By Gabi Ben-Dor
High-speed impression dynamics is of curiosity within the basic sciences, e.g., astrophysics and area sciences, and has a couple of very important functions in army applied sciences, place of birth defense and engineering. compared to experiments or numerical simulations, analytical methods in effect mechanics merely seldom yield beneficial effects. besides the fact that, while profitable, analytical methods let us ensure basic legislation that aren't simply vital in themselves but in addition function benchmarks for next numerical simulations and experiments. the most aim of this monograph is to illustrate the aptitude and effectiveness of analytical tools in utilized high-speed penetration mechanics for 2 periods of challenge. the 1st type of challenge is form optimization of impactors penetrating into ductile, concrete and a few composite media. the second one type of challenge contains research of ballistic houses and optimization of multi-layered shields, together with spaced and two-component ceramic shields. regardless of the big use of mathematical suggestions, the acquired effects have a transparent engineering that 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 complete description of the localized impactor/medium interplay process is given. within the monograph the authors current systematically their theoretical ends up in the sector of high-speed impression dynamics got over the last decade which simply partly seemed in clinical journals and meetings proceedings.
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Extra resources for Applied High-Speed Plate Penetration Dynamics
Formulas provided by LIM with Ω n ( u , v ) = A0 ( u )v α Function/variable 3-D impactor 3-D conical Impactor of impactor revolution Φ ( k 0 + k x )η ( ϑ ) Φ ( x ,ϑ ) Φ( x ) Sharp cone: k 0 = 0 Table 2-1 Table 2-1 Table 2-1 δ ,θ ,Θ ~ Table 2-2 Table 2-2 Table 2-2 σ , u ,U , u Eq. 4) Eq. 20) Eq. 32) B0 Cone of revolution k 0 + kx Table 2-1 Table 2-2 H Eqs. 16) Eqs. 28) Sharp cone: Eq. 30) Eqs. 19) vimp 0 Eq. 15) Eq. 15) Finit ~ Dinit Eq. 13) Eq. 29) Sharp cone: Eq. 31) Eq. 21) Eq. 33) Eqs. 28) Sharp cone: Eq.
If friction between the impactor and the host medium is not taken into account then: µ fr = 0 . 2) Chapter 2 22 Taking into account Eqs. 12), we can rewrite Eq. 3) ∫ 0 where U ( x ,ϑ ) = ( u + µ fr 1 − u 2 )u0 = ΦΦ x + µ fr Φ 2 + Φϑ2 , u( x ,ϑ ) = ΦΦ x . 5) 2 For purpose of convenience, we have summarized all the required for calculations formulas in Table 2-1. All the solutions presented below are derived by applying these general relationships. Table 2-1. 25) The solution of Eq. 20) with initial condition of Eq.
The integral in Eq. 12) ∑ σ (υ~ ,v )⋅δσ ( x ) . n i i i Here, as shown in Figure 2-9, the impactor’s surface that interacts with the shield is divided into sub-areas using the planes x = x i , where θ ( h ) = x1 < x2 < ... < xi < xi + 1 < ... < x N = Θ ( h ) , and σ ( xi ) is the cross-sectional area of the impactor in the plane x = xi , δσ ( xi ) = σ ( xi + 1 ) − σ ( xi ) , υ~i = υ~ ( xi ). ρ ρ = Φ(x) δσ( x i ) ~ υ xi ρi x i +1 x ρ i+1 Figure 2-9. Recht’s (1990) model. Thus, if a penetrator is a body of revolution, Eq.
Applied High-Speed Plate Penetration Dynamics by Gabi Ben-Dor