL
VE
R
SP
RIN
G.
MA
RY
LA
ND
4 UJ0NI-ICL
zLi4-4O CL
0.CL C
4 C
LmI
CL
UZ3
-A
-V
) L
Y-
-0
Z
DL
N
-C
w
fi U
JC
L
L
WIu
x C
D-4
Z) 4
..U
Z-.J2I24M-
aC'0.4
I)a
!~Z
LU~C
-J
J '
L
L.
L
L
L.
I tn
to
2
Z
Z
Z
Z
Z.
..
-.I
N
x z
3E t 0
Z
tr m
m
-
z c
Cc
C Z c
z v
a -
a '
a ,u
u a
w
oI-
cc CD
cc '-.
CD .-
C
a
CC a.
a.
a -
In
9~
~
4 4
1 nD
0
n I-
n I.
I 4
uo
p~
~
CL
4 C
L
4 L
4 C
.4
0
. .4
0.
.4
CL .4
0.
.4 cL
-
L
g.4 (P
l4
O
N
i-
i-4
.3 U
%)
U
I m
) Cr
LU_ U
LU
L -
-_
U
D-12
toI-.JCLCL
o:O
CD
_ X
Yo
2 I-Jz
CL
-w
-
T. <
1 a
,) o
r L
UC Ln
In
U_
_ _
_
-
THE
JOH
NS
HO
PKIN
S U
NIV
ER
SITY
AP
PLIE
D
PH
YS
ICS
LA
BO
RA
TO
RY
SIL
VIR
SPRIN
G.
MA
RY
IAN
D
VLUU
"
4 F
Lu a
Oa~
x
rrC
t
uJ
LU
O
"XW
I-.
Q.
I .
D.
OW
U
a.
O
e4 VU)
-,
4 Q
I
Ln Z
-
'
4 LU
U
a_ I
I z
o
u O
0 H
i ,
-a.
O
wW
D.
Li
Uy
4
LU
iO
[ I
a. a.
W
.cc
4 U
..I X
QC
0
a. CC
V
r= V
.
O
s L
W
-w 0.
LL U
2
O
V
-ut
LU
U
QL
,V
D
--.J J
.J U
-a
<,
z 0
lU Vu-
K
:1: rX
pa
LU
2:a
OI
-
0 Z
L D
-13;
1-
TH
E
JO
HN
S H
OP
KIN
S
UN
IVE
RS
ITY
AP
PL
IED
P
HY
SIC
S L
AB
OR
AT
OR
YS
ILVIIE
I G
11N
. M
AY
ILA
NO
in1m4.m-I
O
IO
at a.
4 0
K
c
o o
Z
ZW
wu
w
wZW
-W
Z
Z
w
Iu
o 0
Vo o
_ _
aU W
z
C
Ca.
u 4o
Cl
o
z
_ -CL
I i
I-
Z
a_-
_
N
a N
a
W
z
o a
V
W
W
Z
Z
U) w
V)
NI
_ _ N
4
* 0
0 ad
V
0) W
1
W
W
V
-U
J V
) V
4
N
U) a.
U)
a. 2
*U L
U
*
* o)
* o)
* a
v)
U)
VI
VI
cl. a
* a
-z
_ _
o L
iO`
.-I"~
I.-
W
a
LL
.5.
Lu
LU
..
o K
K
L.)
Li
N
0 C
)o
U)
N
NW
) W
LU LUJ
wL Lu
0 ID
.4
4 UV)
UV
) V
K
VI
VI
-~
Lu
Lu
UJ
I.- K
3E
x:
V)WU
z Z
.4 IL 2
xZ
C
Z
Or
a a
I.I IL
LI -
C
Z
M
Li
LA W
_ a
· )
· ·
** LU
* *
o *
*
w
:*
V)
LI)
V)
V)
4 W
0.
0.
..
a a
a. z
o U
Li
Li
I a:
aU
j LUJ
w'7
Li
Li
.t M
a
a 2:
OL
I
-,
V
M
C
N
N
UJ
tU
4 W
U
) U
U)
nz U
) U
)')
) V
) V
)V
) V
I WL
W
KZ
Oz
a
U
-_
_-
U)
I. I-
CL
<
<t
IJ a
t M
M
_ U
IJ
: U
. IL
U.
K
K
U.
-*
a. *
**
Ui *
4**
UL *
*
D-14
Ula.
uJ'g[o`(-
Na.-K<
.'
I-V)
auJi.laK
MULia -r-4sr
a0rI-owwI
I--JC.
LUC.()M
U
KLUIw
M L
)
-JZ
J.2 o
-Z
-Jal.
w
U-J0o
Lu
o.
.4Z
MU
)W
.JCZ
ILu
)rL
cI w
M -a
TH
E
JO
HN
S
HO
PK
INS
U
NIV
ER
SIT
Y
AP
PL
IED
P
HY
SIC
S
LA
BO
RA
TO
RY
SIL
VE
R
sPR
ING
. M
AR
YLA
ND
O
000000
0000
000000000
0 0
C
0 0
0 C
0 040C
0
0 0
0 OO
O
C'
O
C
0 0
0
0 0
0-r
0U)
LIZ,w
0000000000000000000000000
OOJJ
OO
OO
OO
O
OO
OO
OO
OC
JOO
O*..*
.*.v
....---.-**-*
-.**
01-
ul-4
V0D
UUL'0,
v-v
00
00
0c
00
Z-
z N
'
4 o
C
o C
O
OO
C
&
000000000
m
4
V)
0 V1
z0 ........
