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LS-DYNA FOR BEGINNERS

Qasim H. Shah Hasan M. Abid

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Disclaimer The information contained in this book has been obtained from personal experience with the software. The information provided may not be correct, complete or accurate. The authors do not take any responsibility for any losses resulting from using this information.

Qasim H. Shah Associate Professor Department of Mechanical Engineering International Islamic University Malaysia Jalan Gombak Kuala Lumpur 50728 Malaysia. Email: [email protected] http://staff.iium.edu.my/hqasim/ March 22, 2012

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Table of Contents LS-DYNA FOR BEGINNERS ................................................................................................................ 0 Disclaimer .............................................................................................................................................. 2 Preface ................................................................................................................................................. 10 CHAPTER 1.......................................................................................................................................... 11 Introduction͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ ͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ϭϭ Units͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ ͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ϭϭ LS PREPOST Versions͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ ͘͘ϭϭ ELEMENTS AND FEA MODEL͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ ϭϮ MATERIAL MODELS͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ ͘͘͘͘͘͘ϭϮ LSPREPOST PAGES͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ ͘͘͘͘͘ϭϯ K FILE͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ ͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ϭϯ COMMON KEYWORDS͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ ͘ϭϰ Termination time͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ ͘͘͘͘͘͘͘͘͘͘ϭϰ ͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ ͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ϭϰ d3plot͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ ͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ϭϰ MAT͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ ͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ϭϰ PART͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ ͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ϭϰ Section͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ ͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ϭϰ RIGIDWALL͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ ͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ϭϰ BOUNDARY͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ ͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ϭϰ DEFINE_CURVE͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ ͘͘͘͘͘͘͘͘͘ϭϰ ROTATING A MODEL͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ ϭϰ ZOOM IN ZOOM OUT͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ ϭϱ LSDYNA & LSPREPOST INTERNET FORUMS͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ϭϱ LSDYNA HELP SITES͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ ͘͘͘͘ϭϱ CHAPTER 2.......................................................................................................................................... 16 IMPACT͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ ͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ϭϲ MODEL MESHING͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ ͘͘͘͘͘͘͘͘͘͘ϭϲ MATERIAL MODELS͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ ͘͘͘͘͘͘ϭϴ SECTION PROPERTIES͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ ϭϵ PART͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ ͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ϭϵ PROJECTILE VELOCITY͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ ϮϬ ϯ

>^ͺzE&KZ'/EEZ^ ͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ ͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ϮϬ FIXING EDGES͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ ͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ϮϬ END TIME͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ ͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘Ϯϭ SHELL THICKNESS VARIATION CALCULATION͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘Ϯϭ GRAPHIC OUTPUT FILES͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ Ϯϭ SAVE THE K FILE͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ ͘͘͘͘͘͘͘͘͘͘͘Ϯϭ LS-DYNA SOLVER͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ ͘͘͘͘͘͘͘͘͘Ϯϭ POST PROCESSING THE RESULTS͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ Ϯϭ CHAPTER 3.......................................................................................................................................... 23 ROTATING TARGET͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ ͘͘͘͘͘͘Ϯϯ POST PROCESSING͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ ͘͘͘͘͘Ϯϳ CHAPTER 4.......................................................................................................................................... 29 FRICTION TO HEAT͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ ͘͘͘͘͘͘͘Ϯϵ *DEFINE_CURVE͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ ͘͘͘͘͘͘͘͘͘͘͘͘ϯϰ CHAPTER 5.......................................................................................................................................... 38 RUBBER MODELING͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ ͘͘͘͘͘ϯϴ CHAPTER 6.......................................................................................................................................... 43 TIE BREAK͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ ͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ϰϯ DEFINING MATERIALS AND SECTIONS͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ ϰϰ CREATING NODE SETS͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ ϰϰ APPLY DISPLACEMENT ONE EDGE͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ ϰϱ TO CONSTRAIN THE OTHER EDGE͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ ϰϱ CONSTRAINED_TIE_BREAK͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ ϰϱ RESULT͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ ͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ϰϲ Note͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ ͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ϰϲ CHAPTER 7.......................................................................................................................................... 47 LEAD PROJECTILE DEFORMATION͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ ϰϳ CHAPTER 8.......................................................................................................................................... 50 INTERNAL PRESSURE͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ ͘ϱϬ MATERIAL͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ ͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ϱϮ CONSTRAINTS͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ ͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ϱϮ Note͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ ͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ϱϯ APPLY PRESSURE͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ ͘͘͘͘͘͘͘͘ϱϯ ϰ

>^ͺzE&KZ'/EEZ^ RESULTS͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ ͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ϱϰ CHAPTER 9.......................................................................................................................................... 56 METAL CUTTING USING SPH͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ ϱϲ OVERVIEW͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ ͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ϱϲ BUILDING THE SPH MODEL͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ ϱϳ PARTCILE FILLING IN A SHELL BOX͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ ϱϳ ͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ ͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ϱϵ TOOL TRAVERSING͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ ͘͘͘͘͘͘ϲϬ SPH SPECIFIC͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ ͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ϲϭ RESULTS͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ ͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ϲϭ CHAPTER 10........................................................................................................................................ 62 VIBRATION ANALYSIS͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ ͘͘ϲϮ CHAPTER 11........................................................................................................................................ 65 IMPACT ON CONCRETE͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ ϲϱ CHAPTER 12........................................................................................................................................ 67 SLOSHING SIMULATION͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ ϲϳ Water and Air Modeling͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ ͘͘ϲϴ Node Merging͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ ͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ϳϮ Tank Shell Elements͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ ͘͘͘͘͘͘͘ϳϰ Part-Set Node-Set of Water and Air͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ ϳϵ Node-Set for Tank Velocity and Constrain͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ ϴϮ Material selection *MAT͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ ͘͘ϴϰ Water & Void Material͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ ͘ϴϰ Tank Material of Polycarbonate͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ ϴϱ Section type selection “*SECTION”͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ ϴϲ Water & Void/Air (*SECTION_SOLID_ALE)͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ϴϲ Tank (*SECTION_SHELL)͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ ϴϲ *EOS_GRUNEISEN͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ ͘͘͘͘͘͘͘͘ϴϳ *HOURGLASS͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ ͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ϴϳ *PART͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ ͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ϴϴ *DEFINE_CURVE͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ ͘͘͘͘͘͘͘͘͘͘͘͘ϴϵ * INITIAL_VOID_PART͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ ͘͘͘ϵϬ *INITIAL_VELOCITY͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ ͘͘͘͘͘͘͘ϵϭ ϱ

>^ͺzE&KZ'/EEZ^ *LOAD_BODY_Y͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ ͘͘͘͘͘͘͘͘͘͘͘͘͘ϵϭ Identifying Reference Nodes for ALE͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ ϵϮ Identifying the three reference nodes͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ ϵϯ *ALE͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ ͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ϵϰ *ALE_REFERENCE_SYSTEM_NODE͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ ϵϰ *ALE_REFERNCE_SYSTEM_GROUP͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ ϵϰ *BOUNDARY_PRESCRIBED_MOTION_SET͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ϵϱ *BOUNDARY_SPC_SET͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ ϵϱ *CONSTARINED_LAGRAGE_IN_SOLID͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ ϵϲ *CONTROL͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ ͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ϵϳ *CONTROL_ALE͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ ͘͘͘͘͘͘͘͘͘ϵϳ *CONTROL_ENERGY͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ ϵϳ *CONTROL_TERMINATION͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ ϵϳ *CONTROL_TIMESTEP͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ ϵϴ *DATABASE͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ ͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ϵϴ *DATABASE_OPTION͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ ϵϴ *DATABASE_BINARY_D3PLOT͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ ϵϵ *DATABASE_BINARY_FSIFOR͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ ϭϬϬ *DATABASE_EXTENT_BINARY͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ ϭϬϬ *DATABASE_FSI͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ ͘͘͘͘͘͘͘ϭϬϬ Result͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ ͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ϭϬϮ CHAPTER 13...................................................................................................................................... 103 EFFECT OF EXPLOSION ON A CONCRETE WALL͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ϭϬϯ GENERATING PARTS͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ ͘ϭϬϰ SECTION PROPERTIES͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ ϭϬϱ MATERIAL PROPERTIES͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ ϭϬϱ EQUATIONS OF STATE (EOS)͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ ϭϬϲ ALE CARDS͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ ͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ϭϬϲ PART SETS͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ ͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ϭϬϳ CONSTRAINED_LAGRANGE_IN_SOLID͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ϭϬϴ INITIAL_DETONATION͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ ϭϬϵ TIME STEP SIZE͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ ͘͘͘͘͘͘͘͘͘͘͘ϭϬϵ ϲ

>^ͺzE&KZ'/EEZ^ RESULTS͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ ͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ϭϭϬ CHAPTER 14...................................................................................................................................... 111 LSPREPOST & LSDYNA TIPS͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ ϭϭϭ *Interface_Springback_Lsdyna͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ ϭϭϭ How to view node and element numbers?͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ϭϭϭ SPH Appearance͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ ͘͘͘͘͘͘͘͘͘͘͘ϭϭϭ SPH PART GENERATION͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ ϭϭϭ Refining Mesh͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ ͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ϭϭϮ Increasing memory in SPH analysis͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ ϭϭϮ SPH particles through shell or solid elements͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ϭϭϮ Filling SPH particles as a liquid in a tilted container͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ϭϭϮ Element failure criteria͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ ͘͘ϭϭϯ 2D Analysis͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ ͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ϭϭϯ *_Tiebreak_Surface_to_Surface͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ ϭϭϯ SPH to model foam͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ ͘͘͘͘͘͘͘ϭϭϯ Applying Pressure on liquid surface͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ ϭϭϯ Generating a new part from a portion of an existing part͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ϭϭϰ OUT OF RANGE VELOCITY IN ALE SIMULATION͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ϭϭϱ HOW TO DISPLAY ELASTIC STRAIN VALUES?͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ϭϭϱ WHEN EOS IS REQUIRED?͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ ϭϭϱ *MAT_ADD_EROSION USAGE͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ ϭϭϱ HOW TO USE MAT_084?͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ ϭϭϲ HIGH VELOCITY IMPACT͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ ϭϭϲ HEB AND AIR MODELING͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ ϭϭϳ COMBATTING INSTABILITY IN ALE͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ ϭϭϳ USING *MAT_CONCRETE_DAMAGE_REL3 (MAT_072 R3)͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ϭϭϳ USING *CONSTRAINED_NODAL_RIGID_BODY͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ϭϭϴ USING ELASTIC_PLASTIC_HYDRO MATERIAL͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ϭϭϴ HOW TO DISPLAY STRAIN IN VECTOR FORM?͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ϭϭϴ NECESSARY INPUT TO EXTRACT VIBRATION MODES͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ϭϭϵ HOLE FILL WITH SHELL ELEMENTS͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ ϭϭϵ IN POST PROCESSING WHAT DOES PRESSURE MEAN?͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ϭϮϬ ϳ

>^ͺzE&KZ'/EEZ^ NOTE ON JOHNSON COOK MATERIAL MODEL͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ϭϮϬ PATH PLOT͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ ͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ϭϮϭ HOW TO ERASE ELEMENTS BUT KEEP THE SURFACES TO REMESH AGAIN͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ϭϮϭ FULLY INTEGRATED SHELL ELEMENTS͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ϭϮϮ FILE GLSTAT͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ ͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ϭϮϮ FILE MATSUM͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ ͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ϭϮϮ VIEWING FRICTIONAL ENERGY[*]͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ϭϮϮ HOW TO CONNECT SPH PART TO SOLID ELEMENT PART͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ϭϮϯ CHAPTER 15...................................................................................................................................... 125 USAGE of LOAD BLAST ENHANCED͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ ϭϮϱ MATERIAL PROPERTIES͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ ϭϮϱ SECTION PROPERTIES͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ ϭϮϲ BOUNDARY CONDITIONS͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ ϭϮϲ TERMINATION TIME & TIME STEP͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ ϭϮϲ *LOAD_BLAST_ENHANCED͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ ϭϮϲ *LOAD_BLAST_SEGMENT_SET͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ ϭϮϲ UN-REFERENCED CURVES͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ ϭϮϳ DATABASE_BINARY_BLSTFOR͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ ϭϮϳ PARTIAL INPUT͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ ͘͘͘͘͘͘͘͘͘͘͘͘ϭϮϳ CHAPTER 16...................................................................................................................................... 129 Spot Weld͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ ͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ϭϮϵ ^ƉŽƚtĞůĚĚĂƚĂ͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ ͘͘͘͘͘͘͘͘͘͘͘͘͘ϭϮϵ CHAPTER 17...................................................................................................................................... 132 LS-DYNA MATERIAL MODELS ........................................................................................................ 132 MAT_SOIL_AND_FOAM_FAILURE (*MAT_005)͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ϭϯϮ MAT_HIGH_EXPLOSIVE_BURN (*MAT_008) C4͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ϭϯϮ EOS_JWL͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ ͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ϭϯϯ DdͺDK/&/ͺW/t/^ͺ>/EZͺW>^d//dz;ΎDdͺϭϮϯͿ͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ϭϯϯ Ddͺ:K,E^KEͺKK<;ΎDdͺϬϭϱͿWK>zZKEd͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ϭϯϯ Ddͺ:K,E^KEͺKK<;ΎDdͺϬϭϱͿ&KZKWWZ͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ϭϯϰ ZĞĨĞƌĞŶĐĞƐ͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ ͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ϭϯϱ CHAPTER 18...................................................................................................................................... 136 INITIAL VOLUME FRACTION ........................................................................................................... 137 ϴ

>^ͺzE&KZ'/EEZ^ džĂŵƉůĞ͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ ͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ϭϯϳ KƵƚƉƵƚ͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ ͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ϭϰϮ References......................................................................................................................................... 144

ϵ

>^ͺzE&KZ'/EEZ^

Preface This book is the updated edition of previous publication ( “From Ls-Prepost to Ls-Dyna” published by LAP Lambert Publishers in July 2011). LS DYNA is one of the most popular explicit finite element based hydro-codes used to simulate structural response when the structures are subjected to dynamic loads. The software is used in the industry for design and prediction of structural response of varying nature structures ranging from automobiles to aircraft components when subjected to crash and impact loads. LS DYNA is also very popular with academia where researchers in engineering field solve complicated problems using this code. LS DYNA has been developed by Livermore Software Technology Corporation (LSTC). The software manuals are available from the LSTC website free of charge. Because of the large size of the program the Keyword ’s manual that explains the LS DYNA commands in detail spans over 2400 pages of text. Software commands are written in a certain format that has to be followed to create an input file. Among other software LSTC also provides LS-PREPOST software that is very friendly software to create LS DYNA input file and produce the simulation results in graphic and text format. A successful is supposed to integrate LS DYNA Keyword manual commands with LS-PREPOST. There are many websites that explain the usage of this software with the help of examples and FAQs yet the beginners feel they require more friendly instructions to acquaint themselves with LS DYNA. The present effort is a step in this direction to familiarize the beginners with the software. Each chapter of this book contains an example problem explained step by step so that the can easily achieve an insight into the software. Each chapter can be pursued independently but the Introduction chapter at the start of the book (Chapter 1) and tips chapter (Chapter 14) consists of common knowledge regarding LS PREPOST and LS DYNA that should be read before attempting any of the examples. LS-PREPOST usage has been detailed in every chapter because the is supposed to prepare LS DYNA input files using LS-PREPOST although one can type commands in a text editor. It is hoped that this book would come as a handy manual to help the beginners in the usage of LS-PREPOST and LS-DYNA. The input files for all the example problems solved in this book are available on the author’s website: http://staff.iium.edu.my/hqasim/?LS-DYNA_INPUT_FILES University Malaysia. ϭϬ

at International Islamic

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CHAPTER 1 Introduction In this chapter many important points are explained that must be read before solving any of the examples in the forthcoming chapters. This is to be emphasized that LS DYNA is a computer program where the is supposed to use LS DYNA ‘solver’ to perform calculations, all the input and output however is handled by LS-PREPOST. Therefore an expert knowledge of LS-PREPOST is crucial in learning the software. The first of all must understand what sort of simulation is to be performed and how does it match with the physical problem. There are at times many different routes that can be pursued to solve the same problem. Most of the LS DYNA commands listed in ‘Keyword manual’ can be found in the LS PREPOST though there might be exceptions at times for certain commands that have newly been implemented in LS DYNA. Sometimes the commands available in LS PREPOST and in LS DYNA might not be available in the LS DYNA solver because for example a certain ‘material model’ might belong to a third party except whose permission that part of the program might not be accessible. Units In this book a particular set of units would be followed therefore the s are encouraged to refer to section “Getting Started” in the Keyword manual [1] if they wish to use other units. The units used in this book are; kN, GPa, kg, mm, milliseconds. LS PREPOST Versions LS PREPOST is a free software and is available for from http://www.lstc.com/lspp/. Instruction manuals are also available at this site though tutorials are available for an older version (Ver. 2.4). At present there are two existing versions for windows systems. Ver. 2.4 and 3.1. Ver. 2.4 is old version while Ver. 3.1 is current version of the software. New builds of these two versions are made available on weekly and sometimes on daily basis on bug reports by s. In Ver. 3.1 the Ver. 2.4 can be accessed by pressing F11 key on the keyboard. The author is more familiar with Ver. 2.4 and finds it very helpful but Ver. 3.1 has ϭϭ

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enhanced capabilities s to build an FEA mod del in it. A screen sho ot is shown n in Fig. 1 for Ver. 2 2.4., where e the commands used could be id dentified byy blue highlighted colorr.

