By Gabi Ben-Dor
High-speed influence dynamics is of curiosity within the basic sciences, e.g., astrophysics and house sciences, and has a few vital purposes in army applied sciences, native land safety and engineering. compared to experiments or numerical simulations, analytical techniques in influence mechanics in basic terms seldom yield precious effects. despite the fact that, while winning, analytical methods let us ensure normal legislation that aren't in basic terms very important in themselves but additionally function benchmarks for next numerical simulations and experiments. the most objective of this monograph is to illustrate the capability and effectiveness of analytical tools in utilized high-speed penetration mechanics for 2 sessions of challenge. the 1st category of challenge is form optimization of impactors penetrating into ductile, concrete and a few composite media. the second one category of challenge contains research of ballistic homes and optimization of multi-layered shields, together with spaced and two-component ceramic shields. regardless of the large use of mathematical strategies, the got effects have a transparent engineering which means and are provided in an easy-to-use shape. one of many chapters is dedicated exclusively to a couple universal approximate types, and this is often the 1st time accomplished description of the localized impactor/medium interplay procedure is given. within the monograph the authors current systematically their theoretical leads to the sphere of high-speed impression dynamics bought over the past decade which in basic terms partly seemed in medical journals and meetings proceedings.
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Extra resources for Applied High-Speed Plate Penetration Dynamics
28) where vimp 0 ⎧ L [ 6 A0 ( 1 )σ ( 0 ) + C0 L ( kL + 3k0 )] β ⎫ =⎨ ⎬ 6m ⎩ ⎭ 1β . 28) allow us to calculate the DOP of 3-D conical impactor into a SIS. In the case of a sharp impactor, k0 = 0 , σ ( 0 ) = 0 , and Eqs. 30) if vimp ≥ vimp 0 where vimp 0 ⎛ C kL3 β = ⎜⎜ 0 ⎝ 6m ⎞ ⎟ ⎟ ⎠ 1β . 3 Impactor of revolution In the case of an impactor of revolution penetrating a SIS, Eqs. 19) for calculating H and Eq. 33) 0 h ~ Dinit ( h ) = π [ A0 ( 1 )Φ 2 ( 0 ) + 2 B0 ( x )dx ] . 34) are obtained from Eqs. 13) using Table 2-2.
1) The derived final expressions are summarized in Table 2-4 and Table 2-5. 1 General solution for a tree-dimensional impactor Taking into account Eq. 1), Eq. 2) where f i ( h ) = Ai ( 1 )σ ( 0 )δ ( h ) + Θ( h ) 2π θ( h ) 0 ∫ dx ∫ A (u( x ,ϑ ))U ( x ,ϑ )dϑ . 3) The equation of motion (Eq. 20) becomes: m dv + f 2 ( h ) v + f0 ( h )vα −1 = 0 . 4) This is an ordinary differential equation of the Bernoulli type. 5) where, as before, β = 2 − α , Eq. 4) can be transformed into a linear ordinary differential equation: dw β + [ f 2 ( h ) w + f 0 ( h )] = 0 .
12) Sharp cone: Eq. 24) Eq. 13) Sharp cone: Eq. 21) Eq. 16) Cone of revolution: Eq. 17) C0 , C 2 8. 3 Eq. 12) Eq. 13) Generalized “Newton’s model” The most widely used model of the type determined by Eq. 26) A0 ( u ) = a0 vα , A2 ( u ) = a2 u 2 . 27) i. , Although commonly used values of the constants are α = 0 and β = 2 − α = 2 , we still consider the case with 0 ≤ α < 2 , since it does not complicate the obtained formulas or the exposition. Transition from the model determined by Eq. , transition to the model determined by Eq.