Z
OC
:OO
OO
OO
;
0-UU
u 0
Q 000000
C
Q
C 0
CJ
000000000000000
00
0-
I I
45
I W
I4
4
I I
I4
I I
I II4
444I
I II4n
V4- 11U4
N
._ D
N
1-N
O
U' U
' 4S
O---O
-U--
_---4
-4-U
--
-_OO
4
-NN
- 4-
0000
0000
0000
00
00
0
00
0.0
UN U`
VI
VI
Vu U
) .D
U
) V
U
w w
0 U
) W% UN
w0 WN
U
U
LU
L
Ju
uU
W
I ultu
L
L "
I .u
I IU
Il
LI
u)
-A r
"I'"
U)
N-
M a)
.4
_ U
) M
l C,
_ _
O
V_ N
r o
X
a _
o u
, r-
C,
M r-
N
-r u0
la
VI a,
ca ,O
C )
VI
U)
LA
n
_ N
o12
0-
tco
N
11P 0
'W
r-4-
O'0
N 45
'01 41
N
W O
Y- 4 ~
N
4 !'0
45
4'M
U
4 4
N
V'
0'
0 D
_
N
LI U
D
U'
a N
O
-U
ND
0
0 _
_ 0
N
00 414
O
OC
-- 4
- u.
4,0
i'0M
. 4
I -4
---
M
_-
4 D
r
_ O
N
.*
..
* *
* @
@
.
* *
* *
* -
*"
-4 0
00
L0
00
00
J 000%
00000
u C
Q
O
u C
VC
z
000
00V
I I
UU
U
U
UJ
U)
UU
Ui
UJ
U
LU
L
I0 O
D
N
N -
--
-N
W
U.
4-1
0U
_
4 V
' 4W
r4
N0
410IN
N
V-
4 454
40
00
0V
V)
II
UU
I-40
UU
-
I4
.JZ
ZIL
Crz
U) V
I
LU0.0
~~
~~
~~
~0000000000000000
0
4--
0 _
N
44 4
U
r- Ir`
0_ -
IV
;r U
4*
-'
I W
-
MN M
N
7
UV
-_I4
- -
-N
N
N
N
NN
00LL
z0-.vJ
0IVI-.a
0 0'-I0
0 U
UU
U
I~~~~j~
.c
rW
It '40)
N
NO
0
0~ 0
0
IN44
N000
0~m
0 N
o4
VI
4 '
-' 0
I
UU
r-
D-15
0
u\ vV
aoV)
0040.NrUr0p-I04L4JQ.
UU
LT
LL.
40_ 0
zo-
WO
JZ
I
-z
z01--4CV)
VI
0
.
L
TH
E
JOH
NS
H
OP
KIN
S
UN
IVE
RS
ITY
AP
PL
IED
PH
YS
ICS
L
AB
OR
AT
OR
YS
ILVE
R
SP
RIN
G.
MA
RY
LA
ND
aw
4
V
u
L U
VO
OC
OO
OO
OO
OC
OC
OO
C
u
I
LU
4_ 0
IIll
4
N
XLU
U
o
J x
LU
I L
:O O
O
O
: eeO
OeeC
OeeO
O
O
OO
OO
OO
OO
OO
OO
q 0uJ
4 iL
lU
Z
-JuJ
O
00
00
00
OO
OO
OO
0L
I
LUz
IU
Z
0. Z
O
-L
-J
D-1
6
TH
E
JOH
NS
H
OP
KIN
S
UN
IVE
RS
ITY
AP
PL
IED
P
HY
SIC
S
LA
BO
RA
TO
RY
SILV
ER
S
PR
ING
. M
AR
YLA
ND
00
00
00
_ 0
0
00
__
__
00
_- __
__
__
__
_ 00
00
00
00
00
0 0
0 00
00
00
00
00
00
Q0
CO
C
O
oU
W
U
J W
.U
W
l U
l W
W
W
oW
oW
W
W
o.
W
W.
W
W
o o
oo
o U
.4
u o WU
Wo
3N A
C
Or
U,
NI D
N
NI- P
1- 44
44
0
VI
44
cr
I NN
N
N
N
l N
iN
NN
X
4 00 O
O
w
u u
) r14.
co
o 00
NN
4
4
0 N
N
N4
00
inO
U
) -4
.00
0O
4.4
0w
0' '0
crU
1411
' 0 u
NN
N
N
c0r 1 u
NN
N
U,
Cl
_ _
L
cr
r0 _
_ U'So
t 00 O
N
N
_.
_ _.
NN
'0
0 Ir' N
N
_ _
cr .
0g @
(
G, 0
_4
N
N
0, 0o
--V7
00
INN
O
'0c N
IN
NN
U7 U
4
44
o
g
44
m,
c'c
r N
N
44
0vrc
NN
V
'4 ' C
IN
N
N
cr N
N
11
N
n N N
N
NN
l4
4
4-I
_ 44
_ cr
In
N
__
+¢
a7
__
;¢
-_
__
0
0
__
:~
Q
_
-1 ~: 9.
: ¢
C-
.4
4
v~
a,
I -oo:
N
Vz
4.
Z WI.--
UUI.
' I
C ..