F Fig.1. Page 3 of LS-PR REPOST ELEMENTS AND FEA A MODEL A Among ma any types of elements the most common c ele ements ava ailable in LS S DYNA arre solid, s shell, beam m, and ma ass elemen nts. Depen nding upon the usage the ‘secction’ differe entiates between the t elements selected. For example e u under Secttion_Shell there are e many f formulation ns available to be chosen. c Siimilarly Se ection_Solid d provides various element e f formulation ns for a solid d element. Model geometry can be importe ed into LS PREPOST T from CAD D software as IGES files and t then meshe ed into app propriate ele ements. File es from oth her FE softw ware like NASTRAN can c also be imported d. FE mode els could be e built direcctly within LS L PREPOS ST although complex models pose difficu ulties and in nstead sho ould be imported. Prim mitives like Solid S Box, Shell Cylinder etc. could be meshed m using LS PRE EPOST. Ve er. 3.1 facilitates build ding model geometry and FE models effe ectively. MATERIAL L MODELS S T There are more than 255 materrial models available in LSDYNA A. These material mod dels are on constituttive equatio ons and th he ability to o select th he most ap ppropriate material m based upo model for a problem at a hand is very v importtant. Many material models can pose p difficu ulties as ϭϮ

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their input parameters might not be easily available to the . Some models do not have the explanation for their input parameters written in the software manuals instead the spaces are left blank. Same material may behave differently when subjected to varying strain rates therefore even if one set of input parameters are available one should make sure that those parameters were suitable under the given strain rates and other boundary conditions. From the author’s experience selection of material input parameters is the most difficult task in performing LSDYNA simulations. A beginner can start with simple material model examples and slowly learn more complex material models at a suitable pace. A thorough explanation on many aspects of LSDYNA could be found on the internet [2] including some material models. To start with a beginner is encouraged to use the material models available at the following website [3]. Material selector for LSDYNA is a very informative and helpful browser available at http://app.d3view.com/d3mat/index. LSPREPOST PAGES As shown in Fig.1 LSPREPOST Ver. 2.4 interface consists of page 1 through 7 and D page. Page 1 is used to see the simulation results. Page 2 and 3 are to build the FEA model. Here page 3 carries most of the required keywords (commands) in most of the input files. A description of all the pages and commands could e found at LSTC site [4]. Tutorials are also available on this site. K FILE LSDYNA standard input file extensions are ‘.k’ or ‘.dyn’. LSPREPOST automatically writes the input files with extension ‘.k’. K files are text files and can be opened in any text editor. Microsoft Wordpad is a suitable text editor for k files but UltraEdit is considered a luxury. K files can have commands in any sequence. Once the file is generated using LSPREPOST the need not worry about the file format. It is possible to type commands in a text editor as mentioned before though the process may be cumbersome. In certain cases one may be required to type some brief information using a text editor when copying information between multiple files. A large K file can be truncated into small pieces and these could be called using the keyword *include. All small files can have extension ‘.k’.

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COMMON KEYWORDS Termination time This is the time required to complete the calculation. It is required keyword in a K file so that LSDYNA knows when to stop. It is included using *Control_Termination. A value is assigned to ‘ENDTIM’ under *Control_Termination card. This command defines the between different parts in a simulation. There are many types of s available. could be defined between various parts or as self when a part deforms enough to come into with itself. d3plot Graphic output files (binary files) are named d3plot…. Depending upon the size of simulation there maybe multiple d3plot files output starting with d3plot, d3plot01, d3plot02, etc. This file is generated using *Database_Binary_d3plot keyword. The time interval between plots can be controlled by inputting an appropriate value for ‘dt’. MAT Clicking this Tab on page 3 would open a list of all material models available. PART Each part essentially consists of material and section properties besides other parameters like EOSID, HGID, etc. Section: Under this keyword a shell, solid, beam, mass, etc are defined. A thin structure would normally consist of shell elements. Shell thickness, number of integration points, and the element formulations are defined here. Depending upon the element formulations one may decide how the element will respond to external loads. Section Solid or Section Beam defines solid element and beam element parameters. Section SPH defines the particle elements. RIGIDWALL: Various types of rigid walls can be defined that do not deform under loads. BOUNDARY: A large number of boundary conditions can be defined using this keyword. Constraints on nodes or parts are defined. Moreover translating/rotating parts are also defined. DEFINE_CURVE Although keyword ‘define’ can define parameters, define curve is the most commonly used command to define curves like time versus velocity/displacement etc. ROTATING A MODEL Rotating a model on screen is done by left mouse button while keeping SHIFT key pressed down. ϭϰ

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ZOOM IN ZOOM OUT Use right mouse button to zoom in and zoom out while keeping SHIFT key pressed down. LSDYNA & LSPREPOST INTERNET FORUMS There is an LSDYNA forum as Yahoo LSDYNA group. s with Yahoo can become member for LSDYNA Yahoo group where they can share information regarding the software usage with other people. There is also a group for LSPREPOST for people with Google where questions and answers are entertained regarding the usage of LSPREPOST. Input files and tips are ed on both of the above mentioned two groups by s on daily basis. LSDYNA HELP SITES http://www.cadfem.de/en.html http://www.lsdyna.eu/index.php?id=706 http://www.dynalook.com/ http://www.dyna.com/

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CHAPTER 2

IMPACT

Fig. 2.1 In this chapter a step by step example would be solved to simulate a projectile impact on a plate using LSPREPOST and LSDYNA. Start the LSPREPOST and toggle F11 key on the keyboard so that the menu like the one shown in Fig.2.1 is displayed. Click on page 6>mesh> MODEL MESHING In the Entity select box select 4N-Shell. Click on P1 and insert coordinates for point 1 as x,y,z (0.0, 0.0, 0.0) and click ‘done’. Now click P2 and insert coordinates for point 2 as (100.0, 0.0, 0.0) and click ‘done’. Insert for point 3 and 4 the coordinates as follows; 3( 100.0, 50.0, 0.0), 4(0.0, 50.0, 0.0). Next insert 100 and 50 in the fields NxNo and NyNo respectively and click on ‘Create’ and ‘Accept’ buttons. Using Shift + right mouse button reduce the model size to fit in the window. This has resulted in a plate of 100X50 mm meshed with 100 elements in x and 50 elements in y direction and is shown in Fig.2.2.

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Fig. 2.2 Me eshing plate e model W would next model a cylindriccal projectille in front of We o the plate at a small distance frrom the ndow as sh hown in Fig g.2.3. Here the cylinde er radius = 6 mm, plate. Fill the Cylinder_Solid win 2 mm, num mber of elem ments in ciircumferenttial direction are = 16 6 and in the e length length = 12 d direction th here are 12 elements. The cylinde er center iss located at x = 50 mm m , y = 25 mm, m and z = 5 mm, and a the cylinder length h is parallell to z direction (dirz = 1).

Fig. 2.3 Input parameters for a solid cylin nder T model would look The k like the one displaye ed in Fig.2..4. Let us pause p and see what we w have d done until this t point. We W have meshed m a re ectangular plate p and created c a cyylindrical prrojectile in front of it. We would need to now n define the materials and secction prope erties for the ese two ϭϳ

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parts. We would w also constraint the extrem me edges of o the plate e and define e a velocityy of the projectile. As A the proje ectile is goiing to impa act the plate e, the conta act between n them hass also to be defined..

Fig. 2.4 Pla ate and Pro ojectile Messh: Isometriic view. MATERIAL L MODELS S First of all let us defin ne the matterial prope erties for the plate and d the projectile. Click the top n ‘*MAT’ on n page 3 of LSPREPO OST. Chang ge the field ‘Sort’ to ‘tyype’ and ‘M Model’ to right button ‘All’. A ma aterial mode el list will be displaye ed. Click on o ‘003-Pla astic_kinem matic’ and ‘Edit’. A w window as shown in Fig. F 2.5 will be displaye ed. Click ‘A Add’ and fill in the field ds as shown n in Fig. 2 and clicck ‘accept’ and 2.5 a ‘done’. Now repea at the above e procedure e to select second ma aterial for ‘0 020-Rigid’ and a fill in th he fields as shown in n Fig. 2.6.

Fig. 2.5 5 Plate Mate erial ϭϴ

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Fig. 2.6 Projectile P Material T material propertie The es in Fig. 2.5 are for material m 1 arre as follow ws; Density = 2.7 2 kg/mm3 (2700 kg/m m3), Elasticc Modulus = 70 GPa, Poisson’s Ratio R = 0.34, Yield Strength = 0.267 GPa a (267 MPa), Tangen nt Modulus = 0.32GPa a (320 MPa), and the e failure s strain = 0.2 28 (28%). T Rigid material The m mo odel parameters are shown s in Fig g. 2.6. Thiss is conside ered to be material m 2 in this mo odel. IES SECTION PROPERT P Click ‘*secction’ and th he ‘shell’ on n page 3>Edit Click ‘Add’ and insert parameterss as shown n in Fig. 2.7

Fig. 2.7 7 Section_S Shell S factorr = 0.833 (this ( value is used to control In this figure Shell thickness = 0.4 mm, Shear N of Inte egration po oints throu ugh the th hickness = 5, and element e hourglass modes), No. f formulation n 2 (Belytsc chko-Tsay fo ormulation)) has been used. Now repea at the prece eding proce edure for ‘ssection_solid’. Click ‘A Add’ , ‘acce ept’, and ‘d done’ At t this stage no n input forr this card iss required. PART Now click ‘PART’ from m page 3 and a click ‘Ed dit’. In the window w asssign materiial 1 and se ection 1 t PART 1 and materrial 2 and section to s 2 to o PART 2. Click ‘acce ept’, and ‘do one’. At thiis stage h been assigned with w their respective material and section pro operties. both parts have

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PROJECTIILE VELOC CITY Click ‘*Initia al_Velocity_ _Generatio on’ on page e 3 and inse ert values as a shown in n Fig. 2.8. ‘S STYP = 2 means this velocity 2’ y is assigne ed to a PART while NSID/PID N = 2 means PART 2 ha as been v Pa art 2 movess in negativve z directtion. Click ‘accept’ an nd ‘done’ as a usual assigned velocity. here.

Fig.. 2.8 Assign ning projecttile velocityy T A After cruising for a sho ort time the e projectile will come in nto with the ta arget plate. To let it ct’ on page e 3 and the en ‘automa atic_surface e_to_surfacce’ from the e list of happen clicck ‘*contac s. Fill F up the window w fields as shown n in Fig. 2.9 9.

Fig. 2.9 Conta act between n two parts. SSID 2 is an abbreviation for Slave S set ID D and MSIID stands for f Master set ID. He ere Part 2(projectile e) is a slave e and Part 1(plate) 1 is a master in LS DYNA terminolog gy. SSTYP = 3 and MSTYP = 3 says thatt slave and master are e both partts. Drop down menu gives g details about o other possiible choices s. FIXING ED DGES W would now constrrain the two We o vertical edges of the e plate. Firsst click ‘SettD’ on page e 5 and t then ‘create e’. Now che eck radio button b ‘Area a’ from the south-westt of the scre een and ma ake two boxes arou und both ed dges so tha at all the ve ertical edge e nodes are e selected. Then clickk ‘Apply’ and ‘Done’. By doing this nodes on both ve ertical edge es have bee en selected d and a nod de set 1 has been generated. g Next click ‘Boundary’’ from page 3 and se elect ‘SPC C-SET’ ‘Editt’ and in th he window w that is d displayed c click on ‘Ad dd’ then sellect NSID as a 1 and re eplace 0 witth 1 in DOF FX, DOFY, DOFZ, DOFRX, DOFRY, DO OFRZ. That constrains node set 1(vertical ed dge nodes on o plate) in n 6 DOF.

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END TIME Click ‘*Control_Termination’ ‘Edit’ and insert 0.5 in ENDTIM field. This means that the calculations would be done until 0.5 milliseconds. SHELL THICKNESS VARIATION CALCULATION To calculate the plate thickness variation and being able to display this information in the output another control card is required. Click ‘*Control_Shell’ and insert 1 in ISTUPD field. Click ‘accept’ and ‘done’. GRAPHIC OUTPUT FILES To obtain the graphic results click ‘*Dbase’ and then ‘BINARY_D3PLOT’ and insert 0.01 under ‘dt’ field. Click ‘accept’, and ‘done’. This will generate plot files every 0.01 milliseconds. SAVE THE K FILE At this stage the input file should be saved with an extension as ‘.k’. LS-DYNA SOLVER Start LS-DYNA solver and execute the input file. This will generate d3hsp, d3plot, and some other files depending upon the parameters selected in the input file. On windows based computers the environments differs slightly depending on the interface being used. Linux systems use a script file to run LS DYNA jobs. POST PROCESSING THE RESULTS The results from the LSDYNA simulations can be viewed in LSPREPOST. Output is available through page 1 of LSPREPOST. The results consist of structural deformations, strains, stresses, forces, reactions, nodal and element histories, pressures, temperatures and a lot of other information. Page 1 is shown in Fig. 2.10. Most of the information can be accessed through ‘Fcomp’ button.

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F 2.10 Pa Fig. age 1 LSPR REPOST V Von-Mises stresses are a displaye ed in Fig. 2.11 2 after the t projectile es through the e target ample. plate in ourr impact exa

Fig. 2.11 Von-Misess Stresses in the targe et plate at 0.06 millisecconds.

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CHAPTER 3 ROTATING TARGET

Fig. 3.1 At times a target plate might be in motion. In this chapter an example would be solved where a circular deformable plate is rotating about its central axis and is struck by a rigid spherical projectile near its periphery normal to the plane of the plate. To model a circular plate toggle F11 button on the keyboard to display the LSPREPOST ver 3.1 interface as shown in Fig. 3.2. First click on ‘element and mesh’ icon as shown by arrow 1 and then click ‘shape mesher’ icon as shown by arrow 2. Shape mesher window will be displayed. Fill the fields as shown and click ‘create’ and ‘accept’ buttons. A meshed plate is the result. this needs some experience to obtain a regular shape mesh like this.

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Fig. 3.2 Creating Circular plate To create the projectile, repeat the above procedure for “Sphere_Solid” as shown in Fig. 3.3. A sphere is generated in front of the circular plate. Now repeat the material selection for both the plate and the spherical projectile as we have done in Chapter 2. Solid and Shell section should be created with the same values. In this model circular plate has PART ID #1 and the projectile is PART 2.

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Fig. 3.3 Creating Solid Sphere Once the two material models and section properties have been decided the next step is to assign these to the respective parts. Click PART on page 3, edit the parts one by one by inserting ‘section’ and ‘material’ IDs into the PART fields. Now the parts information is complete. In this example we intend to rotate the circular target plate (PART#1) and impact it with the sphere (PART#2). To rotate the plate let us assume that the plate is rotating at 5000 rpm which is equal to 0.5235 radians per milliseconds. To achieve this first define a curve using ‘define’ on page 3 and then select ‘curve’ from the drop down list.

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Fig. 3.3 Define curve e input. In the ‘defin ne curve’ ca ard insert values v unde er A1 (absccissa) and O1 O (ordinate) as show wn in Fig. 3.3. and sa ave it. 5000 0 in the ord dinate field stands forr 5000 milliseconds. This T card in ndicates t that velocity remains s constant for this duration. d A the targ As get plate iss assumed d to be d deformable e the rotate e command d is applied d to its nod des. From page 5 cre eate a node e set of plate and save it. Now N click ‘*Boundary’’ and then n click ‘Pre escribed_Motion_Set’. In the s in Fiig. 3.4 slectt 1 under NSID. N DOF stands for degree d of freedom. f resulting window as shown w means the plate e rotates in y-z plane (about x axxis). VAD input i show ws if it is Select 9 which v velocity, accceleration, or displaccement. In n our exam mple it is 0 (zero) wh hich indicattes it is v velocity. A value of 1 under u LCID D stands forr load curve e ID. Here 1 means loa ad curve 1 is to be s card show wn in Fig. 3.4 3 we wou uld constraiin the innerr edge of th he plate used. Afterr saving this in x directio on (perpend dicular to th he plane of the plate).

