# Chapter15.pdf

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Chapter 15 Explicit Dynamics   1 Chapter 15 Explicit Dynamics 15.1   Basics of Explicit Dynamics15.2   Step-by-Step: High-Speed Impact15.3   Step-by-Step: Drop Test15.4   Review  Chapter 15 Explicit Dynamics   Section 15.1 Basics of Explicit Dynamics   2 Section 15.1 Basics of Explicit Dynamics Key Concepts ã Implicit Integration Methods ã Explicit Integration Methods ã Solution Accuracy ã Integration Time Steps ã Automatic Mass Scaling ã Static Damping  Chapter 15 Explicit Dynamics   Section 15.1 Basics of Explicit Dynamics   3 Implicit Integration Methods    M ⎡⎣ ⎤⎦   D { } + C  ⎡⎣ ⎤⎦   D { } + K  ⎡⎣ ⎤⎦ D { } = F  { } ã <Transient Structural> solves the above equation using the following algorithm:    D n + 1 =   D n  + Δ t   γ     D n + 1 + (1 − γ   )  D n ⎡⎣ ⎤⎦   D n + 1 = D n  + Δ t    D n  + 12  Δ t  2 2 β   D n + 1 + (1 − 2 β  )  D n ⎡⎣ ⎤⎦ ã The parameters γ    and β   are chosen to control characteristics of the algorithm such as accuracy, numerical stability, etc. ã It is called an implicit method   because the response at the current time step depends on not only the historical information but also the current information; iterations are needed in a single time step.  Chapter 15 Explicit Dynamics   Section 15.1 Basics of Explicit Dynamics   4 Explicit Integration Methods    M ⎡⎣ ⎤⎦   D { } + C  ⎡⎣ ⎤⎦   D { } + K  ⎡⎣ ⎤⎦ D { } = F  { } ã <Explicit Dynamics> solves the above equation using the following algorithm:    D n + 12 =   D n − 12 +   D n Δ t    D n + 1 = D n  +   D n + 12 Δ t  ã It is called explicit methods  because the response at the current time can be calculated explicitly; no iterations within a time step is needed.

Oct 7, 2019

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Oct 7, 2019
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