UJ
2 4
Z
I-J
r to
o
u
J2UO
IJ
LZ
UJ
I-4.4CLU0 UJ
o m
JYLd 1:
q U
L
<k
AaB
OO
O
C
OC
0 o
OO
O
O
O
0 O
o
C
CO
O
O
oo
O
G00
00
000
00
00
0
00
0
0
00
0
0
00
cC
0
0
00
00
00
W
W
Il W
WUJ
U
WW W
u UU
W W
W
W
UlU
W
U
WU
W
W
U
U
U., W
IW
__
co C
O
Icr L
o'I crc
r n
NN
I
cIa
I
I c
44 _
_
nn
IN
N
_-
m
I
rM lo)
CO oo
NN
N
N
, -
N N
r- f-
I cn
NN
m t
-I-F
00
NoN
r-- nn
NN
oo
0'0 om
c
n- vc
nu
0'
vrc
r4
inn
oC
oc
l4
o0 crc
'
-I
CC
l. 0
0'.
a,
m
I'.W
U4 r4
'
a- 0
1
r1)1'U
n I
C
N N
.0
D
_
00
.4
O
a 1
v N
N
It N
N
-4. 4
4
V
1 .4
4
4
IN
NNN _
N
NN
IN
N
NN
_
. _ 4
r l7
.7 _
__
N
N
lr rD
.K7 4
o o n~o o 8 0
no
oo
o°o o
oo
oo
o oe
II U
U
l UW W
W
W
W
W
W
W
W
W
W
w
W
uJ
w
W
I U
_ 0
r(- r
0 44 '7
N
jN
N
r' N
N
.O
W
ID (n
m
7 m
4U
m
44 N
N
m a o
--
N N
Its
N
I N
44
1 N
N
I t
I IT
n44
IN
II I
I I
I, n_I-4
_)
U)
.- 1n4
u.__4 N
IN
Un
u IF
un N
N
) cr
NIN
_
I u7 U
, nIN
D
J N
r-r- nn
oo00
r-r I U
N
NN
'4
t C
IO,
CC
.
-D0
CO
-r-(
0, 0
ec
r-r-IN
N
NN
N
n4) n
n1n
N INN
N
N
OC
cr0
cr u
1)n
C
C
o Ln)
00
1
11
4n
4
cr o
I r-
r-
NIN
_- _
4 t
1 I
1._
N
N
_.
INN
.'
'4
_ _
_ N
IN
K7 ID
INN
N
N
(-4".
O0 G7
0 0 00
~
_ 0
97 m
, 0
cv
oo
cr cr0
67 _
o oo
_G
0
'4'
.44
0'@
n)4n oo
57G4 N
N
toul
__4
00
0
0
00
I'r-r
0'0
00
00 n
4 4
0 '
4)
0 n
cr
c4
NN
m
m
nm
00
@U
)U
14
v- 0
0
0 0n
'4
'04
r-- .4
.4
NN
4'
tono r-r-
__
mn
.t 44 14 1
__
NN
4'.t
II II
II II
II II
II II
II II
II II
II II
I ll
ll
0000LU LU
0 0
00C.0
0C
-4''
00II
N
N
00
N
NIIO
w
vI
uJl
c)
o
V)
XV
I w
W
U
E12
NN
V1A
CC
Cy
Z
\t~V
)
Li@ 00.
z '~
It
N
NLU
I I
U],
00O
Uo U
.
N
N
00om
I I
00 ..I
UJ U4
N
N
1 -
q:, U
,
W
IN
IN
J00
00@2
II I
IZ
LU
WUJ
U.JU
UO
4-
U
¢ .4
co
u z
arv
cr
c
0 Ucc
@0
(' @
0'
u u.~
cr c
r vu v
o Q
.
* ..
0V7
-I q , -
-,
00
00
C
O
00
.-
0000
00
00
0
0
00
00
Ili c',I
U
U
.41±1 .
W
.4.4
1 4 I
C
O
0 0
m
'?'4
I 4
.4' 'C
oo
oo
o U
c
oo
m
O
O 0
O0
c o0
a- 04 0
II a, IT
II
II II
II
Na
N
N
O` V
_
NN
m
mr-
Ul) U
" (
vl
Nn
U
` 0 1
7 1
00
-1
41
4
4 .
4 1
1 l
.4 I4
00
00o- o
I I
0 0
-Z
00
00
coW,
--
NN
44 <
NN
_ -_
II I
I
0000o
'trI
II
I
W W
_ _
0 0
I I
0 0
O I I
.·
_ Il l
_ _
I I
00.4.
mmI
I
I'm mU
ON
N
00..
_I _1
00
CO
C
OO
C)
00
00
IW U
UIJ
W
UI
N N
U
V
4
ItN
N
441 1
OD
crv
r a7 I
r- 1-
NIN
44
-.4'
00U
0U
0
c
a 0 N
.N
v
cr
U@
n m
)
1
II II
-4 ''l
" 0~
Cd 0"
U
0 0U
0
--
C.) C
O
C
G O
C
) O
Q
_
_ -_
CO
O
0
0
0 o
00
O
0
00
"Q
II
mm
m
m
It'?
.- 1(U"
u `1
m m
LA
in
mm
4 4
c.4.4 It'4'
4 4
0 u
), i
U)
C
OD0' ?
'?
o m
4 e4 @0
I' -
IN
N
N 1
-- 1
- '0
NN
0
OD
a'
NI N
00
N
N
N
N
_4 4
4
.0 _
mm
N
N
_. -
' m
nII II
II~
~~~~,1~W~U
O
C
IN
N
NI I
I
i0
U0
N
N
N
N
ttOr
, C
00
W
L
U
U,
n r-I r.-I
0o
0
r-rPOO
CD U
) U
lz 4 4 ~
0C00) U)IN
IN
0 .4.
Wl
.7
m
N
Nr- r-r- r-
I .
C
a
WL
Ucoa
ro r-
r r-(n~
INN
IN
N
N
INN
N
N
N
N
N
N N
N N
N
N
N
IN
N
NIN
IN
00
00
00
00
00
00
00
00
00
O
00
00
I I
J,
I II
II II
I II
I L
II
I I
a, 00
00
a 0
1 .
1 4
.4.
.4.
14 1
.4 1 4
4
c s.r
4 o1
01
4 a
a. c
@0' @
0'
@0'
@0'~
~ ~ I0 0
0 0
0 0
0 0
0 0
m
D-1
7D-l?