Fig. 3.4 Bounday_Pr B rescribed_M Motion_Sett input.

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T create node To n set off nodes at the inner edge e of the plate go to o page 5 and a click on n SetD> Create> no ode-Set. No ow check ‘B ByEdge’ an nd ‘Prop’ bu uttons and click on the e inner edg ge. This w select all will a nodes att the inner edge. e Click ‘Apply’ and d ‘Done’. T apply a translation To nal velocity to the proje ectile click on ‘Initial’ > Velocity_ _Generation n and in t subseq the quent windo ow fill the ne ecessary fie elds as sho own in Fig. 3.5. 3

Fig g. 3.5 Initial Velocity generation g STYP = 2 stands s for ‘P PART’ NSID/PID = 2 means part # 2 (prrojectile) V = 90.00 VX 0 means the e projectile velocity in x direction (perpendiccular to plate plane). Save this card. c W now se We et the conta act between n the two parts p using * T command d on page 3. Click * * T and selec ct ‘Automatic_Surface_ _to_Surface’. Follow Fig. F 2.9 to complete c th he input. Set the te ermination time as 20 2 milliseco onds unde er EDNTIM M from *Co ontrol_Term mination command. Insert 0.05 5 under ‘DT T’ in d3plot card und der *Dbase that show ws that d3p plot files wo ould be o output everry 0.05 milliseconds. Execute the e LSDYNA and procee ed for post processing g session.

POST PRO OCESSING G V Von-Mises stress plott is shown in Fig. 3.6 after the projectile p ha as rebounded from the e target get plate is rotating. One O obviouss applicatio on is the biird strike on the aircra aft axial plate. Targ compresso or blades.

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Fig. 3.6 Von-Mises stresses in the rotating plate after impact by projectile

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CHAPTER 4 FRICTION TO HEAT

Fig. 4.1 Disk brake with friction pads. As two parts slide against each other their temperature rises due to friction. There are numerous applications in engineering where friction results in heat generation. In this chapter a simple example of this phenomenon would be presented with necessary details. The model shown in Fig. 4.1 is rather complex for the beginners therefore a simple model would be presented in this chapter. A square static plate with a rotating cylindrical roller against the plate will be modeled. In this example we will also generate two parts. To generate the square plate open the LS PREPOST interface for ver 3.1. Click on the two icons in sequence shown by Fig. 3.2 and input dimensions and mesh parameters as shown in Fig. 4.2 to generate a 4-N_SHELL also

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shown under the same figure. Next generate the second part which is a solid cylinder. Follow Fig. 2.3 to create a solid cylinder of appropriate dimensions and mesh.

Fig. 4.2 Generating a meshed square plate. Result should look like the isometric view in Fig. 4.3. Instead of modeling like in Fig. 4.1 we would attempt to make a simple model like the one shown in Fig. 4.3.

Fig. 4.3 Part generation The material properties for the plate (MID = 1) and the cylinder (MID = 2) are given in Fig. 4.4 for both the materials. MAT_PLASTIC_KINEMATIC (MAT_003) is the material model used. ϯϬ

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Material #1 has material properties for an aluminum alloy and materrial #2 posssesses properties for f steel.

Fig. 4.4 4 Elastic Pla astic Materiial model (**MAT_PLAS STIC_KINE EMATIC) fo or the plate and c cylinder. For a probllem where we intend to convert friction ene ergy into he eat in LSDY YNA simula ation we require to define d another set of material m pro operties carrds as show wn in Fig. 4.5. 4 Note th hat even t though we have already provided d material properties p u under mate erial model 1 & 2 we sttill need t define tw to wo more material m properties carrds to menttion the the ermal prope erties of the same materials ID Ds that is material m #1 & #2

Fig. 4.5 4 MAT_THERMAL_ISOTROPIC

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Now to define d sec ction prop perties use e the carrd ‘SECTION’ on page p 3. First a SECTION_ _SHELL and then SEC CTION_SOLID for platte and cylin nder must be b defined. Section cards for plate and cy ylinder are shown s in Fig. 4.6. For details of the parametters in thesse cards t is referred to the latest LSDYNA the L Ke eyword use er manual.

Fig. 4.6 4 Section cards to de efine and sh hell and solid structure es. Open ‘PAR RT’ and ass sign SECTIION#1 and MAT#1 to PART #1 (Plate) and d SECTION N#2 and MAT#2 to PART#2 P (so olid cylinde er) respectivvely. Next constrain the pla ate edges using u ‘*Bou undary_SPC_SET’. Node set should be cre eated to d this as mentioned do m earlier. e Next task is i to assign n angular velocity v to the solid cylinder abo out its axis (z-axis). Define D a curve as shown s in Fig. F 4.7 with the vallues shown n in the te ext below Fig. 4.7. Apply A a t translation to (z directtion) the so olid cylinderr so that it is forced against a the plate follow wing the of solid s sequence i Fig. 4.8. The details of both curves in c (for angular velocity and translation t cylinder) arre shown in n the text prrovided belo ow Fig. 4.8.

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Fig. 4.7 Two T comma ands to apply angular velocity v to the t solid cyylinder.

Fig. 4.8 8 Two comm mands to asssign transllation to the e solid cylin nder.

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*DEFINE_CURVE $#

lcid

sidr

1

0 1.000000 1.000000

$#

sfa

a1 0.000

sfo

offa

offo 0.000

dattyp 0.000

0

o1 2.0000000

10.0000000

2.0000000

*DEFINE_CURVE $# $#

lcid

sidr

2

0 1.000000 1.000000 a1 0.000

sfa

sfo

offa

offo 0.000

dattyp 0.000

0

o1 0.000

0.2000000

-0.5000000

0.3000000

-1.0000000

0.4000000

-1.5000000

0.5000000

-2.0000000

0.6000000

-2.5000000

0.7000000

-3.0000000

0.8000000

-3.5000000

0.9000000

-4.0000000

1.0000000

-4.5000000

1.1000000

-5.0000000

1.2000000

-5.5000000

1.3000000

-5.5000000

5.0000000

-5.5000000

To define the between the solid cylinder and the plate click * on page 3 using “_AUTOMATIC_SURFACE_TO_SURFACE” and insert parameters as shown in Fig. 4.9.

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Fig. F 4.9 Carrd to define between part 2 and 1. Next define e initial tem mperature off the structure at hand d to a very small value e as shown n in Fig. 4 4.10.

Fig. 4.10 Defin ne initial tem mperature. Other nece essary com mmands to be used in n this anallysis are sh hown in Fig. 4.11. Th he s should read d about the ese commands in deta ail in the late est LSDYNA A Keyword ’s man nual.

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Fig. 4.11 Other O necesssary cards required fo or the frictio on to heat analysis. a A After all the e above co ommands are a impleme ented in the e k file the may solve the problem p using LSDY YNA solverr. One of the representative outpu ut of tempe erature profile is shown n in Fig. 4 4.12.

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Fig. 4.12 Temperature profile of the plate and the cylinder.

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CHAPTER 5 RUBBER MODELING

Fig. 5.1 Displacement iso-surfaces of a bouncing rubber block. Having access to LSDYNA simulations could prove to be fun at times. Same are we going to do in this chapter. You might playing with a rubber ball that bounces back and forth until all its energy is dissipated. Here instead of thinking about its importance in engineering we would like to see how rubber can bounce back from hard surfaces on impact and how it deforms elastically until it settles down to its original shape and size. Let us model a solid box made up of rubber as shown in Fig. 5.2. Click on icons 1 and 2 as shown in Fig. 3.2 to make a solid box as shown in Fig. 5.2. The box dimensions are 40 mm each in X, Y, and Z directions with 10 elements divisions in each direction.

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Fig. 5.2 5 Rubber block 40 X 40 X 40 mm T come up To p with a hard surface we w would use u a comm mand called d “*RIGID_W WALL_PLA ANAR” f from input page p 3 of LSPREPOS L ST where it is shown as a a button “*Rgdwal” with w input parameterss as in Fig. 5.3. To add d this card after clickin ng on the “**Rgdwal” bu utton click Edit E and in the window w clic ck on “Add” button. The only values input are e YT and YH Y which sttand for ‘Y tail’ and ‘Y head’. This T means wall faces upward tha at is in Y dirrection or in n other words the w is mad wall de below the e solid box because solid box center is loca ated at (0.0,, 0.0, 0.0) in n this case.

Fig. 5.3 Rigid wall input. ϯϵ

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T rigid wall The w generated is shown in Fig. 5.4 4.

5 Rigid wall w below th he solid boxx. Fig. 5.4 Next define e the materrial properties for rubb ber. At this stage s *MAT T_027 can be used ass shown in Fig. 5.6 6. For the details of this materiial model the t can c read under this material m d description DYNA Keyw word manua al. Further details can n be obtaine ed from search on in the LSD t internett. the

Fig. 5.6 Rubber material model m inputt. In this exa ample only one PART T is require ed. The other entity is a rigid wall w that do oes not require ma aterial prope erties or se ection prop perties. Forr materials like rubberr it is advissable to use hourglass in the PART card d. The PAR RT and the HOURGLA ASS cards are shown n in Fig. 5.7

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Fig. 5.7 The PART T and HOUR RGLASS ca ards. A large de As eformations s are expeccted after th he rectangu ular solid ru ubber box comes c into w with the rigid r wall, defining the t interiorr between solid s box elements is also recommend ded as sho own in Fig. 5.8. For this to happ pen and pa art set has to be used d in the T_INTERIOR R card whicch includess only the PART #1.

Fig g. 5.8 Conta act interior for f the elem ments of rub bber block. T The velocitty of the ru ubber blockk is defined d as shown in Fig. 5.9 9. Here ST TYP = 2 sta ands for PART and NSID/PID indicates th he part ID fo or the part which w is asssigned thiss velocity.

Fig. 5.9 Rubbe er block movves in nega ative Y direction at 30 mm / millissec velocity.

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Rest of the necessary commands to be added are the “Control_Termination” and “*Dbase”. Once the k file is complete the k file can be run under LSDYNA.

Fig. 5.10 Shear stresses in the rubber block on impact.

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CHAPTER 6 TIE BREAK In this chapter the separation of two shell parts by pulling them apart would be demonstrated using a command “*Constrained_Tie_Break” on page 3 of LSPREPOST. The purpose is to be able to predict the failure of t between structures. The structure might have been glued together by some means and upon application of force the two structures separate based upon their plastic strain value. The structure is shown in Fig. 6.1 where two thin plates ( 1 mm thickness ) of same material ( an aluminum alloy ) are bonded together and their initial shape is shown in the figure. Top and bottom edges are pulled outward and after a certain plastic strain is encountered in the plate material the plates start tearing apart. In this model 4 node sets are constructed. Two node sets are the nodes located at the top and bottom edge as shown in the figure. Two other node sets consist of the nodes of the portion of two shell plates that are glued together. Among the nodes that are glued together one set that belongs to one plate are called the slave nodes and the other plate nodes are called master nodes.

Fig. 6.1 Two shell parts subjected to a tear apart based upon plastic failure strain.

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DEFINING MATERIA ALS AND SECTIONS Material an nd section cards sho ould be deffined as mentioned m in earlier chapters. c F your For reference the t images s of those 4 cards are e presented in Fig. 6.2. The inp put files forr all the examples are a availablle on the author’s a web bsite. T materiial propertie The es and the section pro operties for both partss in this exxample are same , t they should d therefore be repeate ed for both parts. p

Fig. 6.2 Ma aterial properties and section s card input. CREATING G NODE SE ETS Create two o node sets from the edges e of ea ach part as shown in Fig. F 1. As you y that t node sets are deffined using command “SetD” on page 5 of LSPREPOS the ST. To gen nerate a node set fro om one edg ge follow th he procedurre below. Click “SetD D” on page 5 > Create e > Node_S Set > By Ed dge ( from the t bottom of screen ) > prop > 45 and th hen click on the edge e. All the ed dge nodes would be highlighted. h Click “App ply” and “Done” to complete c the command d. T generatte the node To e sets of the e nodes tha at are glued d to each other o from two t parts th he most effective method m is to o select a single s part using u “SelP Par” from page p 1. When a single e part is d displayed r reorient it in n such a wa ay that the nodes requ uired to makke a set co ould be encllosed in a rectangular box. Ne ext Click “Se etD” on pag ge 5 > Crea ate > Node e Set > area a ( this buttton is at t bottom left of the screen the s ). Make M a box around the target nodes using mouse. m Clickk “Apply” ete the selecction. and “Done”” to comple

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A APPLY DIS SPLACEMENT ONE EDGE E T move one To o edge node set in a certain direction, d define a currve as give en in the input file. Next using “Boundary y_Prescribe ed_Motion_ _Set” apply displacement on the edge node e set as s shown in Fig. 6.3.

Fig. 6.3 Applying disp placement to a set of nodes. n

T CONST TO TRAIN THE E OTHER EDGE E One edge nodes ha ave to be constrained for all six s DOF. Using U “Bou undary_SPC C_SET” a edg ge nodes ass shown in Fig. 6.4. constrain another

Fig. 6.4 Constrainin ng a node set s in all 6 DOF. D CONSTRA AINED_TIE_ _BREAK T constrain the two parts togetther with th To he condition n that if the eir plastic strain reaches 0.15 t that is 15 % the parrts would tear t apart is done byy using “CONSTRAIN NED_TIE_B BREAK” a shown in Fig. 6.5. SNSID = 2 is the slavve node se et 2 and MN NSID = 1 in ndicates command as master nod de set.

onstrained tie break co ommand. Fig. 6.5 The usage of co T The

r

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to

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all

other

common

“CONTROL L_TERMINATION”, “C CONTROL_ _TIME_STE EP”, and “D Dbase” etc.

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RESULT T resultss for plastic strain are shown in Fig. The F 6.6 whe ere the 0.16 6 strain can n be seen near n the s separation zone while e plastic strrain for the potions tha at have alre eady separrated range es up to 0.83 ( 83% ).

Fig. 6.6 Plastic sttrain in the two shell pa arts when they t separa ate. Note W While mode eling the tw wo plates a gap of equ ual to twice the half thicckness of the plate sh hould be kept between two matting surface es as shown in Fig. 6.7 7.

Fig. 6.7 7 The gap between b sh hell structurres.

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CHAPTER 7

LEAD PROJECTILE DEFORMATION

Fig. 7.1 A lead projectile impacted on an aluminum block. Lead is known as a dense, soft, and ductile metal that undergoes large deformation when subjected to dynamic loads. In this chapter the procedure to conduct a simulation with a high velocity lead projectile coming into with an aluminum block would be discussed briefly. By now the is supposed to know how to create these two parts using LSPREPOST as shown in Fig. 7.1. The only difference between previous chapters and this chapter is that in the present example the projectile and the target plate are both considered to be deformable. After the model for the aluminum block and the projectile is made using LSPREPOST the material properties and section properties are defined as shown in Fig. 7.2 and Fig. 7.3 respectively.

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Fig. 7.2 Plastic Kin nematic mo odel for alum minum and lead materrials.

Fig. 7.3 Solid S sectio on is define ed for both parts. p T fixed edges The e of the e aluminum m block are highlighted d in Fig. 7.4.

Fig. 7.4 7 Fixed ed dges nodess highlighted. ϰϴ

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A surface to surface is defined between the projectile and the block. The problem is solved using LSDYNA solver and the result is shown in Fig. 7.5 regarding the plastic strain. It is upon the to investigate whether these results are realistic or not or what changes are needed to select a proper material model that matches the experimental evidence. All values given for material properties are approximate in this book. The is required to make suitable input files that suit his/her experimental work and the materials involved.

Fig. 7.5 Massive plastic strain in lead projectile.

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CHAPTER 8 INTERNAL PRESSURE In this chapter we will learn how to apply internal pressure on a cylindrical pressure vessel and observe the effect on the cylinder deformations and stresses. To construct a cylinder follow the input sequence given in Fig. 8.1 to make a cylinder with a radius of 60 mm and a length of 120 mm. The main axis of this cylinder is along Y direction. to check “Top and Bottom” if you desire a closed cylinder. Page 6 > Mesh > Cylinder_Shell.

Fig. 8.1 Construction of a cylindrical pressure vessel. As we are required to apply the internal pressure on the cylinder walls we must make sure if the orientation of the shell elements is suitable to apply internal pressure. This is done by clicking on Page 2 and then pressing “Normals”. The input sequence and its result is shown in Fig. 8.2. As it can be seen that the shell normals of the cylinder except its one end face of the cylinder are facing outwards. This is not going to let us apply internal pressure on the cylinder ϱϬ

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walls from inside. The shell normals of all shell elements facing outward have to e reversed. This is done by following the sequence as follows; Auto Reverse > Click on the region whose vector direction is to be followed > Auto Reverse. Make sure “By Part” is selected. Now the all the arrows should point inwards which is displayed in Fig. 8.3. This allows us to apply internal pressure correctly.

