Table Of ContentAir Gun Launch Simulation Modeling and Finite
Element Model Sensitivity Analysis
by Mostafiz R. Chowdhury and Ala Tabiei
ARL-TR-3703 January 2006
Approved for public release; distribution is unlimited.
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Army Research Laboratory
Adelphi, MD 20783-1145
ARL-TR-3703 January 2006
Air Gun Launch Simulation Modeling and Finite
Element Model Sensitivity Analysis
Mostafiz R. Chowdhury
Weapons and Materials Research Directorate, ARL
Ala Tabiei
Private Contractor
Approved for public release; distribution is unlimited.
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4. TITLE AND SUBTITLE 5a. CONTRACT NUMBER
Air Gun Launch Simulation Modeling and Finite Element Model Sensitivity 5b. GRANT NUMBER
Analysis
5c. PROGRAM ELEMENT NUMBER
6. AUTHOR(S) 5d. PROJECT NUMBER
622618H80
Mostafiz R. Chowdhury (ARL); Ala Tabiei (private contractor)
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U.S. Army Research Laboratory
ARL-TR-3703
Weapons & Materials Research Directorate
Adelphi, MD 20783-1197
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14. ABSTRACT
This report presents in two parts analytical simulation results of a test item launched in an air gun test. The first part of the
report presents a discrete mass-spring model to predict the transient response of a generic artillery component subjected to
launch simulation in an air gun test environment. A 2-degree-of-freedom model is developed to simulate the air gun launch
environment in which a test object mounted on a projectile is launched through the air gun and decelerated by a crushing
aluminum honeycomb mitigator. The mitigator in turn impacts the momentum exchange mass (MEM) before being stopped at
the retrieving end. The present model achieved a good prediction of the period and peak acceleration of the on-board recorder.
The sensitivity of finite element (FE) model parameters affecting the dynamics of a test object launched in an air gun test is
discussed in the second part of the report. An LS-DYNA1 FE model previously developed to simulate the impact mitigation
environment is used to investigate the sensitivity of FE model parameters. The sensitivity study clearly indicates the necessity of
honeycomb material characterization under very high impact loading for effective modeling of the strain rate effects. The FE
analysis also suggests that intermittent eigenvalue analyses during an impact simulation could be useful in identifying the
dominant modes of vibration governing the dynamics of the test items and verifying the predictive capability of the FE model.
An efficient procedure using a decoupled model is proposed to simulate the response of a test item launched in an air gun test.
In this approach, the contact force generated from the discrete analytical model is applied on a detailed FE mesh of the test item
for a given impact velocity. The acceleration data obtained with this procedure compared well with those predicted from the full
FE analysis. The simplified model runs in less than 1 minute.
1LS-DYNA, which is not an acronym, is a trademark of Livermore Software Technology Corp.
15. SUBJECT TERMS
air gun launch simulation; aluminum honeycomb; analytical simulation; discrete spring-mass model; sensitivity
17. LIMITATION 18. NUMBER 19a. NAME OF RESPONSIBLE PERSON
16. SECURITY CLASSIFICATION OF: OF ABSTRACT OF PAGES Mostafiz Chowdhury
SAR 65
a. REPORT b. ABSTRACT c. THIS PAGE 19b. TELEPHONE NUMBER (Include area code)
Unclassified Unclassified Unclassified 301-394-6308
Standard Form 298 (Rev. 8/98)
Prescribed by ANSI Std. Z39.18
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Contents
List of Figures iv
Acknowledgments vii
1. Part I: Air Gun Modeling 1
1.1 Introduction.....................................................................................................................1
1.2 Model Formulation..........................................................................................................2
1.2.1 Assumptions........................................................................................................2
1.2.2 Rigid Body Dynamics System............................................................................2
1.3 System Parameters Definition.........................................................................................5
1.3.1 OBR and MEM...................................................................................................5
1.3.2 Mitigator..............................................................................................................5
1.3.3 Strain Rate Effects...............................................................................................8
1.4 Results and Discussion....................................................................................................9
1.4.1 Validation of Present Model................................................................................9
1.5 Parameter Variation Sensitivity.....................................................................................16
1.6 Conclusion.....................................................................................................................19
2. Part II: Air Gun Finite Element Simulation 20
2.1 Review of Previous Work.............................................................................................20
2.2 Finite Element Model Sensitivity Study.......................................................................21
2.2.1 Double Versus Single Precision Code...............................................................21
2.2.2 Time Step Size Effect........................................................................................23
2.2.3 Different Output Intervals.................................................................................24
2.2.4 All Damping Options in LS-DYNA Investigated.............................................25