_ ._
THE
JO
HN
S H
OP
KIN
S
UN
IVE
RS
ITYA
PP
LIE
D
PH
YS
ICS
LA
BO
RA
TO
RY
SILV
EtR
S
PR
ING
. M
AR
YL
AN
D
_l N
UJ
U)
GI[
a.0~
N
N
LU
I -
t C
4rl ~ ~ ~ ~
~ ~
~ ~
~ ~
~ ~
~ ~
' ·
:Ca~
£ *
..
..
..
U
..
..
..
.
a.~
~~
~.
£ *
* *
* .
.
..
.z
L z
..
z *-
* u.
* U
,.I/_
0
It c
4
W
2 <
_
_ a
0 .
U
-
-FI-
cc*
IO
* W
VI
LU Z
C
LU
U .
-
0. U
I 0
0 .
4a.
LU.
a .-
--. O
u
J -
8 U
Z
_
W I
4 4
Z
>
Z
O
4 *
-_
U
-U
a
__
o U
l W
U
l U
l J
IA. U
a.
W
O
Ul
LULU
Z~
~~
r LU
W
Z
(_14~~~~ 4W
F
- K
1
Ul
(D
'A
<
1
Ca.~
0 U
C
C
LU
LU
4 U
Z
4 a
4 4
LU
Z
N
IL. NC
K
N
I IC
a.
U
Z
LU L
0 L
e
C
V
a. U
.
e-
a 0
U
U
..AZ
(V
a N
cc
a L
I -a
* c
* *
U* *
0 *
LUw*
0) *
m
* o
TH
E JO
HN
S H
OP
KIN
S
UN
IVE
RS
ITY
AP
PLIE
D
PH
YS
ICS
LA
BO
RA
TO
RY
SILV
ER
SP
RIN
G.
MA
RY
LA
ND
uj V
)In
-N
N4
LL
w
-4
4L0r
N
O
N00
r LU
r-a' "4
t,V
r
N
V-
t 'V
.G
'4
0 -
LU *
UI
( 000
I
4 4
I r'IW
N
U
W
e.
J -J
-N
I J
IV W
0.1
I)Lu
U.
J U
_ J
V)
Z
CL
Z
O-
L-
V)
IlWL
U Il
4 IP
N-
LU *
*
I- LU
I
0.
4 -1 a,
0.
C ?
.oo'0
u
0
Z.
Z
zo
. z
C
.) 4y
m
L
-(S
-.Z
LL L
00
TH
E
JOH
NS
H
OP
KIN
S
UN
IVE
RS
ITY
AP
PL
IED
PH
YS
ICS
LA
BO
RA
TO
RY
SILV
ER
S
PR
ING
. M
AR
YL
AN
D
N
I V
IN
40l ,
e
N
0000
0C
00
0
0000
00
00
cr
W
UIW
ul W
W
W WW
UL
uW
WW
u.
WW
WW
_0 a
Ni W
cr1
a,
, N
V
) N
N
-a,
Lo
N~
94
D
i..I ~
~ ~ D
iWV
U,
V.-V
_
cr
uN
o U
,1 I.
uI
_ in
000
NO
. r
r s:0
C
N
0O
O0
r O
0
0 0
0
I O
m
_I
IN -N
1 _ -_
--
___O
N
00
00
0
00
0
00
00
0
00
0
.4I
I m c
i oN
0g I
-IN
_ o
rn
1 1
N a,
Z
U:,iC
N
N
_ CD
0W N
IF
'l I
c0000c0
u, V-N
I
0, 0
-0
CD In
00
0n
-
In 0I
00000
in
-n
r
0N
N
I
U)
0 W
N
N
1
I N_
, In~
......li ......
till t
-
00
1 1 D
1 1
1--n
- 1
-1
-Lin
LI
" °
ID TU
' ,
co o V
W
o
WW
>
o, c
r U
, I f-C
) t
r r f-
_4 o0
4O
Z
c)~~o uF N
u
tr Q
r
0 o >n
r o N
CD O
-O
C
a
O O
O
17 4 4
4 B
t
W
I I
I.I I
I I
I I
I I
I I
I I
I IN
I
I I
a ..iN
O
ulm
P0
0 ..
00
0
..i-
cr
N
r cU,
r" m
rI
1- 4
o wU
zr cz
co r
_
JJ N
CJ
0 INWn
CD -rr
_w
uu
r S
~D
N
IN
4 %
T
iU,
mV
04N
V4im
V.
0 0 O
O
4 N
4
4 r
IN
I'- o
r 0
CD N
I'l
co
IA
U,
N
, CDi
,U
U
I I
I I
I II I
I I
.4000
.4.4
00
-4.4
N
--- 0000
<4 W
UW
U
UJW
UUW
W
U
j WW U
UW
W
L
UU
l W
U
U
1 co"N
w
N
CD
C
om
oz
0 0
w
C
0 uD
_
,C
CY
z a cr
,IIII Iz
III II
I U
II
II
w
N
mU
o 4I
V
NU
0
0.
0 I-.D
D
.m.
U,1
4
N0
.N
r1i4
0 Z
JY
L
D-
OU W
-Z
Z- <I _-
_ -
N
LI
-W
TH
E JO
HN
S
HO
PK
INS
U
NIV
ER
SIT
Y
AP
PLIE
D
PH
YS
ICS
LA
BO
RA
TO
RY
SILV
ER
S
PlR
NG
. M
.RY
LA
ND
NV1
N
4tD
D_ C
O
C
O
O
C
OO
O
OC
OO
C
O
OO
OC
OC
OC
OO
C
C C
O
O
CC
0 00
0 C
0 O
CC
OC
C
C
CC
0 0
C' C0
C
_-
--
_ N
---
--
--
N
OO
' O
0 0
00
0
00
0
OC
C'C
I w
w
w
I I
II I
w
w
_ 0~
ere
4UtUi
WI
0 -
oo
c
mO
N
In
I IC
U
N
0
0 a_ D
_C
N
m V
IC
D
0 '
ID tr~ I, 0 D
,
o C
0
N0
N0
.. -..