Fig. 8.2 View the shell normals.

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Fig. 8.3 All shell no ormals facin ng inwards such that applying a inte ernal presssure is posssible. MATERIAL L T material propertie The es ( MAT _0 003) and th he section properties p fo or this exam mple are sh hown in he shell thic ckness is 0..35 mm and d the failure e strain is 0.15 0 ( 15% ). ) Fig. 8.4. Th

F 8.4 The Fig. e material properties p and the secttion propertties for the cylinder. CONSTRA AINTS Using “Bou undary_SPC C_SET” on a set of ed dge nodes the t edge ca an be consttrained as shown s in Fig. 8.5. ϱϮ

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Fig. 8.5 Constraint on cylinder edge nodes. Note To make a node set of the edge nodes of the cylinder follow the sequence; Page 5 > SetD > Create > Node Set > By Edge (at the bottom of screen) > prop > Ang = 45 > Click on the edge > Apply > Done. APPLY PRESSURE To apply the internal pressure, define a curve which represents a relation between the time and pressure value. This is shown in Fig. 8.6.

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Fig. 8..6 Defining time versuss pressure using DEFINE_CURV VE. Next using LOAD_SE EGMENT_S SET apply the t pressurre on shell segments defined byy Create NT_SET fro om SetD of page 5. Th he image is shown in Fig. F 8.7. > SEGMEN

Fig. 8.7 Applying pressure of shell s segme ents.

RESULTS T Von-M The Mises stress s contours are a shown from the solution of this example in Fig. 8..8. Note t that increasing the prressure so that the plastic strain n rises beyo ond 15 % , the failure e of the cylinder can also be visualized. v

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Fig. 8.8 Von-Mises stress contours of a cylinder with an internal pressure.

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CHAPTER 9 METAL CUTTING USING SPH

Fig. 9.1 The model for metal cutting using SPH method. OVERVIEW An aluminum work-piece is to be machined using a rigid non-deformable cutting tool. The work-piece consists of particles instead of elements. The method adapted is called the Smooth Particle Hydrodynamics (SPH). In this example the cutting tool is made up of solid elements but the work-piece contains particles. The advantage of SPH is that the particles are free to move in space and they do not get entangled into each other like ordinary elements in finite element analysis. This method can also be used when the simulations of fluid structure interaction are performed. Moreover this method is very convenient of model large deformations of softer materials which otherwise is not possible using Lagrangian

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formulations. Modeling failure of very brittle materials is also possible using this method. Among few limitations one may be considered the computational cost incurred. BUILDING THE SPH MODEL There are different methods that can be used to build the mesh-less models in SPH. The particles can be generated from scratch by defining their coordinates and mass. The SPH particles can also be generated from solid elements and later the solid elements can be deleted. A third way of achieving the same goal is by making a shell box using “mesh” on page 6 of LSPREPOST. The empty shell box is then filled up by particles by adjusting the density of particles, material density, and percentage fill in a certain direction. To generate the model in this example this third procedure was used. The sequence for building SPH is to first generate a BOX_SHELL of required dimensions and deciding about the number of elements in X, Y, and Z directions. This is done on page 6. Next the shell box has to be filled. PARTCILE FILLING IN A SHELL BOX The sequence for filling a shell box is as follows; Page 7 > SphGen > Select Pick Part > Click on the shell box > Fill the fields as shown in Fig. 9.2 >Apply >Accept > Done.

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Fig. 9.2 SPH S particle e filling in a rectangula ar box. Next delete e the Shell Part. Only particles wo ould be leftt in the mod del as show wn in Fig. 9..3. Note t that the spa acing betwe een the particles is de ecided by PitX, P PitY, and a PitZ as shown in Fig. F 9.2. “Den” stand ds for mate erial densityy. This will also a assign mass to ea ach particle e. It is advissed that particle spa acing should be kept as regularr as possib ble to assist computattions. “Fill% %” when o other than 100 % the box can be filled in X, X Y, or, Z direction ussing “Dirx”, “Diry”, and d, “Dirz” respectivelyy.

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Fig. 9.3 SPH particcles. T The rigid body cuttin ng tool ca an be mod deled as any a other solid s body which ha as been mentioned in previous s chapters. Let us asssume we now have th he complete e model tha at looks as in Fig. 9.4. 9

Fig. 9.4 The work-piecce (SPH) and the cuttiing tool.

T T The contacct between n SPH parrts and the e shell or solid s eleme ents is alw ways “CON NTACT_ A AUTOMAT TIC_ NODE ES_ TO_ SURFACE” S . In this exa ample SPH H is PART #3 # and the e cutting t tool is PAR RT #1. The e co ommand ussed is show wn in Fig. 9.5. 9 In conttact betwee en SPH ϱϵ

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particles an nd shell or solid s eleme ents the SPH part is always considered to be e slave parrt. Slave part ID app pears underr SSID and the masterr part appea ars under MSID. M

Fig. 9.5 5 The conta act between n SPH partiicles and ellements. SP PH is alwayys slave entity. T TOOL TRA AVERSING T Tool motion is define ed using a curve relatting time with w the vellocity of po osition of to ool at a certain tim me. In the present example e v velocity in X directio on has be een defined d by a “Define_Cu urve” and “**Boundary_ _Prescribed d_Motion_R Rigid” as sh hown in Fig.. 9.6.

Fig g. 9.6 Tool traverse co ommands.

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SPH SPEC CIFIC T section The n property for f SPH part is set usiing the com mmand show wn in Fig. 9.7. 9 The be eginners can rely on n default values.

Fig. 9.7 SECTION_ S _SPH

RESULTS Shear stresss results fo or metal cutting are sh hown in Fig. 9.8.

Fig. F 9.8 She ear stress during d meta al cutting op peration.

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CHAPTER 10 VIBRATION ANALYSIS

Fig. 10.1 Mode extraction In this chapter we would solve an example to extract the vibration modes of a rectangular plate of 50 X 50 mm as shown in Fig. 10.2. The left edge nodes are fixed in all 6 DOF. The plate thickness is 0.5 mm which is given under Section_Shell card in the input file accompanying this book.

Fig. 10.2 The cantilever beam of 50 X 50 X 0.50 mm. Vibration analysis in LS DYNA is usually performed using implicit solver. The necessary commands to perform implicit analysis are shown in Fig. 10.3. “Control_Implicit_Eigenvalue” is used especially to extract vibration modes. ϲϮ

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Fig. 10.3 The req quired commands to perform p imp plicit analyssis. A After the so olution is available a the post proccessing is done by firrst reading in the “d3p plot” file and subsequently als so reading “d3eigv” fille. Each mode m can be b viewed by b moving playing odes are sh hown in Fig.. 10.4. next frame. Partial mo

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Fig. 10.4 Eigen values.

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CHAPTER 11 IMPACT ON CONCRETE

Fig. 11.1 1 Projectile Impact on a concrete wall. T This is a te est examplle where th he is asked to solve s the problem beffore looking g at the input file. The T only diffference is the materia al model. The T materia al properties are given n in Fig. 11.2 for refference.

Fig. F 11.2 Co oncrete ma aterial mode el MAT_159 9 usage.

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Fig. 11.3 Concrete damage and failure.

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CHAPTER 12 SLOSHIN NG SIMULA ATION In this chap pter we are e going to learn how to t perform sloshing s sim mulation off a half fille ed water t tank when it comes to rest abru uptly due to o applicatio on of a sudden brake or collision n with a o vehiclle. The procedure to construct c th he FEA mo odel would be shown in i detail barrier or other along with the resultts. This sim mulation is much more complexx than the ones narrrated in hapters. It is i however hoped tha at the can c advancce his know wledge of Arbitrary A previous ch Lagrange Eulerian E (AL LE) method d utilized in LS-DYNA by following this chap pter carefullyy. T input fiile has been made ava The ailable on the author’ss website fo or training purposes. p Create the solid mode el of water and a void, an nd then upo on that crea ate the tankk shell as fo ollow:

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- Create the solid cylinder model as shown in Fig. 12.1. Select page-7 then select ‘Mesh’ - Select ‘Entity: Cylinder_Solid’ - Input the radius, length of the tank, number of elements in circumferential direction and along the length of the cylinder. - Select ‘z-direction’. - Click ‘Create’ at the right bottom - Click ‘Accept’ at the right bottom - Click ‘Done’ at the right bottom - Save. Water and Air Modeling Open the previous solid model and delete the upper half group of elements to create ‘water’ section Fig. 12.4, as follow: - Select page-2 - Select ‘ElEdit’ (Element Edit) - Below ‘Element’ column, activate ‘Delete’ as shown in Fig. 12.2 - Shade the upper section by ‘Area’ type of selection at the left bottom - Click ‘Delete’ at the right bottom - Click ‘Accept’ at the right bottom - Save as ‘water.k’

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Open the file of ‘Water’ section then rotate it 180º to create ‘Air’ section Fig. 12.6, as follow: - Select page-2 - Select ‘Rotate’ - Select ‘Z-direction’ for ‘Rot.Axis:’ - ‘Rot. Angle:’ 180 º - Select the water part ϳϬ

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- Click ‘Rottate –‘ - Click ‘Acccept’ - Click ‘Don ne’ - Save as ‘a air.k’

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Node Merging Open “water.k” file and then import “air.k” file by ‘Import Offset’ option Fig. 12.7, then merge the water and air nodes as follow:

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- Select page-2 - Click ‘DupNod’ (duplicate nodes) - Click ‘Show Dup. Nodes’, Fig. 12.8 - Click ‘Merge Dup. Nodes’ - Click ‘Accept’ at the right bottom - Click ‘Done’ at the right bottom

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Tank Shell Elements Create a segment-set for tank shell structure, - Select page-5, Fig. 12.10 - Click ‘SetD’ - Select ‘Create’ - Select ‘*SET_SEG’ - Select ‘ByElem’, activate ‘Prop’, ‘Ang:’ 45.0, Fig. 12.11 - Click on the front, mid and back section of the model, Fig. 12.12 ϳϰ

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- Click ‘App ply’ - Click ‘Don ne’

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Generating g the shell elements e fro om the segment set, - Select page-2, Fig. 12.13 1 - Click ‘ElG Gen’ (Eleme ent Generattion) - Select ‘Sh hell’ type - Select ‘Sh hell By: Seg gment_Set’, click ‘1 Se eg-Set’ Fig. 12.14 4 - Click ‘Cre eate’ at the right bottom m - Click ‘Acccept’ at the right bottom m - Click ‘Don ne’ at the rig ght bottom ϳϲ

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- See Fig. 12.15 1

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Part-Set Node-Set off Water and d Air ater and air as follow: Create Parrt-Set of wa - Select page-5, Fig. 12.16 1 - Select ‘Crreate’ - Select ‘*S SET_PART’’ - Click on th he water an nd air mode el, Fig. 12.1 17 - Click ‘App ply’ - Click ‘Don ne’

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Create Nod-Set of water and air for velocity option, as follow: - Select page-5 - Select ‘Create’ - Select ‘*SET_NODE’ Fig. 12.18 - Activate ‘Pick’ fig. 12.19 - Click on the water and air model, Fig. 12.20 - Click ‘Apply’ - Click ‘Done’

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Node-Set for f Tank Velocity and d Constrain Nodes sele ection from the tank sh hell for velocity and constrain options, - Click ‘Front’

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Material selection *MAT Water & Void Material - Click page-3 - Click on ‘*Mat’ - Select ‘GroupBy: All’, and ‘Sort: Types’ - Select from the list ‘009-NULL’ - Click ‘Edit’ ϴϰ

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- Click ‘New wID’ at the top left of th he card - Input valu ues as show wn in Fig. 12.23 - Click ‘Acccept’ at the right top off the card - Click ‘Don ne’ at the rig ght top of th he card

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T Tank Mate erial of Poly ycarbonate e - Click page e-3 - Click on ‘**Mat’ - Select ‘GrroupBy: All’’, and ‘Sort: Types’ - Select fro om the list ‘0 001-ELAsTIC’ - Click ‘Editt’ - Click ‘New wID’ at the top left of th he card - Input valu ues as show wn in Fig. 12.24 - Click ‘Acccept’ at the right top off the card - Click ‘Don ne’ at the rig ght top of th he card

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Section type selectio on “*SECT TION” W Water & Vo oid/Air (*SECTION_S SOLID_ALE E) - Select page-3 - Click ‘*Se ection’ - Select ‘So olid_ALE’ Fig. F 12.25 - Click ‘Editt’ - Click ‘New wID’ at the left top of th he card - Click ‘ELF FORM: 12’ - Click ‘Acccept’ at the right top off the card - Click ‘Don ne’ at the rig ght top of th he card

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T Tank (*SEC CTION_SH HELL) - Select page-3 - Click ‘*Se ection’ - Select ‘SH HELL’ Fig. 12.26 - Click ‘Editt’ - Click ‘New wID’ at the left top of th he card - Input ‘SHRF=0.833’ and thickne ess ‘T1:1.5’ then click ‘Enter’ - Click ‘Acccept’ at the right top off the card - Click ‘Don ne’ at the rig ght top of th he card

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* *EOS_GRU UNEISEN - Select page-3 - Click ‘*EO OS’ - Select ‘GR RUNEISEN N’ Fig. 12.27 7 - Click ‘Editt’ - Click ‘New wID’ at the left top of th he card - Input as shown s in Fig g. 12.27 - Click ‘Acccept’ at the right top off the card - Click ‘Don ne’ at the rig ght top of th he card

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* *HOURGLA ASS - Select page-3 - Click ‘*Hrg glass’ - Select ‘HO OURGLASS S’ Fig. 12.2 28 - Click ‘Editt’ - Click ‘New wID’ at the left top of th he card - Input as shown s in Fig g. 12.28 - ‘Accept’ at a the right top t of the card - ‘Done’ at the right top of the carrd ϴϳ

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* *PART A Assign the properties for each pa art as follow w: - Select page-3 - Click ‘*Pa art’ - Select ‘PA ART’ - Click ‘Editt’ - Click ‘New wID’ for eve ery part, Fig g. 12.29 - Input as shown s in Fig g. 12.29: a- asssign the properties off water and d void (SEC CID, MID, EOSID, HGID), void me propertie es as waterr. has sam b - assign a the properties p o the tank material of m and section (S SCID, MID)). - Click ‘Acccept’ at the right top off the card - Click ‘Don ne’ at the rig ght top of th he card

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* *DEFINE_C CURVE plot tank ve elocity and gravity curvve: a- Assign A curve es for gravitty and tankk-velocity b- Use U A1 (for time) t and O1 O (for mag gnitude) A following steps: As - Select page-3 - Click ‘*De efine’ - Select ‘CU URVE’ - Click ‘Editt’ - Click ‘New wID’ for eac ch curve - Input as shown s in Fig g. 12.30 an nd Fig. 12.3 31 - Click ‘Acccept’ at the right top off the card - Click ‘Don ne’ at the rig ght top of th he card

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* INITIAL_V VOID_PAR RT T assign the To t void parrt: - Select page-3 - Click ‘*Inittial’ - Select ‘VO OID_PART’ - Click ‘Editt’ - Click ‘New wID’ at the left top of th he card - Click dotte ed button of o ‘PID”, the en select the e void-part Fig. 12.32 2 - Click ‘Acccept’ at the right top off the card - Click ‘Don ne’ at the rig ght top of th he card

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* *INITIAL_V VELOCITY T assign velocity To v for water and air: - Select page-3 - Click ‘*Inittial’ - Select ‘VE ELOCITY’ - Click ‘Editt’ - Click ‘New wID’ at the left top of th he card - Click dotte ed button of o ‘NSID’ an nd select the water and d air nodess-set, Fig. 12.33 - Click dotte ed button of o ‘NSIDEX’’ and selectt the tank velocity v nodes-set, Fig. 12.33 - Input velo ocity value at a ‘VZ’, Fig.. 12.33 - Click ‘Acccept’ at the right top off the card - Click ‘Don ne’ at the rig ght top of th he card

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* *LOAD_BO ODY_Y T activate To e gravity: - Select page-3 - Click ‘*Load’ - Select ‘BO ODY_Y’ to make the gravity g in y-d direction - Click ‘Editt’ - Click ‘New wID’ at the left top of th he card - Click dotte ed button of o ‘LCIDDR’’, then select the curve e for gravityy Fig. 12.34 4 - Click ‘Acccept’ at the right top off the card - Click ‘Don ne’ at the rig ght top of th he card

