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Computer Modeling of Blast Loading Effects on BridgesGreg Black Lafayette College Easton, Pennsylvania Advisor: Dr. Jennifer Righman University of Delaware Newark, Delaware Submitted to NSF-REU 11 August 2006

AbstractThe goal of this report is to evaluate a hydrocode, which is a type of computer program, called AUTODYN for the use of modeling blast loads on bridge sections. Blast modeling is necessary due to the threats posed by terrorist attack and current technology makes computer simulations cheaper than experimental testing. It discusses various options presented by AUTODYN which set it apart from other hydrocodes and other available software. These include the benefits of it graphical interface, modeling options and remapping capabilities. Meanwhile, its large demand on memory for complex models creates issues in the modeling phase, before the models can actually be analyzed. Yet if the user can get past the quirks of the program and work within the memory limits it is possible to obtain fairly accurate results from carefully made models.

Table of ContentsABSTRACT .................................................................................................................................................. 2 1 INTRODUCTION ..................................................................................................................................... 5 2 INTRODUCTION TO BLASTS .............................................................................................................. 5 2.1 EXPLOSIONS ......................................................................................................................................... 6 2.2 CONWEP............................................................................................................................................... 7 3 INTRODUCTION TO HYDROCODES ................................................................................................. 8 3.1 MODELING TECHNIQUES ...................................................................................................................... 9 3.1.1 Structured vs. Unstructured Solvers .......................................................................................... 11 3.1.2 Lagrange Solvers ....................................................................................................................... 13 3.1.3 Euler Solvers.............................................................................................................................. 14 3.1.4 Other Solvers ............................................................................................................................. 16 3.2 INTRODUCTION TO AUTODYN.......................................................................................................... 17 3.2.1 Material Models......................................................................................................................... 18 3.2.2 Parts........................................................................................................................................... 20 4 MODELING AND RESULTS................................................................................................................ 23 4.1 AUTODYN MODELS ......................................................................................................................... 23 4.2 RESULTS AND DISCUSSION ................................................................................................................. 27 4.2.1 Pressure in the Slab ................................................................................................................... 28 4.2.2 Deflection in the Slab................................................................................................................. 32 4.2.3 Effective Strain in the Slab......................................................................................................... 33 4.2.4 Pressure in the Air ..................................................................................................................... 34 4.2.5 Conclusions and Suggestions for Future Investigation.............................................................. 37 5 ACKNOWLEDGEMENTS .................................................................................................................... 38 6 REFERENCES ........................................................................................................................................ 38 APPENDIX MODELING NOTES ........................................................................................................ 40

List of FiguresFigure 2.1 Charge and Blast Wave...............................................................................................6 Figure 2.2 Standard Pressure vs. Time Curve for an Explosion...................................................7 Figure 3.1 Example Grid.............................................................................................................10 Figure 3.2 Typical Calculation Sequence...................................................................................11 Figure 3.3 Structured Grid..........................................................................................................12 Figure 3.4 Unstructured Grid......................................................................................................13 Figure 3.5 Example Lagrange Grid...13 Figure 3.6 Example of Normal Mesh and (a)-(d) Examples of Problematic Mesh Distortion..14 Figure 3.7 Stationary Euler Grid Example15 Figure 3.8 Example SPH Node Dispersal17 Figure 3.9 Example of Erosion..19 Figure 4.1 Standard Slab, Air and Charge Model...24 Figure 4.2 Standard Slab, Air and Charge Model...24 Figure 4.3 (a) Moving Gauges in Slab (b) Fixed Gauges in Air...26 Figure 4.4 Pressure vs. Time for Gauge #1, Same Air Element Size.........................................28 Figure 4.5 Pressure vs. Time for Gauge #2, Same Air Element Size.........................................29 Figure 4.6 Pressure vs. Time for Gauge #1, Same Slab Element Size......................................30 Figure 4.7 Pressure vs. Time for Gauge #2, Same Slab Element Size......................................31 Figure 4.8 Deflection Comparison for the Back Center of the Slab............................................32 Figure 4.9 Effective Strain vs. Time for Gauge #2, Same Air Element Size...............................33 Figure 4.10 Effective Strain vs. Time for Gauge #2, Same Slab Element Size..........................34 Figure 4.11 Initial Pressure Results for 1000mm from Charge Center.......................................35 Figure 4.12 Remap of Wedge onto 20mmel Air and 20mmel Slab.............................................36 Figure 4.13 Comparison of 10mmel Wedge, ConWep and Remapping Results at 1000mm from Center of Charge...........................................................................................................................37

List of TablesTable 4.1 Models........................................................................................................................27 Table 4.2 Gauge #1 Initial Peak Pressure, Same Air Element Size............................................29 Table 4.3 Gauge #2 Initial Peak Pressure, Same Air Element Size...........................................29 Table 4.4 Gauge #1 Initial Peak Pressures, Same Slab Element Size.......................................31 Table 4.5 Gauge #2 Initial Peak Pressures, Same Slab Element Size.......................................31

1 IntroductionThe events of 9/11 continue to have a lasting effect on the US and the world. Everyone on the planet has been affected in some way or another. The implications of the vulnerability of the nations infrastructure to terrorist attack are a concern that should be shared by all engineers. If bridges and other structures may be subjected to severe loads from explosions or other sources, then it is the engineers responsibility to prepare for them. However, before design codes can be better developed or adequate protections can be created it is necessary to gain a better understanding of the complex interactions between structures and explosions. Yet methods for explosive testing are limited due to cost and permissions for experimental results. Therefore, with modern advances in computing technology called hydrocodes may be a better option. This paper will evaluate a hydrocode program called AUTODYN for the use of blast simulation on complex structures, with a focus on hydrocodes as a technology and user interactions with the program as well as the accuracy of the several simulations run in the program. It will also provide the reader with a brief overview of blasts or explosions in order to provide some background on the subject as well as a basis for the comparison of test results.

2 Introduction to BlastsThis section will discuss a few of the basic properties of explosions. Once these ideas are understood, the interactions between explosions and structures can be more easily discussed. It will also discuss ConWep, a blast calculation program distributed by

the United States government (Robert, 2007), which will be used to evaluate the performance of AUTODYN.

2.1 ExplosionsFigure 2.1 depicts a few of the basic characteristics of a simple explosion in air. There is the charge (a), the pressure wave (p) and the standoff distance (r). The main component that any explosion requires is some type of fuel or charge such as TNT. When ignited, this charge rapidly releases energy in the forms such as heat, sound or pressure waves (Robert, 2007). The pressure wave expands out from the charge. The leading edge of this wave is sometimes called the shock front and will generally have the highest pressure in the wave

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