..
.N
4N
00
C
'
I~
Ii ~
| I
II I
I I
I I
I0
00
0
00
00
C
0
0
00
00
WW
W
W
W
W
IWIU
J
WI
II W
W
W
_- D
0 0
0 4
, _
L _c
-2 1m
Z
1la
P
m 0
co 0
DD
0
cr
00
0 0
.0
-I
N
0 -?
O
N
.--.N
z O
-w,
tr _, _
o
_ _
LM
0000
0000e 000I
000I D
II W
I
I I I
oI
I I
I
Z
_ 1t
CD B
C) 1
t fv er rb c; 0 o rs eD
O
¢ Ir
CD
If Il- f`
1- O
'
wU rN
4
0'0
(
-t
D
_N
C
Iz V C
0
D0
0r4- o
WI
oLU
o'I otrm4UO''4U
4N
IJU
VlIN
040N
_
J 0
0 0
N
_,
4 _0
13 e
-4
-40
C 4
Il -
tr U
u0__0 0_-
DU
4'1
I -
_
U_ l
NT
O
A
-
c
00
L
I 0 '
I A
_
N
N
-N
r-
w
1a4I N
N
4
Y
( a
J
UW
U
4I
O_
OZ
-
0 ~~
--2
1
~~JLI
0-2
TH
E J
OH
NS
H
OP
KIN
S
UN
IVE
RS
ITY
AP
PL
IED
P
HY
SIC
S
LA
BO
RA
TO
RY
SILV
EI
SP
RIN
O.
MA
RY
LAN
D
N
I V
lN
40U
'
000
0 0
00
0
OC
" 0 F000
-aU'
WW
UO
IW
WO
WL
U
CU
'UW
C
O
O
C
C
O
O
'I '.-_,c4' *'-N
-
' '
CN
0
N
O~
N~
O
sc~
O
a
~ C
O
O
O
O
U_
I I
{2 I
I I I
I ItI
I m
I
I I
IqV'
UU U
JI*
-- I
I U
Ul U
0
8 UN
a, U
^
C O
'
m
ooo8
Ur''N
' rN
mm
o
o oo
o0^ 4
0'
0N 0 C
_
N
0m
0 4
U m
f
1 N
u
e 0
.)U Ic
II I
I I
I
r.
--
-I
_-
N
1- -_
N
'3C
100
00
0
00
00
0
00
0
IJ W U
W
II W
U
LU
W
W W
IWW
W
I
N
0- 0
O'
U''0
0U
' N
O
N U'v
0'N(I
0 a'
N
414P_ '
NmmUU 11m
0' t-w
U-
0 UN
0,N
0C
_
I 1-
N 0
l '
N
N
0 V
0 D'
N
co 0
0
z 0
Li
_0 st
_' '
N
I -
-U
I-
LU
It 0
N
N
L U
N
0mg
I I lL
IL
I
I I
I- _~
O
_ _
r- _
_ -
_ ___-
UJ
OW
N W
WW
W
r-W
L )
w
0 L
wn1IU
'O
N
N1'1
T
01- '
N
N4
T
N
Xu>
IO
_U
VN
.0
.W
n
m. N
._
-808 0
0 1
.0'C
' 0
'0'U
.n
08
L
e m-m ,
r l
m m
N
m m
r'
N
U
0' 0a
m r
41 0' '
N
4 T
N
W
8
) C0
0'
NN
I0
4p
4 N
'U
IN
C,
, W
JU
' _U
Q)W
a1. -
NV
_
A1 O
L_
1 I
N
NCY, 4
X
.a o
uO
V
I"
0 1
V)
U'
0 0-
0 C
0'
V0
tA o N
_ 'U
W _
0 V
O
C
li C N
a, N
0 T
N
N
I 0 V
-8
_
O
_ r-
8)
.- ILU
i' I
II I-
Il
II
1- C
com
mr
mm
m
cI'II'lm
m
mm
m
OC
U
O
D -2
2
TH
E
JOH
NS
HO
PK
INS
U
NIV
ER
SIT
Y
AP
PLIE
D
PH
YS
ICS
LA
BO
RA
TO
RY
SILV
ER
S
PR
ING
. M
AR
YL
AN
D
Nn4
v)
NUJ
r- L
6N
40 nV
)
W04a0.NU-
crI44
000
0000O
0000
00
0
N
N
N
00
0 0 O
N
o0
0
0 0
00000
u1-
lW W
LU
WU
W
W
WU
W
0 o
a n
N
N
¢NZ
N
4
n m
0
-_
N
OC -
U
0\ eo n
m
'r _
'o
U
-0
N
N
en o0C
0
4 M
G
e .·t
O
40
0-_
4 N
O
G
O
C
N
uO'.S
ON
Cn44
9a
I I~~
I I P
I I
ta
-L M
N
NN
N
0 0
0 0
00000
0 0
0 0
ZU
W
W
UI
LU
L
U
W
Q
a~erer~sco co .
.o
-N
uN
9
, 1
a,
9a
,0'0 N
O
e
.N
0
e~n
lb N
u'C,
.... 0
4 0g
4 n0
4 9
o ar
-''N
o
,, o
.D
N
o 0
.en 0
z I
0 o
o o
000900
In An
4 4
N
0'I')
W
W
U
9 W
W
U W
WW
w
o r
W
NP
o
WN
7 .t
t- _-
m1-t
-4e
........U
.......