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Identifying g Referenc ce Nodes fo or ALE Divide the tank t into tw wo parts and d Identify th hree nodes for ALE reference, - Select page-1, click ‘SPlane’, Fig. F 12.35a - Click ‘NorrmX’, Fig. 12.35b - Select ‘Clip+’, Fig. 12 2.35b - See Fig. 12.36 1

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Identifying g the three reference nodes - Select page-1, click ‘Ident’, activate ‘Node’, Fig. 12.37 7 - Shade byy ‘Area’ the three repre esentative nodes n of the e rear botto om corner of o the tank as s shown in Fig. 12.38

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* *ALE * *ALE_REF FERENCE_ _SYSTEM_ _NODE T assign nodes To n for ALE A reference: - Select page-3 - Click ‘*AL LE’ - Select ‘RE EFERENCE E_SYSTEM M_NODES’ - Click ‘Editt’ - Click ‘New wID’ at the left top of th he card - Input the identity of the t three no odes in seq quence as shown s in Fig. 12.39 - Click ‘Acccept’ at the right top off the card - Click ‘Don ne’ at the rig ght top of th he card

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* *ALE_REF FERNCE_S SYSTEM_G GROUP - Select page-3 - Click ‘*AL LE’ - Select ‘RE EFERENCE E_SYSTEM M_GROUP’ - Click ‘Editt’ - Click ‘New wID’ at the left top of th he card - Input the part-set of water w and air a ‘STYPE’ ‘SID’, refe erence type e ‘PRTYPE’ and define e TEM_NODE) at ‘PRID D’ as shown n in Fig. 12..40 (*REFERENCE_SYST - Click ‘Acccept’ at the right top off the card - Click ‘Don ne’ at the rig ght top of th he card

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* *BOUNDA RY_PRESC CRIBED_M MOTION_SET T apply accceleration and decele To eration for the t tank: - Select page-3 - Click ‘*Bo oundry’ - Select ‘PR RESCRIBE ED_MOTION N_SET’ - Click ‘Editt’ - Click ‘New wID’ at the left top of th he card - Input the tank node-s set ID at ‘N NSID’, selecct z-direction for transla ation at ‘DO OF’, and se elect the v velocity currve foe the tank at ‘LC CID’ Fig. 12..41 - Click ‘Acccept’ at the right top off the card - Click ‘Don ne’ at the rig ght top of th he card

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* *BOUNDA RY_SPC_S SET T constraiin the tank: To - Select page-3 - Click ‘*Bo oundry’ - Select ‘SP PC_SET’ - Click ‘Editt’ - Click ‘New wID’ at the left top of th he card ϵϱ

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- Input the tank node-s set ID at ‘N NSID’, selecct ‘1’ to activvate the constrain in x-direction x a yand d direction, ‘D DOFX’ and ‘DOFY’ Fig g. 12.42 - Click ‘Acccept’ at the right top off the card - Click ‘Don ne’ at the rig ght top of th he card

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* *CONSTAR RINED_LA AGRAGE_IN N_SOLID T apply co To oupling betw ween the water w and air and the ta ank structure: - Select page-3 - Click ‘*Cn nstrnd’ - Select ‘LA AGRANGE_ _IN_SOLID D’ - Click ‘Editt’ - Click ‘New wID’ at the left top of th he card - Select ma aster type as a part-set of o water and air ‘MSTY YP=0’, ‘MA ASTER=1’, and a slave type as a part of the e tank ‘SSTY YP=1’, ‘SLA AVE=3’ - Input the rest of the command c a shown in as n Fig. 12.43 3 - Click ‘Acccept’ at the right top off the card - Click ‘Don ne’ at the rig ght top of th he card

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* *CONTROL L * *CONTROL L_ALE - Select page-3 - Click ‘*Co ontrol’ - Select ‘AL LE’ - Click ‘Editt’ - Input the command as a shown in n Fig. 12.44 4 - Click ‘Acccept’ at the right top off the card - Click ‘Don ne’ at the rig ght top of th he card

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* *CONTROL L_ENERGY Y - Select page-3 - Click ‘*Co ontrol’ - Select ‘EN NERGY’ - Click ‘Editt’ - Input the command as a shown in n Fig. 12.45 5 - Click ‘Acccept’ at the right top off the card - Click ‘Don ne’ at the rig ght top of th he card

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* *CONTROL L_TERMIN NATION T set the desired To d time for the ou utput: - Select page-3 - Click ‘*Co ontrol’ - Select ‘TE ERMINATIO ON’ ϵϳ

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- Click ‘Editt’ - Input the command as a shown in n Fig. 12.46 6 - Click ‘Acccept’ at the right top off the card - Click ‘Don ne’ at the rig ght top of th he card

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* *CONTROL L_TIMESTEP - Select page-3 - Click ‘*Co ontrol’ - Select ‘TIMESTEP’ - Click ‘Editt’ - Input the command as a shown in n Fig. 12.47 7 - Click ‘Acccept’ at the right top off the card - Click ‘Don ne’ at the rig ght top of th he card

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* *DATABAS SE * *DATABAS SE_OPTION - Select page-3 - Click ‘*Db base’ - Select ‘AS SCII_option n’ - Click ‘Editt’ - Activate th he desired outputs and their ‘DT= =1’ as show wn in Fig. 12.48 - Click ‘Acccept’ at the right top off the card - Click ‘Don ne’ at the rig ght top of th he card ϵϴ

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* *DATABAS SE_BINAR RY_D3PLOT T - Select page-3 - Click ‘*Db base’ - Select ‘BINARY_D3P PLOT’ - Click ‘Editt’ - inputtTime e interval between b outtputs ‘DT=1 1’ as shown n in Fig. 12..49 - Click ‘Acccept’ at the right top off the card - Click ‘Don ne’ at the rig ght top of th he card

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* *DATABAS SE_BINAR RY_FSIFOR R - Select page-3 - Click ‘*Db base’ - Select ‘BINARY_FSIIFOR’ - Click ‘Editt’ - Input time e interval be etween outp puts ‘DT=1’ as shown in Fig. 12.5 50 - Click ‘Acccept’ at the e right top of the card - Click ‘Don ne’ at the rig ght top of th he card

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* *DATABAS SE_EXTEN NT_BINARY Y - Select page-3 - Click ‘*Db base’ - Select ‘EX XTENT_BIN NARY’ - Click ‘Editt’ -Click ‘New wID’ at the le eft top of th he card - input the specified s co ommands and a the rest are set ass default, Fiig. 12.51 - Click ‘Acccept’ at the right top off the card - Click ‘Don ne’ at the rig ght top of th he card

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* *DATABAS SE_FSI - Select page-3 - Click ‘*Db base’ - Select ‘FS SI’ - Click ‘Editt’ ϭϬϬ

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-Click ‘New wID’ at the le eft top of th he card - input ‘DT= =1’, ‘DBFSII ID=1’, ‘ST TYPE=1’ as a PART, select s the ta ank as ‘SID=3’, and the en click ‘Insert’, Fig g. 12.52 - Click ‘Acccept’ at the right top off the card - Click ‘Don ne’ at the rig ght top of th he card

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Save as ‘filename.k’ th hen run the e k-file ‘inpu ut = filename.k’.

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Result

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CHAPTER 13 EFFECT E OF F EXPLOSIION ON A CONCRET C TE WALL

Explosive are a used fo or different purposes including explosive e w welding, exp plosive form ming, oil exploration n, or in the production of weapons. To prediict the effecct of explossions on strructures computer simulations s play a great g role because experiment e al work might m prove e to be erties and equations e o state of various of extremely costly and dangerouss. The matterial prope ble in open n literature. There are numerous software to o predict the effect explosives are availab o explosions but LS DYNA of D also possessess a great de eal of abilityy to solve problems p re elated to ange Euleria an (ALE) te echnique. In n the prese ent chapterr we will explosives using Arbittrary Lagra xplosion on n the concre ete wall. explain the effect of ex

Fig. 13.1 Effect E of explosion on the concrette wall. T The modell in the exa ample is a very simp ple structure e where an n explosive e detonatess in the atmosphere e and causes damag ge to a concrete wall located at a a small distance away a as ϭϬϯ

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s shown in Fig. F 13.1. To o constructt the model make two boxes side e by side with w the dime ensions as shown in Fig. 13.2 2. The mode el dimensio ons are sho own inside brackets. The T right most m box w would repre esent the explosive e an nd the large e left box re epresents the air. The 5 mm thickk wall is t the concre ete structure e. To makke the explosive, air, and concrrete regionss follow the steps s shown in Fig. F 13.2 to create each box and complete c it by clicking g “Create” > “Accept” > “Done” buttons.

Fig.. 13.2 Consstruction of the model. TING PART TS GENERAT T explossive and air boxes have to be con The nnected tog gether by merging m their nodes. To o merge t nodes common between the b exp plosive and d air click “DupNod” “ a click “S and Show Dup Nodes”. N T The dupliccate nodes would be e highlighte ed. Click on “Merge Dup Node es” and the en click “Accept”. This T would allow the explosive e no odes to talkk to air nod des. The co oncrete walll needs ϭϬϰ

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not to be merged m or connected. c Now there e are 3 PAR RTS in this model. De etails can be found under “PAR RT” tab on page 3. IES SECTION PROPERT P Define “SECTION_SO OLID” and “SECTION_ “ _SOLID_AL LE” using “SECTION” “ ” on page 3. 3 _SOLID” would w be asssigned to concrete c wa all and “SEC CTION_SO OLID_ALE” would w “SECTION_ be assigned to explos sive and air parts. For “SECTION_SOLID” le eave the de efault valuess but f “SECTIO for ON_SOLID D_ALE” intro oduce “ELF FORM” as 11 1 as show wn in Fig. 13 3.3.

Fig. 13.3 For ALE parts off explosive and air ELF FORM = 11 1. MATERIAL L PROPER RTIES Material prroperties arre given in Fig. 13.4 fo or explosive e, air, and concrete re espectively. These material pro operties an nd the section propertiies discusssed above are a assigne ed to the 3 PARTS mentioned earlier.

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Fig. 13.4 Material M pro operties forr the three materials m used in the model. m EQUATION NS OF STA ATE (EOS) T equations of statte in this pa The articular exxample are required only for the explosive and air. osive material and EO OS_LINEAR R_POLYNO OMIAL is de efined for air. a Both EOS_JWL is for explo o the EOS of S are given in Fig. 13.5. For deta ails of everyy paramete er the reade er is referre ed to LS DYNA man nuals.

erials Fig. 13.5 Equation of state forr ALE mate A ALE CARD DS T ALE cards requirred in this analysis The a are e shown in Fig. 13.6. To declare e ALE partss where p is pressent the AL LE_MULTI-MATERIAL L_GROUP is repeated d for all more than one ALE part here are on nly two ALE E parts (exp plosive and d air) present in this exxample, tw wo cards parts. As th are defined d.

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Fig. 13.6 6 ALE cardss required for f the anallysis. PART SET TS Here two part p sets are e defined. Set S #1 conssists of exp plosive and air while se et #2 has only o one part in it that is concre ete. Part se ets are neccessary to define d the relationship r p between the t ALE ge parts. and lagrang

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Fig. 13.7 PART set# #1 for explossive and air (PART#1 & PART#2 2), PART se et#2 for con ncrete. CONSTRA AINED_LAG GRANGE_IIN_SOLID A the con As ncrete wall is containe ed in the atmosphere (air) this fact f has to be defined d in this command. By using th his comman nd we inten nd to declarre that conccrete which h is a lagran nge part is enclosed d by ALE parts p (explo osive and air). a The im mage of thiss card is sh hown in Fig g. 13.8. T iss encourage The ed to read about a each parameterr in the LS DYNA D manuals.

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Fig. 13.8 SLAVE #2 (concrete) is enclosed d within MA ASTER #1 (PART ( set #1 # with exp plosive a air). and ON INITIAL_DETONATIO ns starts at. It is shown n in Fig. 13 3.9. The Using this command iti is shown where the detonation X XYZ coordinates in th his case are e set to the global orig gin of the model m which h falls at one of the corner of th he explosiv ve box. But this could be anywhe ere within th he explosive e mass dep pending upon wherre the igniition takes place firsst. LT para ameter stan nds for lig ghting time of the explosive.

Fig. 13.9 Initial deto onation loca ation and lig ghting time of the explo osive. T TIME STEP P SIZE W When usin ng ALE sim mulation th he time step size sh hould be kept k smalle er to coun nter the instabilitiess. This is achieved byy keeping TSSFAC T = 0.6 in thiis example e as shown n in Fig. 13.10. In so ome analys sis where th he instabilitty is more severe s the value v of thiis paramete er could be re-adjussted at 0.10 0.

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Fig. 13.10 Time e step size TSSFAC should s be ke ept smallerr. RESULTS T massivve deforma The ation and failure of con ncrete wall is shown in Fig. 13.11.

Fig. 13.11 Effect of exxplosion on the concre ete wall.

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ͳͶ LSPREPOST & LSDYNA TIPS

This part of this book contains the necessary information in bits and pieces that can be helpful to s in solving many different problems. Most of this information has been collected from the LSPREPOST & LSDYNA sites and forums on the internet. Some information was obtained from Dr. James M. Kennedy of KBS2 Inc. who is an authority on LSDYNA. *Interface_Springback_Lsdyna This command is available on page 3 as ‘*intrfac’. When this command is used in an input file ( k file ) this would generate a file called ‘dynain’ on program execution which consists of stresses for the part that is selected under PSID. ‘dynain’ file can be read into another k file by using command ‘*include dynain’. Running new k file will have the pre-stresses available for the part from ‘dynain’. The file ‘dynain’ in this way is used to conduct spring back analysis in forming operation simulations. This command ‘*include’ can be found on page 4 of LSPREPOST.

How to view node and element numbers? Click ‘Indent’ on page 1 on LSPREPOST. Toggle the radio button to select nodes or elements and ‘bypart’ then click on the part whose elements or the nodes have to be identified.

SPH Appearance Click setting>SPH>smooth. This will result in SPH particles to be displayed as large spheres instead of tiny particles.

SPH PART GENERATION There are different methods of generating SPH particles. One of them is to make a shell body and fill it to the required level with SPH particles. It may be necessary to delete the shell part in certain cases so that it does not interfere with other parts un-necessarily. This can be done ϭϭϭ

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by opening the list of parts by clicking on ‘*PART’ on page 3 and deleting the part that is not needed anymore.

Refining Mesh To refine the mesh (solid or shell elements) open page2 and check on ‘split/merge’, select the elements to be refined (by making a box around the elements or picking ‘ByPART’ or using another option). Then click Apply>Accept. Reducing element size helps solve problems with minimum time step problems. This also eliminates the negative volume problem. But to counter the negative volume problems this might not suffice.

Increasing memory in SPH analysis Sometimes the number of SPH particles coming into with each other is very large. This particularly is the case when they flow easily in liquids or fluids or there is massive plastic deformation. To counter the problems and errors and program abort increase the memory in the field ‘memory’ to a higher number under ‘*Control_SPH’. The field FORM = 6 works well with fluids. SPH particles through shell or solid elements To counter this problem use SST = 0.1~1.0 mm under Card as thickness. The particles would not through shell or solid elements. Filling SPH particles as a liquid in a tilted container Make a container in LSPREPOST, tilt it to the required angle using ‘rotate’ on page 2 and fill the SPH particles in it using ‘SphGen’ on page 7 along a certain axis such that it feels as natural under gravity effect. Example is shown in Fig. 14.1

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F 14.1 Fiilling the co Fig. ontainer. Element fa ailure criteria If element erosion is set s as failu ure criterion n then as lo ong as the failure f of elements co ontinues t problem the m should be e allowed to t run. Whe en no more e failure occcurs the LS SDYNA run can be s stopped.

2 Analysis 2D In 2D analyysis shell elements e w formulation 13 are with e used. Forrmulation 13 stands fo or plane s strain cond dition.

* *_T Tiebreak_S Surface_to o_Surface In this type e of contac ct two partss are tied together. t T They may separate s if the tensile e failure s stress value in NFLS filed f or she ear failure sttress SFLS S is encounttered. SPH to mo odel foam W When SP PH is use ed to mo odel foam or meta als instead d of liquiids the keyword k * *Control_B ulk_Viscos sity with deffault parameters shoulld be used to overcom me instabilityy.

A Applying P Pressure on o liquid su urface Input presssure value e in “PREF F” field und der “*Contrrol_ALE”. The T atmosp pheric presssure is roughly equal to 101 kPa. It can be conve erted to GP Pa as 1.01 e-4 which h is equal to t 1 bar pressure.