2.2.5 The OBR Filled With Solid Elements to Represent Beads...............................28
2.2.6 Intermittent Eigenvalues Analysis.....................................................................29
2.3 Simplified Simulation...................................................................................................31
2.4 Conclusion.....................................................................................................................32
3. References 34
Appendix A. Program I/O Files and FORTRAN Source Code 35
Distribution List 42
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List of Figures
Figure 1. Schematic of the air gun.................................................................................................1
Figure 2. Dynamic system representation......................................................................................3
Figure 3. Honeycomb stress-strain curve.......................................................................................6
Figure 4. Plastic shock wave..........................................................................................................6
Figure 5. Mitigator deformation....................................................................................................7
Figure 6. Mitigator wedge deformation zones...............................................................................7
Figure 7. Top acceleration of the OBR unfiltered.......................................................................10
Figure 8. Top acceleration of the OBR filtered at 7000 Hz.........................................................11
Figure 9. Top acceleration of the OBR filtered at 2500 Hz.........................................................11
Figure 10. Top acceleration of the OBR filtered at 1000 Hz.......................................................12
Figure 11. Fast Fourier transform (FFT) of the top acceleration of the OBR.............................12
Figure 12. Top velocity of the OBR............................................................................................13
Figure 13. Top displacement of the OBR....................................................................................14
Figure 14. Mitigator contact forces..............................................................................................14
Figure 15. Mitigator contact force impulse..................................................................................15
Figure 16. Length of mitigator plastic region..............................................................................15
Figure 17. m :m mass ratio sensitivity of model........................................................................16
1 2
Figure 18. Model sensitivity to 10% variation of the value of k ................................................17
1
Figure 19. Model sensitivity to large variation of the value of k ...............................................17
1
Figure 20. Model sensitivity to variation of the solution time step.............................................18
Figure 21. Model sensitivity to 10% variation of the value of mitigator radius..........................19
Figure 22. Acceleration data for the same FE model with two different precisions...................22
Figure 23. FFT of the acceleration data.......................................................................................22
Figure 24. Acceleration data for different integration time steps................................................23
Figure 25. FFT of the acceleration data for different integration time steps...............................23
Figure 26. Acceleration data sampled at different frequencies....................................................24
Figure 27. FFT of the acceleration data sampled at different frequencies...................................24
Figure 28. Acceleration data for simulation with mass proportional damping............................25
Figure 29. FFT of the acceleration data for simulation with mass proportional damping...........25
Figure 30. Acceleration data for simulation and test with mass proportional damping..............26
Figure 32. FFT of the acceleration data for simulation with stiffness proportional damping.....27
Figure 33. Acceleration data for simulation and test with stiffness proportional damping.........27
Figure 34. FFT of the acceleration data for simulation and test with stiffness proportional
damping.................................................................................................................................28
Figure 35. Acceleration data for simulation with filled OBR......................................................28
Figure 36. FFT of the acceleration data for simulation...............................................................29
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Figure 37. Mode shapes for a fundamental frequency.................................................................30
Figure 38. Contact force between the OBR and the mitigator.....................................................31
Figure 39. Acceleration data of the simplified and full model....................................................32
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Acknowledgments
The analytical work presented here was accomplished under a contract (Contract No. DAAD19-
02-D-001, TCN: 03-054) with the Scientific Services Program of U.S. Army Research Office,
Research Triangle Park, North Carolina. Air gun tests were conducted by Mr. Ara Abrahamian
of the Weapons and Materials Research Directorate, U.S. Army Research Laboratory (ARL).
The contributions of Mr. Ara Abrahamian, Mr. Edward Szymanski, and Mr. William McIntosh
of ARL in delivering the air gun test are greatly appreciated. Dr. Dave Hampton of the
U.S. Military Academy at West Point provided a helpful review of the report, which is greatly
appreciated.
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