V7
14
co L
, (LI
NV
) II
Lu
I-W
e-10
LU
a. a
O
-
-J I
WL
Vi
I d
· q
W
.L
0
4
uen z
J- -
W
Y
z4 -
IJ
en eU)
Un U
nn
n rl
n m
N
N
ID
N
eCo_ N
Nm
r
N
U1
-4
en N
en
V'
*e 0
e n 0
-0
_ o_
c LU
0 0
0 0
I.U4CUC
0
J Z W
0I 0440Q
.
u W
UJ
0 _
N
Ie IT
iL
.J ,-
_ 40
.J
_ N
e- ec
U_
-N
N
N
N
N
N
N
49LiG.
00
00
O
CO
000
CC
C0
oo o
00
00
00
0
C'
0C
00
0
N
m
_ N
_
ICO
0 0
0 0
0
0 0
W
LU
w
W
W
W
U
W
Ul
-C'
N
N
-I n
0'r-
N
~Z
N
I¢ >
v
oI I
I I
C
a C
) _
N
o N
o
N
4 co
v 4 N
-4n
ce
.,
_ N
0
00
00
0
0 0
00
0
Z
Ww
W
W
II II
W
W
!0 0
0 0
0 0t
!0i
I en
r en
e N
n
IN
o O
c N
I -
M
F
fn
C
N"
1 -
' a
'3 r
.t U
pi
.4co~~ 0a
0 a
00
0
N
N
e n
N
e
L U
J C
W
a W
W
L
I w
C4
Qa N
n
r e
n
o
.. ..- 0
en ...
en e
00
0
r-0
0 9
0
e _
VC
O
O
0
U.
J CU,u
0'
_4
I-
-ZY
WJ
z
-: {IJ
o 0
o a,
I I
I I
IIU
LU
W
LIi
WJ
N
C,
0 C
N
CN
en
N
m
CO
OO
C
O m
7C
~C
~
I
4. 00
0
00
0
0 O
0O O
000
00
C
O9 N
ee
.1 en
4L C 7
en '0
0 '
ee .71 en
LU
-"-4-I~N
N
~N N
49
D-2
3
W0 4jLI)
TH
E JO
HN
S
HO
PK
INS
U
NIV
ER
SIT
Y
AP
PL
IED
PH
YS
ICS
L
AB
OR
AT
OR
YS
ILVE
R
SP
RIN
G.
MA
RY
LA
ND
NLu
N
40
0 U,
VI
D 4a-NI".
c1r(U'Ia:4IU
U
4
O-IU
O
LL
D
O
N0 -)
OU
W
. D
LI
ZO
LILU L
_W
0
OO
~n000 0
CC
00900
00
O
0 0
0 Q
0
O
Ui LU
LU u LU
LU
jL UW
UJ
N
0 N
_
N-_
-Z
N
O
m
O
O
0 aO
Iao
-O
4
-.o?-'Ir
-N
i1
U'I
0 0
NU
O
C
_ O
N
UI
t 0 'ItI
4 N
OC
C
- C
0
0 O
.*.
..
.....~
.000O
N0.4
O
.-O4'O
N.-
V)
ITIM
0N
._
N
-_
00000
0 0
0 0
zW
S
UiU
l LU
LU LU
L
UO
N
-
N4
, I-
m
u 0
-ON
0 'r co
N
S
a,
0LI
t&0o _
tr _,oA
0
co un
N
UN IT
c
0 IN
w
0
co_
u'O
NU
N
0 A
t 0t
1 ou~
*
9 .~
-
.*C
~
~~
0C
cN40Ifl0(0I0N000o~
·-._1
N- 't
_4 O~
0
1040
N 00O0O0O
z I
I
O
O
0 0
000000
tL W~U
W
UJ
L U
J WuWL
UJ
U( m
V
P-
04,0
I D
N
0
N
0 r
-,-
W
4
N
D D
' _m
' _
U
0 00'
c.j
ID
N
m
*t C
O
OD
- t
C
* 0
N
D1. 01
W0
N
0N0J 00040~0~0'0W4I'W
<
000
C
-C. IN 0
IN
-m I
IN IN
z
I- co
(Tr co
N
N
N
NI
I I
I I
ILU LU
LU LU
LU
t' 'a
I
N
.0N
D
'' -
Oa104.
I0'U
S.4
'U0N
01
LI'
41 L A
OI N
S11'
O-1.-
t 4'
N
t0 N
0
0
0000000
* .
..-....0110
_'
II 00000000000
(- I
N
N
N
) nN
LU
U
U
LU
UU
LU
'. .0
,
., N
0 c
N
N-1
O
L r-
N
,4
LU
I-
LJ
1.1
Nw
V
VI
0 0
U U
,
C
O
4 0
0.
0000000000000000
e e
eIN narC
-e
Ie
e eeee
I'. II
I II..
-II
r ·m
·r· ·
-- rv·r··
l l
l l
l l
l l
l l
l
I
INN-1N.-I
, -m
It01
0ItU
Np
-0
00
00
00
00
00
00
00
0
N
I I
e 4
IU
W
W
4
IN I)
U I
C,
u,
1-.
tlJ
Lu· LULU 0
4.
.- ,
--
--
m
,
-41 ,t O
-1
I LU
LU
LU
Lm
DIU
)LU
w
wU
LIN
UaLa,
t' 0
e 0
N
,, ,
0 _
0 tN
_ -
LU
* t .
N
1 _ N
O U
N,
_ _
I
4
'Z
Z
0 IN
---
00
10
I0
0
t 4 ULI
U'4 VI N .4U'.