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Generating g a new pa art from a portion p of an a existing g part Sometimess it become es necessa ary to generate a new w part from some of th he elementts of an existing part. Followin ng steps are e needed to o achieve this t objectivve. Let us assume a we have a own in the Fig. 14.2. Sequence of actions page5 > SetD S > crea ate >set_so olid > by part as sho elements A this poin At nt select the e elements enclosing the elemen nts in a boxx using buttton ‘area’ and click ‘Apply’ ‘don ne’. An element set iss created. Now N click on o button ‘m movy’ ass shown in figures. T Type ‘2’ in PID field. Select S ‘by set’ s and in the t pop up window se elect the ele ement set number. n A Again click ‘apply’ ‘done’. A seco ond part is generated g c consisting o element set. of s

Fig. F 14.2 Ge enerating a PART from m existing elements. e ϭϭϰ

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OUT OF RA ANGE VEL LOCITY IN ALE SIMU ULATION In ALE sim mulation ‘ou ut of range velocity’ error e can be e avoided by introduccing the ho ourglass and asg it to ALE parts with h following parameterss; ery small value. In ‘*Control_A ‘ ALE’ NADV V = 10 sho ould be IHQ = 4, QM = 0.025 or a ve s abrruptly and the t time ste ep drops en normously low. This is named introduced.. This is if solution as combating instability. HOW TO DISPLAY D ELASTIC E ST TRAIN VAL LUES? Except plastic strain other strain ns are not displayed. To displayy elastic sttrains the keyword k e_Extent_Binary shoulld be includ ded in the k file. Cha ange STRFLG value to t 1. To ‘*Database d display elasstic strains click STRA AIN button under u page e 1.

W WHEN EOS IS REQU UIRED? Please refe er to mate erial selecto or at http:///app.d3view w.com/d3m mat/index fo or this veryy recent information n. Only som me material models req quire EOS. As an example Johnsson_Cook material m model requ uires the EOS only when solid elements e arre used. Fo or the shelll elements EOS is not needed d. Why is it so? This iss because as the solid d elements are under compression their d density ma ay increase and EOS is i the relation between n the applie ed pressure e and the re esulting v volume.

* *MAT_ADD D_EROSIO ON USAGE

Fig. 14.3 Using MAT_ADD_ M _EROSION NS Fig. 14.3 iss the scree en shot of the t keyword d ‘MAT_AD DD_EROSION’. Let uss assume that t our material model m 1 is the MAT_E ELASTIC. When erossion criterio on is used d material number ϭϭϱ

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would remain as 1 as shown in the figure. EXCL field is filled with a value that would be byed. In this example when principal stress 1 reaches 0.5 GPa element erosion will happen. If the eroded elements are to be retained then following procedure should be followed; Use *CONTROL_ card. The parameter “ENMASS” can have three different values. When this is equal to zero the eroding nodes are removed. For ENMASS = 1, the eroding nodes of solid elements are retained and continue to be active in . For ENMASS = 2, the eroding nodes of solid and shell elements are retained and continue to be active in . HOW TO USE MAT_084? Make the model as usual. Include following text at the end of k file *Keyword q = cracking *Database_Binary_d3plot $ dt/cycle 0.0001 *Database_Binary_d3crack $ dt/cycle 0.001 *end When running LSDYNA the Output file field should be appended with the following …….\d3hsp q = cracking Next run LSDYNA using this k file. In the post processing session open ‘d3plot’ file. Next open the ‘d3crack’ file “cracking”. Cracks can be visualized. Note: that at the input stage for MAT_084 the parameter CONM decides the units.

HIGH VELOCITY IMPACT When a high projectile velocity like 2000 meters per second is used in LSDYNA, it is advisable to input TSSFAC = 0.25 ( a small value ) under the ‘*Control_Timestep”. Also use SOFT = 2 in card by enabling card A. ϭϭϲ

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HEB AND AIR MODE ELING

Fig. 14.4 4 Node merrging. W When HEB B and air arre modeled d together the duplicatte nodes th hat are com mmon to both parts s should be merged m tog gether as sh hown in Fig g. 14.4.

COMBATT TING INSTA ABILITY IN N ALE Especially when w simulating explo osives * *CONTROL L_HOURGLASS IHQ = 1 QH = 0.1 * *HOURGLA ASS IHQ = 1 QM = 1.0 E -06 T overcom To me drop in time t step T TSSFAC = 0.1 under *CONTROL_TIMESTEP.

USING *MA AT_CONCRETE_DAM MAGE_REL3 (MAT_0 072 R3) RO = 2.32 E-06 kg/mm m3 PR = 0.19 A = -0.027 A0 71430 GPa a = 27.14 MPa M (Concrrete Strengtth) RSIZE = 0..03937 to convert c leng gth units to mm UCF = 145 5000 to conv vert stress units to GP Pa.

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USING *CO ONSTRAIN NED_NODA AL_RIGID_ _BODY

Fig. 14.5 1 Constrrained noda al rigid bodyy. T use thiss command To d a node set s is generrated using g page 5 in n LSPREPO OST and th hen this node set number is in nserted in the t field NS SID as shown in the Fig. F 14.5 ab bove. On applying a t the load on o the structure these e nodes will w be disp placed toge ether like a rigid bod dy. This t technique c be use can ed for exam mple to two parts by selectin ng certain nodes n which might be represe enting bolts s holding the t two pa arts togethe er without actually modeling m th he bolts physically.

ASTIC_PLA ASTIC_HY YDRO MAT TERIAL USING ELA W When a co omparatively y softer ma aterial is to a hard surfacce, the softt material could c be modeled using u this material m model. To achieve a better resultss it is reco ommended to use SECTION_ _SOLID_AL LE for the solid s elemen nt soft part with eleme ent formulation ELFOR RM = 5. * *CONTROL L_ALE with h following parameters p s may be he elpful 2

1

10

0.100

T_SLIDING_ _ONLY sho ould be use ed if sliding g is the dom minant mod de of deforrmation. Refer to AL LE04 example on http:://www.lsdyyna.eu/inde ex.php?id=3 3999.

HOW TO DISPLAY D STRAIN S IN VECTOR V F FORM? Open the d3plot d file in n LSPREPO OST. Run the an nimation unttil the required time. Click on *V VECTOR on n page 1 Select “Prin n.Strain” fro om the drop p down list. Click Applyy.

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NECESSARY INPUT TO EXTRACT VIBRATION MODES To extract the vibration modes of a structure the input file must have following parameters in it; CONTROL_IMPLICIT_DYNAMICS IMASS = 1 (Dynamic analysis) CONTROL_IMPLICIT_EIGENVALUE NEIG = 20 (number of Eigenvalues to extract) CONTROL_IMPLICIT_GENERAL IMFLAG = 1 (implicit analysis) IMFORM = 2 (retain original element formulation) CONTROL_IMPLICIT_SOLUTION NSOLVER = 1 (Linear) CONTROL_IMPLICIT_SOLVER LSOLVER = 0 SECTION_SHELL (if shell structure is to be analysed) ELFORM = 16 (fully integrated shell element)

HOLE FILL WITH SHELL ELEMENTS A shell structure with a hole is shown in the Fig. 14.6 below. The hole has to be filled with shell elements. On page 2 click element generate button ‘ELGen’ > SHELL > By Fill_Holes. Click at a node at the inner edge and click ‘Create’ and ‘Accept’. The hole will be filled by shell elements but the new elements would generate a new part. If this what is desired then no more action is needed but in case we wish to have only one part then click ‘movy’ on page 2. Set PID = 3. Chose ‘By part’ and click both parts > Apply. A single part is the result.

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Fig. 14 4.6 Hole filling.

IN POST PROCESSIN P NG WHAT DOES PRE ESSURE MEAN? M Pressure = - (V11+V22+V + 33) /3 T This is calle ed mean sttress. Posittive pressure stands fo or compresssion while negative pressure p is tensile sttress.

NOTE ON JOHNSON N COOK MA ATERIAL MODEL M T Temperatu re display in JC mode el is done by displaying extra history variables. Temp perature perature ch hange i.e. ( TR+ Temperature ch hange ) consists off Room Temperature plus Temp w where TR is Room Te emperature. se NEIPS = 6 under extra historyy variables. Click on extra e variable #5 to For shell elements us d display onlyy the temperature cha ange. In JC C model the e increase in temperatture is assu umed to be adiabatiic and thus there is no o heat flow from one element e to another a (takken from message m # 25541 Ya ahoo LSDY YNA Group). Von-Mise es stress iss displayed only when Shear Mod dulus G is input for solid eleme ents, E is used for she ell elementss. el input the e Pressure cut-off valu ue should be b negative e. For exam mple PC = -0.30 (In JC mode 300MPa). ϭϮϬ

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PATH PLO OT T plot som To me variable es like stresss or displa acement etcc. use F11 to toggle to o ver 3.1 interface. Using iconss shown in sequence in Fig. 14.7 below firsst display the t variable e at a certa ain time. Next click icon i 2, sele ect ‘Nodal’ and ‘Along g Path’ butttons then click c on the model at different d locations. Path P will be displayed. Click “PLO OT”.

Fig. 14.7 Path plot seq quence.

HOW TO ERASE E ELE EMENTS BUT B KEEP THE SURF FACES TO REMESH AGAIN T Toggle to ver. v 3.1 of LSPREPO OST. Click on Geome etery > Surfface > Fit from f Pointss/Mesh. Next in win ndow titled as a “Sel. Ele ements” che eck the boxx “prop” and d select “An ng = 45”. Click on the model the elementss of the respective parrt would be highlighted d. Click on “Apply” w “Fit Surface fro om Points… …”. Close th he dialogue e window. under the window Click from the t main menu m FEM > Element Tools T > Element Editin ng > In the “Elem ment Editin ng” window check “delete”. In the e “Del. Elem ment” windo ow click “prop” and s select “Ang g = 45 “. Next clickk on any element e in the model, all the ellements wo ould be highlighted. Next click k on the “de elete” butto on at the bo ottom of “Ellement Editting” windo ow. Now one”. Under the File > Save as > Save geometry as > type the IG GES file click “Accept” and “Do name and save. s In another session op pen the IGES file using Open > IGES File e. You can now re-mesh the model as a refined or coarse mesh as desirred. An exa ample is sho own in the Fig. F 14.8 below. b

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Fig. 14.8 Mesh hed part conversion to o IGES and remeshing g.

FULLY INTE EGRATED SHELL S ELE EMENTS

Fully integrrated shell element e forrmulation ELFORM E = 16 is the best to avoid d hourglas ss effect. It is advisab ble to use this t elemen nt formulatio on if we can n afford it.

FILE GLS STAT GLSTAT iss generated d using AS SCII option and this file containss the total Kinetic K En nergy of t whole model. the m Mas ss and veloccity of all th he nodes is ed d for in K.E.=1/2mV2.

FILE MAT TSUM T This file contains the Kinetic K Energy in eacch particula ar part.

V VIEWING CONTAC CT FRICTIO ONAL ENE ERGY[*] When frictio W on is enablled in conta act treatment using sta atic or dyna amic fricitio on coefficien nts (FS, FD in *CON NTACT), th he energy dissipated d d to frictio due on can be recorded and visualize ed. The parameter that tellls LS-DYN NA to ouput o the frictional energy is FRCENG in * *CONTROL L_CONTAC CT. FRCEN NG by default is set to o 0 to ignore e the recorrding and output of t the frictiona al energy. When FRC CENG is se et to 1, LS-DYNA outtputs the frrictional energy as “Surface Energy Dens sity” into a binary b data abase name e “INTerfacce FORce” (INTFOR) ( f file. The INTFOR fille is not output by de efault and hence to request r th he output, you must use u the keyword *D DATABASE E_BINARY_ _INTFOR with w a frequency of outtput time (D DT) AND prrovide a command line argument “s=Intfo orc_file_name”. Upon n completion of the simulation, you y can read the IN NTFOR file using LS-P PrePost ussing file/Op pen/Interfacce Force File option and a use FCOMP bu utton to fring ge the frictionaly energ gy. If you are perfoming a coupled thermal-m mechanical analysis using the option SOLN N =2 in * *CONTROL L_SOLUTIO ON, then this frictiona al energy can c be con nverted to heat h energ gy to be included byy the thermal solver. ϭϮϮ

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Summary of the steps to output and view frictional energy are included here. 1. Set FRCENG = 1i n Card 4 of *CONTROL_ 2. Use *DATABASE_BINARY_INTFOR with desired output time interval DT 3. Use “s=intforce_file_name” as one of the command line arguments when invoking LSDYNA 4. View the results in LS-PrePost/File/Open/Interface Force File and FCOMP/SurfaceEnergyDensity to contour the results *Taken from ŚƚƚƉ͗ͬͬďůŽŐϮ͘ĚϯǀŝĞǁ͘ĐŽŵ͍ͬƉсϲϰϴ

HOW TO CONNECT SPH PART TO SOLID ELEMENT PART Sometimes it is necessary to tie SPH node elements to solid element parts. An example is shown in Fig. 14.9 where an SPH part is constructed close to the solid elements. A node set is made of the one or two layers of SPH particles next to the solid elements.



Fig. 14.9 Connecting SPH part to Solid element Part SPH part is connected to the solid part through the node set of SPH particles by using the _TIED_NODES_TO_SURFACE_CONSTRAINED_OFFSET as shown in Fig. 14.10. SSTYP = 4 stands for node set and MSTYP = 3 is the PART ID.

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Figg. 14.10 CON NTACT_TIE ED_NODES S_TO_SURF FACE_CON NSTRAINED D_OFFSET

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CHA APTER 15 5 USAGE of LOAD BLAST B ENHANCED It is quite well known n that using ALE for explosionss is the be est approacch in LS DYNA to attempt pro oblems rega arding bom mb explosion n but this command c iss more hand dy and veryy cheap t obtain some rou to ugh resultss. In this chapter the usage e of the command called *Load_Bla ast_Enhanc ced is explained. To use this command c c construct a rectangula ar plate w dimensions X = 6 meters Y = 4 meters and mesh it as shown with n in Fig. 15.1.

er plate me eshed with 60 6 shell ele ements in X direction and a 40 elem ments in Fig. 15.1 A 6 X 4 mete Y direction.

MATERIA AL PROPE ERTIES Provide ma aterial properties as sh hown in Fig g. 15.2. The e units here e are kg, meter, m pasca als, and s seconds. T These units are differen nt than in th he rest of th his book to utilize the default d unitts under command *Load_Bla * st_Enhanc ced.

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Fig. 15 5.2 Material propertiess of aluminu um.

SECTION PROPER RTIES Section pro operties are e shown in Fig. 15.3.

Fig. 15.3 1 Section n propertiess for a 2 mm m thick alum minum platte.

BOUNDARY COND DITIONS Constrain the t left and right verticcal edges off the plate using u the SPC_SET co ommand on n a pres selected no ode set mad de from the e boundary nodes.

T TERMINA ATION TIM ME & TIME STEP Set 0.5 secconds the te ermination time and tim me step alsso as 0.5. R both of these v values have entirely different d me eanings.

* *LOAD_B BLAST_EN NHANCED D This comm T mand is show wn in Fig. 15.4. 1 M stan nds for TNT T mass of 6 kg. This 6 kg bomb iss placed 6 meters m in fro ont of the pla ate with ZB BO = 6.

Fig. F 15.4 Ussage of Loa ad_Blast_En nhanced co ommand.

* *LOAD_B BLAST_SE EGMENT_S SET This comm T mand follows s the above e command d. This referrs to the se egments wh hose distorttion and f force and pressure data d are to o be genera ated. Beforre using th his comman nd a segm ment set s should be genera ated using g SET_S SGMENT on page 5. Dettailed inp put for _segment_s set is show wn in Fig. 15.5. load_blast_

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Fig. 15 5.5 Using Lo oad_Blast_ _Segment_S Set.

UN-REFERENCED CURVES Two curvess must be generated T g u using *Defin ne_Curve even e though h they mayy not be refe erenced anywhere. This comm mand called d Load_Bllast_Enhan nced may not work without w perrforming t this seemin ngly unnece essary taskk.

DATABAS SE_BINAR RY_BLSTF FOR This comm T mand is requ uired to obtain the forcce and presssure historry on the structures su ubjected t blast load generate to ed by explossives.

Fig. 15.6 This T comma and outputss the necesssary data including fo orce and pre essure app plied on the e structure.

PARTIAL INPUT A partial inp put is show wn below ussed in the in nput file.

