By Gabi Ben-Dor
High-speed influence dynamics is of curiosity within the primary sciences, e.g., astrophysics and house sciences, and has a couple of very important purposes in army applied sciences, place of birth safeguard and engineering. compared to experiments or numerical simulations, analytical methods in influence mechanics in simple terms seldom yield worthy effects. even if, while profitable, analytical methods let us make sure common legislation that aren't in simple terms vital in themselves but in addition function benchmarks for next numerical simulations and experiments. the most objective of this monograph is to illustrate the aptitude and effectiveness of analytical tools in utilized high-speed penetration mechanics for 2 sessions of challenge. the 1st classification of challenge is form optimization of impactors penetrating into ductile, concrete and a few composite media. the second one classification of challenge contains research of ballistic homes and optimization of multi-layered shields, together with spaced and two-component ceramic shields. regardless of the big use of mathematical innovations, the acquired effects have a transparent engineering which means and are offered in an easy-to-use shape. one of many chapters is dedicated completely to a couple universal approximate versions, and this can be the 1st time finished description of the localized impactor/medium interplay procedure is given. within the monograph the authors current systematically their theoretical ends up in the sector of high-speed effect dynamics got over the last decade which basically in part seemed in medical journals and meetings proceedings.
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Extra info for Applied High-Speed Plate Penetration Dynamics
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. 26) DOP for SFT Θ( h ) θ( h ) 4. SFT SIS CONSIDERED SHAPES OF THE IMPACTOR Formulas for calculations using the general model determined by Eq.
The latter survey also briefly summarized the findings of the earlier studies for concrete shields. 2 “Tangent cones” approaches In all the below-described methods, the force at the location of the interaction between the projectile and the host medium is assumed to be equal to the force at the surface of the tangent cone at this location, when the projectile velocity and the host medium are the same in both cases. Different versions of such an approach are known in aerodynamics as “methods of tangent cones” (Chernyi, 1969; Hayes and Probstein, 1959).
18) Using the same reasoning as in the case of the SIS, we arrive at the following formula that determines the model: Ω n (u ,v ) = −1 ⎡ ∂bˆ(sin −1 υ ,v ) ⎤ ⎢ ⎥ . 19) Note that the idea to restore a model using a known DOP function was used by Eisler et al. (1998) for the simplest degenerate model with Hˆ ( vimp ) , D = D( v ) , without considering the stage of incomplete immersion of the projectile into the target. 3 From aerodynamics to impact dynamics The conception and development of LIT (primarily for aerodynamic applications) have been discussed in monographs written by Bunimovich and Dubinsky (1995) and Miroshin and Khalidov (2002), as well as in the review of Bunimovich and Dubinsky (1996).