-r-?-
LII-
-lU
-
O_______________
oJ IoD
44tn
4
'- 4
00
1F
_U N
0
N
0 1
N
0'r- N
I
0
1-
N
1 N
-
I I
n In
N
0
[ r-
N
I I
D
aUz
LU4uJa-
LUo
LU
U. JJ
.--J Y
· I-
-J Z
LU V
)
I L
LU
0 I
NN
-_O
N
-_
_ -_-
_C
-O
_ _
- Q
z 0O
OoO
OoO
OoO
O
OLU
I
I
Z
N4U
4 444 _
14
N-
NI
N
t 0
-m
0
0O
O
N
_
0 0
0 N
0
_ O
_
t Ln
Z
On
N
0 m
O
aN, D
-N
MO
*U
U
N
_N
0
C
0 In
_
--
LA , O
0D N
-It
N -
N'
0'
U' .
0` C
N
In
_
P-
N
z -
Z
_U
*
D
C
X
IJYU
L
UL
-J
LI 0
D-24
THE
JO
HN
S H
OP
KIN
S
UN
IVE
RS
ITY
AP
PLIE
D P
HY
SIC
S
LA
BO
RA
TO
RY
SILV
ER
S
PR
ING
. M
AR
YLA
ND
Im N
N
N
M
N
N
N
N
N
N
N
N
N
-0000000000000000
W
W
W
LU
J
W U
WU
U
UJ W
U
UJ W
U M
LU W
4 N
M
M -
V'
V- N
1
I .0
_
UJ
>
U N
O
-1
.D
N
O
lo
0 C
N
N
'0I
NcrN
4_
'0 f'V
N
._
0NN
Vi
4't V-
N
0 O
Lf_ N
O
iO1
0
Ct~
4N N
Q
U~
U M
N
I~ 0
4 0'
'0'
WU V
A
* *
* *
A
* -
.*
* *
* *
* *
0 'C
N
I I I I
I
0' 0
V)
I.3V
) 4
Ul
(3'CaNr-I4n
zW
UU C
U
C
Z
'C LU
Um
uJ
o0 Z
IA
-IV
0
JY
3
zW
0)4
LLU
i
iLD
-4
c-
Y LU
UU
V)
JC
i
mm
NN
N
NN
M
NN
NN
NN
N
bO
O
O
C' c
O
C O
N
O
O
C
' O
O
I N
-MU
'U'C
ILN
Z
I I
I I
LU
UlLU
1 N
N_-N
N
NN
N
-
N
N
N
LUI W
UU
JU
JW
LU
lU
WU
lWU
*U
UlU
UJL
UU
-44
r fli LA
0 0
a,
' N
,
a,
, N
_
p
aS A
O
. .
O
4 I0
A
' 4n
0 a
' C
'
0 ,
-c '
CN
If-- O
f' 0
M4L
w.- N
-
V
O
1-
I I
.111
1-..1
1
O
i N
_
NN
N
N
N
NN
N
N
O
-
.1 1`
UL 1-
0 U
U
, N
0. C
UL
0
QU
l
0 rI'.4
U r-
U, U
' 1-N
U
U
lM
rn0
N
O
N
' N
mO
N
00'N
0
U0
Z
IJ _
^0 0
_ U
M w
0IF
N
M
M
_ O
F
DJ
IN
N
IN
_ N
4 N
" N
IN
N
.IN
-
C
_W
rjc
O
aO O
o )
O
~ ~
l O
a
O
J)
t Q
O
o N
NN
ND
m
NN
cN
rN O
Z
tJ
OO
OO
OO
O iO
L)C
TO
DO
Oa.
LW
LW
J4JJU
IUJU
LL
I '0
1'
;- O
U,
MO
rU-
a, a,
z cr
_C
r- -_-I _
' u' N
o
>0
IA U'
'C 4
0¢a
N_ l r-
' N
Co
m
N
ON
0U
0'
* 'C .'
44 U'
N
N
-C
.4
9' 0'
.c
_ 0
4 M
C
It_
_cc~
~
~~
~~
~Q
F
_.N 1
'1. U.
i-W
e
r C
_
N
r ,
U,
,0
CI
WU -
W
1 C
N
-
N
ffI N
N
II) N
it
_o000000000000000
4 O
Q
.C0 N
u
in
4 0 '
o Q
w
_
4U
-
1 0 M
'0
1-
N V
' -_
W
m
4 'C D
M
N
I r
r- 0IA
V' f0
N.r
lIA
-CC N
N
V)
W-0
NO 0M
0 NC
0 M'
O a,
.C
N
_
W
V
**
**
**
0 0
_.V
)
UJ
D
¢3Libf
N
l
I -I
JU
4-
-Ja:UJ
W3
.ZCZ
-4
U
a U
U.n
Z
ca V
)
u_ J o
o zo'
O
II 0
ci
JJ.
Z
ClZ
0 0
00
0
00
00
00
00
C'
0
WU
U
U
W
W
W W
U
IJ ul
UU
U
UU
UU U
J UU
UL
I l
D'
D
0 O
' 'r
N
c 0
I a,
o0 C
CU )(
0 U'
4 w
P- N
PA
It
N
-t C
l- _ _
N
.C
4 M
,
I N -
G
IA 'C
1- C
4
0 _-
Nz
I I
L I O
I
I
2 N
N
-I'C'f
IU'
U
'cr tr
'o' 0-
I D
LA N
0
C
0 N
'
m
' N
N
r m
0i I
mI-
IUN
N
C
N
N
I -
v 4
_4 m
c
-'-
IN
O
, 0
0 O
c
N
0 I
O
u'3I
NI N
'
I N
N
.I I
III I
I I
II III
L U
WL
UW
WL
UW
lWL
UL
lW
I )
0' 0UC
IA C
N
N
IA
IAo
un IA
N
R
Cr U'
111
IIN
0 N
_
N
_ _
I X(
0 4
U
-N
_
N
IA In
un
U
C IA
N
I I
I I
| |
II II
oLU
Lu
D-2
5
TH
E JO
HN
S
HO
PK
INS
U
NIV
ER
SIT
Y
AP
PL
IED
P
HY
SIC
S
LA
BO
RA
TO
RY
SILV
ER
S
PR
ING
. M
AR
YL
AN
D
N
Zu VJ
Q.
z
cc-i
UJ
L
WI
L
_
I U
I0 Li
Z
Z
0 IY
U Z
Z
o LU
4 -
a~~
r-I-LUXWI
LU4 VUII
o ,
0 r
*.