$# LS-DYNA A Keyword file creat ted by LS-P PrePost 3.2 (Beta) - 29Jun201 11(16:05) $# Created d on Jul-20-2011 (09 9:56:31) *KEYWORD _SPC_SET *BOUNDARY_ 1 1 0 1 1 1 1 *SET_NODE_ _LIST 1 0.000 00 0.00 00 0.0 000MECH 0.00 6 5 1 2 3 4 7 13 14 9 10 1 11 1 12 15 22 17 7 18 1 19 2 20 21 23 25 5 26 2 27 2 28 30 29 31 37 33 3 34 4 3 35 3 36 38 39 41 1 2461 246 62 246 63 24 464 24 465 2 2466 2468 8 2469 247 70 247 71 24 472 24 473 2 2474 2476 6 2477 247 78 247 79 24 480 24 481 2 2482 2484 4 2485 248 86 248 87 24 488 24 489 2 2490

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1 8 16 24 32 40 2 2467 2 2475 2 2483 2 2491

>^ͺzE&KZ'/EEZ^ 2492 2493 2494 2500 2501 0 *LOAD_BLAST_SEGMENT_SET 1 1 0 *LOAD_BLAST_ENHANCED 1 6.000000 3.000000 0.000 0.000 0.000 *DATABASE_BINARY_BLSTFOR 1.0000E-4 0 0 *DATABASE_BINARY_D3PLOT 1.0000E-4 0 0 0 *CONTROL_TERMINATION 1.500000 0 0.000 *CONTROL_TIMESTEP 0.000 0.500000 0 0.000 0 0 *DEFINE_CURVE 1 0 1.000000 0.000 1.0000000 *DEFINE_CURVE 2 0 1.000000 0.000 1.0000000 *NODE 1 0.000 2 0.000 3 0.000 4 0.000

2495 0

0.500000 0.000

2496 0

2497 0

2498 0

2499 0

6.000000 0.000 01.0000E+20

2 0

2

0

0

0

0

0

0.000

0.000

0.000

0.000

0

0

1.000000 0.000 1.0000000

0.000

0.000

0

1.000000 0.000 1.0000000

0.000

0.000

0

0.000 0.1000000 0.2000000 0.3000000

0.000 0.000 0.000 0.000

*SECTION_SHELL 1 2 1.000000 2 1 0 0.002000 0.002000 0.002000 0.002000 0.000 0.000 *PART shell_4p 1 1 1 0 0 0 *MAT_PLASTIC_KINEMATIC 1 2700.00007.0000E+10 0.340000 2.6700E+8 3.2000E+8 0.000 0.000 0.000 0.000 *ELEMENT_SHELL 1 1 42 43 2 1 0 2 1 43 44 3 2 0 3 1 44 45 4 3 0 4 1 45 46 5 4 0 5 1 46 47 6 5 0 6 1 47 48 7 6 0 ……… *SET_SEGMENT 1 2336 2081 1826 1571

0.000 2337 2082 1827 1572

0.000 2296 2041 1786 1531

0.000 2295 2040 1785 1530

0.000 0.000 0.000 0.000 0.000

…………

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0.000 0.000 0.000 0.000

0 0 0 0

0 0 0 0 0 0.000

1 0

0

0

0.000 0 0 0 0 0 0

0 0 0 0 0 0

0.000 0.000 0.000 0.000

0 0 0 0 0 0

0.000 0.000 0.000 0.000

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CHA APTER 16 6 Spot Weld d



In this exam mple we will w learn how to generrate 2 beam m type spott welds on 2 parts. Th he XML d data for the e two spot welds w is givven in Table e 16.1. T TABLE 16.1 ’‘–‡Ž†† †ƒ–ƒ.

X XML versio on of spot weld file

<xxml version n="1.0"> <W Welds> <W Weld id="100"> <X X>10.0 > 5.0 1.0 1

2

<W Weld id="200"> <X X>10.0 > 10.0 > 1.0 1

2

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The two pa T arts to be welded w togetther are shown in Fig.. 16.1 with all a necessa ary details liike spot w weld coordinates, fixe ed end of on ne plate and d the displa acement ap pplied to the e right hand d end of t other plate. the



Fig.16 6.1. Two pla ates (PART T1 and PAR RT2) to be spot s welded d with weld coordinate es.

T The two plates to be e welded to ogether are e modeled in LS-PRE EPOST witth their resspective odels (MAT T_003 in thiis case) and d section properties p (S SECTION_ _SHELL). Th he weld material mo information n is read in by using the spot weld d icon show wn in Fig. 16 6.2.

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Fig. 16.2. Steps S required in introd ducing spott welds.

Once the spot s weld symbols s appear at the e required coordinates c s the K filess should be e saved along with all other ne ecessary inp put. For furrther detailss refer to the e input file “spotweld0 01.k”. Run the LS S-DYNA sollver and check your re esults͘

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CHA APTER 17 7 LS-D DYNA MA ATERIAL MODELS S DŽĚĞůŝŶŐƚŚĞĞƌĞĂůďĞŚĂǀŝŽ ŽƌŽĨŵĂƚĞƌŝĂůƐŝŶĂŶLJƐŽĨƚǁ ǁĂƌĞƌĞŵĂŝŶƐƐĂǀĞƌLJĐŽŵƉ ƉůĞdžƚĂƐŬďƵƚĨŽƌŵĂŶLJĞŶŐŐŝŶĞĞƌŝŶŐ ƉƵƌƉŽƐĞƐƚŚĞĞĂƉƉƌŽdžŝŵĂƚĞ ĞŵĂƚĞƌŝĂůďĞĞŚĂǀŝŽƌŝƐƉŽƐƐƐŝďůĞ͘DŽƐƚŽ ŽĨƚŚĞĚĂƚĂƉ ƉƌĞƐĞŶƚĞĚŝŶƚƚŚĞĨŽůůŽǁŝŶŐŐƚĂďůĞƐŝƐ ĞdžƚƌĂĐƚĞĚ ĨƌŽ Žŵ ǀĂƌŝŽƵƐ ƐŽ ŽƵƌĐĞƐ ĂŶĚ ŝƚƚ ǁĂƐ ĨŽƵŶĚ ƚŚĂƚ ƚ ƚŚĞƐĞ ŵĂƚĞƌŝĂů ŵŽĚĞĞůƐ ĐĂŶ ƐŝŵƵůĂĂƚĞ ƚŚĞ ƌĞĂů ŵĂƚĞƌŝĂůƐ ŵ ǁ ǁŝƚŚ Ă ŐŽŽĚ Ě ĂƉƉƌŽdžŝŵĂƚƚŝŽŶ͘ ^ŽŵĞ ŽĨ Ž ƚŚĞ ŵĂƚĞƌƌŝĂů ŵŽĚĞůƐ ƌĞƋƵŝƌĞ ƌ ĂŶ ĞƋƵĂƚŝŽŶ ŽĨ ƐƚĂƚĞ Ɛ ;K^Ϳ ƚŚĞƌĞĨŽƌĞ ƚ ŶĞĐĞƐƐĂƌLJK K^ǀĂůƵĞƐŚĂǀĞ ĞďĞĞŶƉƌŽǀŝĚ ĚĞĚĨŽƌƚŚĞƵƐƐĞƌƚŽƉƌĂĐƚŝĐĞǁŝƚŚƚŚĞŵ͘

MAT_SOIL M L_AND_FO OAM_FAIL LURE (*MA AT_005)

MAT_HIGH M H_EXPLOS SIVE_BUR RN (*MAT_ _008) C4

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EO OS_JWL



Note: MAT T_008 requiires Equatio on of State (EOS_JWL L) which is shown in th he above ta able.

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Note 01: n It stands for cut-off stre ess. PC values should be negative. m mod del has follo owing param meters. Gruneisen EOS used with this material ϭϯϯ

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C = 1933 m/sec. m S1 = -3.49 S2 = 8.19 S3 = -9.6 GAMAO = 0.61 _ _________ __________ _________ __________ _________ __________ __________ ____ T CARD SURF_TO_SU URF should d use SOFT T = 2 underr card A ena abled. Hourglass IHQ = 4, QM = 0.1 CONTROL L_BULK_VISCOSITY Q1 = 1.5, Q2 Q = 0.06 Note 02 : Shell eleme ents do nott require EO OS. Note 03: T = 388oK = 114oC, TR = 295oK = 21.85oC TM Note 04: V = 0.0 de VP efault. Poisson’s Ratio R = 0.37 7 seems to be a better choice forr polycarbonate.

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Note 01 EN EOS Pa arameters are a GRUNEISE C = 3940 m/s m S1 = 1.489 9 GAMMO = 2.02 ϭϯϰ

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A = 0.47 Note 02 Conversion from 300oK to oC = 300-273.15 =26.85oC ‡ˆ‡”‡…‡•

1. A. Raczy, W.J.Altenhof, A.T. Alpas, An eularian Finite Element model of the metal cutting process, 8th Int. LS-DYNA s Conference (Metal Forming). 2. Ansys/LS-DYNA s guide, Ansys release 6.0 (2001).

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ϭϯϲ

>^ͺzE&KZ Z'/EEZ^^

/ŶŵŽĚĞůƐƉĞĞƌƚĂŝŶŝŶŐƚŽ ƌďŝƚƌĂƌLJ>ĂŐƌĂŶŐĞƵůĂƌŝĂŶ Ŷ;>ͿĨŽƌŵƵ ƵůĂƚŝŽŶǁŚĞŶ ŶǁĞĚĞĂůǁŝƚŚŵƵůƚŝͲŵĂƚĞĞƌŝĂůƐŝŶĂ ĚŽŵĂŝŶ ƚŚĞ ͚/ŶŝƚŝĂů ͚ sŽůƵŵ ŵĞ ĨƌĂĐƚŝŽŶ͛ ĐĂŶ ďĞ ǀĞƌLJ ŚĞůƉĨƵů Ś ƚŽ Ĩŝůů ǀĂƌŝŽƵƐ ǀŽůƵŵĞƐ ǁŝƚŚ ĚŝĨĨĨĞƌĞŶƚ ŵĂƚĞƌƌŝĂůƐ͘ dŚŝƐ Ĩ ĨĞĂƚƵƌĞŝƐĂǀĂ ĂŝůĂďůĞŝŶ>ƐͲW WƌĞƉŽƐƚƐŝŶĐĞĞǀĞƌ͘ϯ͘ϭŽƌĞĞĂƌůŝĞƌƵŶĚĞƌ ͚>^ĞƚƵƉ͛͘ ĨĨĞĐƚŝǀĞƵƐĂŐĞŽĨƚŚŝƐĨĞĂĂƚƵƌĞĐĂŶ ĂĐĐĞůĞƌĂƚĞƚŚĞƉĂĐĞŽĨŵŽ ŽĚĞůŝŶŐďĞĐĂƵ ƵƐĞŝƚĂƵƚŽŵĂƚƚŝĐĂůůLJĂƐƐŝŐŶƐƐƚŚĞŵĂƚĞƌŝĂĂůŵŽĚĞůƐ͕ĞƋƵ ƵĂƚŝŽŶƐŽĨƐƚĂĂƚĞ͕ŚŽƵƌͲ Ő ŐůĂƐƐ͕ƐĞĐƚŝŽŶ ŶƐ͕ŝŶŝƚŝĂůĐŽŶĚ ĚŝƚŝŽŶƐ͕ĂŶĚŵ ŵĂŶLJŵŽƌĞĞƐƐƐĞŶƚŝĂůƐǁŝƚŚ ŚŽƵƚŚĂǀŝŶŐĂŶLJŶĞĞĚƚŽƌĞĞŵĞŵďĞƌƚŚĞĞŽƌĚĞƌŝŶ ǁ ǁŚŝĐŚ ƚŚĞ ŶĞĞĐĞƐƐĂƌLJ ƐƚĞƉ ƉƐ ĂƌĞ ƉƌŽĐĞĞƐƐĞĚ͘ /Ŷ ƚŚŝŝƐ ĐŚĂƉƚĞƌ ĂŶ Ŷ ĞdžĂŵƉůĞ ŽŶ ĞdžƉůŽƐŝǀĞ ĚĞƚŽŶĂƚŝŽŶ ǁŽƵůĚ ǁ ďĞ ĚĞƚĂŝůĞĚƵƐŝŶŐƚŚĞ>ƐĞƚƚƵƉ͘ůƚŚŽƵŐŚ ŚƚŚĞĞdžĂŵƉůĞĞƐŚŽǁƐŚŽǁƚŽƐĞƚƵƉƚŚĞĞdžƉůŽƐŝǀĞĚĞƚƚŽŶĂƚŝŽŶƵŶĚĞƌǁĂƚĞƌ͕ ƐŝŵŝůĂƌƉƌŽĐĞĚƵƌĞĐĂŶďĞƵ ƵƐĞĚƚŽŵŽĚĞĞůǀĂƌŝŽƵƐŽƚŚĞƌƉƌŽďůĞŵƐŝŶ>ƐͲLJŶĂƚŚĂƚŝŶǀŽůǀĞŵƵ ƵůƚŝͲŵĂƚĞƌŝĂůƐƐ͘

šƒ’Ž‡ ƌĞĂƚĞĂŵĞƐƐŚĞĚƐŽůŝĚďŽdžŽĨϮϬdžϮϬdžϮϬŵŵƐƚĂƌƚŝŶ ŶŐĂƚ;Ϭ͘Ϭ͕Ϭ͘Ϭ͕Ϭ͘ϬͿĂŶĚƚĞƌŵ ŵŝŶĂƚŝŶŐĂƚ;Ϯ ϮϬ͘Ϭ͕ϮϬ͘Ϭ͕ϮϬ͘Ϭ ϬͿ͘/ŶƚŚŝƐ ĞdžĂŵƉůĞĂƋƵ ƵĂƌƚĞƌƐLJŵŵĞ ĞƚƌŝĐŵŽĚĞůŽ ŽĨĂǁĂƚĞƌďŽ ŽĚLJŚĂǀŝŶŐĂŶ ŶĞdžƉůŽƐŝǀĞĐŚ ŚĂƌŐĞŽĨĐLJůŝŶ ŶĚƌŝĐĂůƐŚĂƉĞ ŽĨϰŵŵ ƌĂĚŝƵƐĂŶĚϭϬ ϬŵŵůĞŶŐƚŚĂƚƚŚĞďŽƚƚŽ ŽŵŽĨƚŚĞĐƵď ďŝĐǁĂƚĞƌŵĂƐƐ;njсϬ͘ϬͿǁ ǁŽƵůĚďĞŐĞŶĞƌĂƚĞĚ͘EĞdžƚĐƌĞĂƚĞĂ ĐLJůŝŶĚĞƌͲƐŚĞůů ŽĨ ϰ ŵŵ ƌĂĂĚŝƵƐ ĂŶĚ ϭϬ ŵŵ ůĞŶŐƚŚ ŝŶ LJͲĚŝƌĞĐƚŝŽŶ Ŷ͘ dŚĞ ƌĞƐƵůƚŝŶŐ ŵŽĚĞů ŽĨĨ ǁĂƚĞƌ ĂŶĚ ĞdžƉůŽƐŝǀĞ Ğ ĐLJůŝŶĚĞƌĂƌĞƐƐŚŽǁŝŶ&ŝŐ͘ϭϴ ϴ͘ϭ͘

&ŝŐ͘ϭϴ͘ϭ ZĞŵĞŵďĞƌ ƚŚŝƐ ĐLJůŝŶĚƌŝĐĂĂů ƐŚĞůů ǁŽƵůĚ Ě ďĞ ĨŝůůĞĚ ǁŝƚƚŚ ĞdžƉůŽƐŝǀĞ ŵĂƚĞƌŝĂů ůĂƚĞĞƌ ŝŶ ƚŚŝƐ ĞdžĂŵƉůĞ͘ EĞdžƚ ƐĞůĞĐƚ ƚŚĞ >ƐĞƚƵƉĨƌŽ ŽŵƉƉůŝĐĂƚŝŽ ŽŶ͘EĞdžƚƚŽ'ƌƌŽƵƉEĂŵĞƚLJLJƉĞtĂƚĞƌĂŶ ŶĚĐůŝĐŬŽŶĚ ĚĚ'ƌŽƵƉ͘ZĞƉ ƉĞĂƚƚŚŝƐĨŽƌdžƉůŽƐŝǀĞ ĂŶĚŝƌƚŽŽďƚĂŝŶϯŐƌŽƵƉƐƐĂŶĚĐŚĞĐŬĂůůƚŚƌĞĞĞŵƉƚƚLJďŽdžĞƐĂƐƐŚ ŚŽǁŶŝŶ&ŝŐ͘ϭϴ͘Ϯ͘ ϭϯϳ