4 0
-
.LU 0
VJ
-
-N
'
LU 1
-VNW
I
V
I
V)O
0 C
00
z C
I _,
Z
.WI
l
U
<
D-2
6
-U
i0N0' -IU-9
LU
04
.r
r-ct3E
-Jr~
00V-
a-Lu
IT:
4-JUl0
UI
0
O C
aZ
C.
-°
L. wY
U
1- L m
U.l
Z}
vLU uJa.uJLU CcI4U
2 LU
w-
44 IoLU c---
uUJ -JU
Di
Q.
4.L(:LU-J
4 -3-.
0.
C,
LU
VI40
W
J
O
;
I-0O
_4
I U
U-
I0
O
J L
w
-Vc
1-LAC-
0-JQ.
I- LU
-CUJ
a:4ZO
. o arZ LU
-Q
YU
LU
m
-Jz
2. DI
LU I.- Z
TH
E
JOH
NS
HO
PK
INS
U
NIV
ER
SIT
Y
AP
PL
IED
P
HY
SIC
S L
AB
OR
AT
OR
YS
ILVE
R
SP
RIN
G.
MA
RY
LA
ND
0 UVL, 4xW
C1
U2:ZI-U-4LU
I UD,
.O
.
r I
LU
u
4 U0 LU
1-
I 0 0
.
-1
40 0n
4
ZI UL
Z4
0W
V'A1:WI
UW Dr
C,
4 C
U
-J
QA
U
I
r'. I
* U
L
-'
u.,N
I
IO
LU --
1-N
W
UN
O
i
_N L
4-4
ZO
V1
0
4 O
O
-W
UI
OW
L
LI UO
U
CL_ 0U
_L C
Z
Z
z
0 WO
Wr
o
CL
InU
. 0
'Dm
4 I
-Z
Z W
--Z
W
U
UmVW
.Z
D-27
U.)
040.NP-
Cr
0~I U,
LI CL.
a:42:
NLUa,,C
o
-Jr4U!
ulzLU0WZ
Ui
-aNI-p
17
-40 0IwI-U,
L.
XL
-4LIU.) 2w
0 C
lU
Z
CL
-l4 Y
U
J L
I 1-
£44-
.
V0.-
vo wI-o0zo2n ww .: 0LI
C3 -IU
1-
ULIU9-r
LULU
-4
*0:U** U.
LiZ
TH
E JO
HN
S
HO
PK
INS
U
NIV
ER
SIT
Y
AP
PL
IED
P
HY
SIC
S
LA
BO
RA
TO
RY
SILV
ER
SPW
ING
. M
AR
YLA
ND
hi~
~~
~:
N~
~~
~
~'~
~~
~~
~~
~~
,.
/ (
L
~ It
Ci
a~~~~~~~~~I w
~~~L
w~
~
J X
N
a R
hh
lL
N~
~~
~~
~~~"
~ z:
o:u
O ~
~ ~
-"
w
N
~<<
·~~
~ ~
Z-
LjJ~~~~~~~~~~~~~tiL<,
r(I U
0
LU
,J/ _ln
-J
Z
Z<[
n I(
'
'Z-Lz
N
a a
N
wco
D
I-2
N~
~~
~~
~~
~~
~u
0~wC D,,
It 0O
Nw
I~~
'Im
[3 ~~~~~~~~~~~~~LL
/I a
D-28 ~
~ w
C
TH
E
JOH
NS
H
OP
KIN
S
UN
IVE
RS
ITY
AP
PL
IED
P
HY
SIC
S
LA
BO
RA
TO
RY
SILV
ER
SP
RIN
G.
MA
RY
LA
ND
Lb _ I-
Li
I
~ii ico
i-J ~
/"-
/~~~~~~~~Z
0
w
iw
O
,,,,<I-QL
u
uii
· ·w
L
z<
-O0<
n
-Z
ld<
<i
wc i<cn E
.J ~.'
I'-
011
I~ U
~U
Iz
CN
coJC:-
/~~
~~
~~
~~
~~
~~
~~
~~
~~
~~
~F
En
~,
C~
F,;-
D-2
9
TH
E
JOH
NS
H
OP
KIN
S
UN
IVE
RS
ITY
APPL
IED
PHY
SICS L
AB
OR
AT
OR
YS
ILV
ER
S
PR
ING
. M
AR
YLA
ND
z
'7~
~~
~~
~~
~~
~~
~~
~I
_=0m/
A
Wti
-ir
Mto
0
N
~~~~~~~~~~-J
CL
a <
LU Inr
/
'J m
I
i zz-J
.Ico
cr cl;
w
u1
(ww
,' · ~~~~~~~~~~~~~~~ -i
L h
· '~
I'~~~~~~~~~~~~ -
.~ a:LL
UbJ
0e4O
hw
w
O
w
~~~~~~~~~~~~~~~~~~~~~~~.'-- cj
D-<
0
I I
--I
~~~L
0~
~
U
Li --
v
ML
'L7rI-S
I~~
I
V~~~~~~~~~~~~~
D-3
0