>^ͺzE&KZ Z'/EEZ^^

&ŝŐ͘ϭϴ͘ϮƌĞĂƚŝŶŐϯŐƌƌŽƵƉƐ EĞdžƚĐůŝĐŬƚŚĞĞDĂƚƚĂďĂŶĚ ĚŝŶƐĞƌƚƚŚĞĚ ĚĂƚĂĨŽƌĂůůƚŚ ŚƌĞĞŐƌŽƵƉƐĨŽ ŽƌƚŚĞŝƌŵĂƚĞĞƌŝĂůƉƌŽƉĞƌƚŝĞĞƐ͕ĞƋƵĂƚŝŽŶƐƐŽĨƐƚĂƚĞ͕ ĂŶĚŚŽƵƌŐůĂƐƐƐ͘/ƚǁĂƐĨŽƵŶ ŶĚƚŚĂƚŝĨƚŚĞĞƚŚƌĞĞŵĂƚĞƌƌŝĂůŵŽĚĞůƐĂƌĞƉƌĞĚĞĨŝŶĞĚ ĚŝŶƚŚĞŝŶƉƵƚƚĨŝůĞŝƚǁŽƵůĚ ĚƐŝŵƉůŝĨLJ ƚ ƚŚŝƐƉƌŽĐĞĚƵƌ ƌĞďLJũƵƐƚƐĞůĞ ĞĐƚŝŶŐƚŚĞŵĂĂƚĞƌŝĂůŵŽĚĞůƐƐŽŶĞďLJŽŶĞĂŶĚƐĂǀŝŶŐƚŚ ŚĞŵĂƐƐŚŽǁŶ ŶŝŶ&ŝŐ͘ϭϴ͘ϯ͘

&ŝŐŐ͘ϭϴ͘ϯĞĨŝŶĞ ĞƚŚĞŵĂƚĞƌŝĂůůŵŽĚĞůƐĨŽƌǁ ǁĂƚĞƌ͕ĞdžƉůŽƐŝǀĞ͕ĂŶĚĂŝƌĂďŽǀĞƚŚĞǁĂƚƚĞƌƐƵƌĨĂĐĞ͘ EĞdžƚĐůŝĐŬŽŶƚŚĞsŽůƵŵĞ ƚĂď͘/ŶƚŚĞs sŽůƵŵĞŝŶƚĞƌĨĨĂĐĞĨŝƌƐƚƌŝŐŚ ŚƚĐůŝĐŬŝŶƚŚĞĞŵƉƚLJďŽdžƵ ƵŶĚĞƌůĞDĞĞƐŚWĂƌƚƐ ĚĚWĂƌƚ͕ƐĞůĞ ĞĐƚϭďŽdžƐŽůŝĚ ĚĂŶĚƚŚĞŶĚ ĚĚĂƐƐŚŽǁŶŝŶ&ŝŐ͘ϭϴ͘ϰ͘ϭ ϭďŽdžƐŽůŝĚǁŽ ŽƵůĚĂƉƉĞĂƌƵ ƵŶĚĞƌůĞ ĂŶĚĐůŝĐŬŽŶ D DĞƐŚWĂƌƚƐ͘ ϭϯϴ

>^ͺzE&KZ Z'/EEZ^^

&ŝŐ͘ϭϴ ϴ͘ϰĚĚŝŶŐƉĂƌƚƐ EĞdžƚĐůŝĐŬŽŶ ŶƚŚĞϮĐLJůŝŶĚ ĚĞƌƐŚĞůůĂŶĚĐĐůŝĐŬƐĂǀĞďƵƚƚƚŽŶ͘EĞdžƚĐŚĂŶŐĞϮdžƉůŽ ŽƐŝǀĞǁŝƚŚϯ ŝƌŝŶƚŚĞďŽdždžDĂƚďLJ 'ƌŽƵƉ/Ě͗ĂŶ ŶĚƌĞƉůĂĐĞ'Ğ ĞŽŵĞƚƌLJdLJƉĞĞƚŽWůĂŶĞĂŶ ŶĚƚLJƉĞnjсϭϱ ĂŶĚƉƌĞƐƐƐĂ ĂǀĞďƵƚƚŽŶ͘ddŚĞĂƉƉĞĂƌĂŶĐĞŽĨƚŚĞ >ƐĞƚƵƉǁŝŶ ŶĚŽǁƐŚŽƵůĚůŽŽŬůŝŬĞ&ŝŐ͘ϭϴ͘ϱ͘

&ŝŐ͘ϭϴ͘ϱƐƐŝŐŶŝŶŐŵĂƚĞƌŝĂůƐƚŽǀŽůƵŵĞƐ͘ EĞdžƚŝƐĂǀĞƌLJLJĐƌŝƚŝĐĂůƐƚĞƉ ƉƚŽďĞĨŽůůŽǁ ǁĞĚǀĞƌLJĐĂƌĞĞĨƵůůLJ͘ůŝĐŬŽŶ'ƌŽƵƉͬD dƚĂďĂŶĚƚŚĞŶŽŶ'ƌŽƵƉƚĂď͘dŚĞ >ƐĞƚƵƉǁŝ ŶĚŽǁŶŽǁƐŚ ŚŽƵůĚůŽŽŬůŝŬŬĞ&ŝŐ͘ϭϴ͘ϲ͘Z ZŝŐŚƚůŝĐŬŽŶtĂƚĞƌĂŶĚŝŶƐĞůĞĐƚĚĚ WĂƌƚ͘ƐŵĂůůǁŝŶĚŽǁ ϭϯϵ

Z'/EEZ^^ >^ͺzE&KZ ƐŚŽǁƐϭďŽdžƐƐŽůŝĚ͘^ĞůĞĐƚϭ ϭďŽdžƐŽůŝĚĂŶ ŶĚƚŚĞŶƉƌĞƐƐƐĚĚďƵƚƚŽŶ͘͘ZĞƉĞĂƚƚŚŝƐ ĨŽƌdžƉůŽƐŝǀĞĞĂŶĚŝƌ͘ůƚŚ ŚŽƵŐŚŶŽ ƐŵĂůůǁŝŶĚŽǁ ǁĂƉƉĞĂƌƐũƵƐƚĐůŝĐŬŽŶĚĚ ĚWĂƌƚĨŽƌĂůůŐŐƌŽƵƉƐ͘

&ŝŐ͘ϭϴ͘ϲZŝŐŚƚĐůŝĐŬƐĞĞĐƌĞƚ /ĨĞǀĞƌLJƚŚŝŶŐŚĂƐďĞĞŶĚŽŶ ŶĞĐŽƌƌĞĐƚůLJƚƚŚĞ>ƐĞƚƵƉ ƉǁŝŶĚŽǁƐŚŽ ŽƵůĚĂƉƉĞĂƌůŝŬĞ&ŝŐ͘ϭϴ͘ϳ͘ddŚĞŵŽƐƚŶĞĞĞĚĞĚƐƚĞƉ ď ĐŽŵƉůĞ ĞƚĞĚ͘ dŚĞ ƵƐĞĞƌ ĐĂŶ ŶŽǁ ƐĞůĞĐƚ Ɛ ƐŝŵƵůĂƚƚŝŽŶ ĐŽŶƚƌŽů ƚĂď ƚ ĂŶĚ ƐĞƚ ĂƉƉƌŽƉƌŝĂƚĞ ǀĂůƵĞƐ ŝŶ ŚĂƐ ĂůƌĞĂĚLJ ďĞĞŶ ĚŝĨĨĞƌĞŶƚĨŝĞůĚ ĚƐ͘>ĞƚƵƐŝŶƐĞƌƚdŝŵĞсϬ͘͘ϯĂŶĚEŽ͘ŽĨĨKƵƚƉƵƚƐĂƐ ϯϬ͘/ƚŝƐŶŽƚƉ ƉŽƐƐŝďůĞŚĞƌĞĞƚŽƉƌŽǀŝĚĞĂĂůůĚĞƚĂŝůƐ ƉĞƌƚĂŝŶŝŶŐƚŽƚŚŝƐƐƚĞƉĂƐƚƚŚĞŽďũĞĐƚŝǀĞŽĨƚŚŝƐĐŚĂƉƚĞƌŝƐŽŶůLJƚŽĨĨŽĐƵƐƵƉŽŶƚŚ ŚĞ/ŶŝƚŝĂůsŽůƵ ƵŵĞ&ƌĂĐƚŝŽŶ͘ EĞdžƚĐůŝĐŬŽŶ^ĞƚƵƉďƵƚƚŽŶŝŶƚŚĞƚŽƉͲƌŝŐŚƚĐŽƌŶĞƌĂĂŶĚƐĞůĞĐƚŵŵ͕ŵƐĞĐ͕ĂŶĚ ĚŬŐĂƐƵŶŝƚƐ ĂŶĚĐůŝĐŬŽŬ͘ ƐĂůĂƐƚ ǁŚĞƌĞϯŝŶƉƵ ƵƚĨŝůĞƐŚĂǀĞƚŽ ŽďĞƐĂǀĞĚ͘ůŝĐŬŽŶKƵƚƉƵ ƵƚLJŶĂďƵƚƚŽ ŽŶĂŶĚĂůů ƐƚĞƉĐůŝĐŬŽŶKƵƚƉƵƚ͘^ĞůĞĐĐƚƚŚĞĨŽůĚĞƌǁ ϯĨŝůĞƐǁŽƵůĚďĞƐĂǀĞĚ͘dŚŝƐŝƐƐŚŽǁŶŝŶ Ŷ&ŝŐ͘ϭϴ͘ϴ͘>ƐͲͲWƌĞƉŽƐƚĐĂŶďĞĐůŽƐĞĚĂƚƚƚŚŝƐƐƚĂŐĞ͘

ϭϰϬ

>^ͺzE&KZ Z'/EEZ^^

&ŝŐ͘ϭϴ͘ϳ'ƌŽƵƉƐǁŝƚŚƚŚĞŝƌƌĞƐƉĞĐƚƚŝǀĞŵĂƚĞƌŝĂů͕K^͕ĂŶĚŚŽƵƌŐůĂƐƐŝĚĞŶƚŝƚŝĞƐ͘

&ŝŐ͘ϭϴ͘ϴ&ŝůůĞŽƵƚƉƵƚƉƌŽ ŽĐĞĚƵƌĞ &ĞǁƚŚŝŶŐƐĂƌƌĞŝŵƉŽƌƚĂŶƚƚŽƌĞŵĞŵďĞƌƌŚĞƌĞƌĞŐĂƌĚŝŶŐƚŚĞŝŶƉƵƚĨŝůĞƐ͘/ĨƚŚĞĨŝŝůĞŶĂŵĞƐĂƌĞĞŶŽƚŐŝǀĞŶďLJLJƚŚĞƵƐĞƌ ƚ ŝŶƉƵƚ Ŭ ĨŝůĞ ƚŚĞ Ĩ ŶĂŵĞ ĚĞĨĨĂƵůƚƐ ƚŽ ůƐͺĂ ĂůĞ͘Ŭ ĂŶĚ sŽůůƵŵĞ ĨƌĂĐƚŝŽŶ Ŷ ĨŝůĞ ǁŽƵůĚ ďĞĂƌ ď Ă ŶĂŵĞĞ ůŝŬĞ ůƐͺĂůĞͺǀǀĨƌ͘Ŭ ĂŶĚ ŵŽĚĞůĨŝůĞĂƐ ůƐͺĂůĞͺŵŽĚĞĞů͘ŬĂƐƐŚŽǁŶ ŶŝŶ&ŝŐ͘ϭϴ͘ϴ͘ůƐͺĂůĞ͘ŬŝƐƚŚĞŵĂŝŶĨŝůĞ͘/ƚƚĐĂůůƐŽƚŚĞƌƚƚǁŽĨŝůĞƐƵƐŝŶŐŝŶĐůƵĚĞ ĐŽŵŵĂŶĚ͘ ϭϰϭ

Z'/EEZ^^ >^ͺzE&KZ &ƵƌƚŚĞƌ ĚĞƉĞĞŶĚŝŶŐ ƵƉŽŶ ƚŚĞ ĚĞƚĂŝůĞĚ ŝŶƉƵƚ ƉŚĂĂƐĞ ƐŽŵĞ ƉĂƌĂŵĞƚĞƌƐ ŵĂĂLJ ďĞ ĨŽƵŶĚ ŵŝƐƐŝŶŐ Žƌ ǁŝƚŚ ŝŶͲ ĂƉƉƌŽƉƌŝĂƚĞǀǀĂůƵĞƐĚƵĞƚŽ ŽƚŚĞĐĂƌĞůĞƐƐŶĞƐƐŽĨƚŚĞƵ ƵƐĞƌ͘dŚŽƐĞƉĂĂƌĂŵĞƚĞƌƐŵƵ ƵƐƚďĞĐŽƌƌĞĐƚƚĞĚďĞĨŽƌĞƐƵ ƵďŵŝƚƚŝŶŐ ƚ ƚŚĞĨŝůĞĨŽƌĞdž džĞĐƵƚŝŽŶ͘/ŶŝƚƚŝĂůĚĞƚŽŶĂƚŝŽ ŽŶǀĂůƵĞƐŵƵƐƚďĞĐŚĞĐŬĞĚ͘ϯƉůŽƚĂŶĚ ĚĚϯŚĚƚƚŝŵĞĞŝŶƚĞƌǀĂůƐƐŚŽƵůĚĂůƐŽ ďĞ ĐŚĞĐŬĞĚ ĨŽƌ Ĩ ĂŶLJ ƵŶǁĂĂŶƚĞĚ ŝŶƉƵƚ͘ ŶĚ ƚŚĞ ŵŽƐƐƚ ŝŵƉŽƌƚĂŶƚ ŽĨ Ăůů ŝƐ ƚŽ ĚĞůĞƚĞ Ě ƚŚĞ ƐŚĞůů ƐƚƌƵĐƚƵƌĞ ;ĐLJůŝŶĚĞƌ ƐŚĞůůͿǁŚŝĐŚǁ ǁĂƐĨŝůůĞĚǁŝƚŚĞdžƉůŽƐŝǀĞŵ ŵĂƚĞƌŝĂůŝĨŝƚŝƐƐŶŽƚƌĞƋƵŝƌĞĚ ĚŝŶƚŚĞĂŶĂůLJƐŝƐ͘ d dŽĨĂĐŝůŝƚĂƚĞƚ ƚŚĞƵƐĞƌƚŚĞƌƌĞůĂƚĞĚŝŶƉƵƚĨŝůĞƐǁŽƵůĚďĞŵĂĚĞĂǀĂŝůĂĂďůĞŽŶĂŽƌĂƚƚŚĞĨŽůůŽ ŽǁŝŶŐǁĞďƐŝƚĞ͘ ŚƚƚƉ͗ͬͬƐƚĂĨĨ͘ŝŝƵŵ͘ĞĚƵ͘ŵLJͬŚ ŚƋĂƐŝŵͬŝŶƉƵƚƚĨŝůĞƐ͘njŝƉ

—–’—– KŶĐĞƚŚŝƐƉƌŽ ŽďůĞŵŚĂƐďĞĞŶƐŽůǀĞĚƚŚĞĞŶĞdžƚŝŵƉŽƌƚƚĂŶƚƚĂƐŬŝƐƚŽ ŽǀŝƐƵĂůŝnjĞƚŚĞĞƌĞƐƵůƚƐƵƐŝŶŐŐůĂƚĞƐƚ>ƐͲWƌĞĞƉŽƐƚ͘dŽ ĚŽƚŚŝƐŽƉĞŶƚŚĞĚϯƉůŽƚĨŝůĞŝŶ>ƐͲWƌĞƉŽ ŽƐƚĂŶĚĐůŝĐŬŽ ŽŶƚŚĞŝĐŽŶƐĂƐƐŚŽǁŶǁŝƚŚ Śϭ͕Ϯ͕ĂŶĚϯ͘

&ŝŐ͘ϭϴ͘ϵ ĨƚĞƌƚŚĞĂďŽ ŽǀĞĐůŝĐŬƐƐŚŽ ŽǁŶŝŶ&ŝŐ͘ϭϴ ϴ͘ϵƚŚĞ>ƉĂĂƌƚƐƐŚŽƵůĚďĞĞǀŝƐŝďůĞĂƐƐŚ ŚŽǁŶŝŶ&ŝŐ͘ϭ ϭϴ͘ϭϬ͘&ůƵŝĚĚ ĚĞŶƐŝƚLJĂƚ Ϭ Ϭ͘ϬϰϵϴϵϮŵŝů ůŝƐĞĐƐƐŚŽƵůĚĂƉƉĞĂƌĂƐŝŶ&ŝŐ͘ϭϴ͘ϭϭ͘

ϭϰϮ

Z'/EEZ^^ >^ͺzE&KZ

& &ŝŐ͘ϭϴ͘ϭϬ

&ŝŐ͘ϭϴ͘ϭϭ&ůƵŝĚĚĞŶƐŝƚLJĐŽ ŽŶƚŽƵƌƐ͘

ϭϰϯ

>^ͺzE&KZ'/EEZ^

References 1. LS-DYNA Keyword ’s manual, Livermore Software Technology Corporation. 2. http://www.dyna.com/ 3. http://www.varmintal.com/aengr.htm/ 4. http://www.lstc.com/lspp/

ϭϰϰ

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