By Gabi Ben-Dor

The monograph relies at the result of the authors bought over the past decade and merely partly released in medical periodicals. half I provides a few universal equipment of engineering penetration modeling. specific cognizance is given to 2 heavily comparable ways: the localized interplay and hollow space enlargement approximations which are typical within the monograph. during this half for the 1st time seems a accomplished description of the localized interplay technique and the instruments for its program to penetration mechanics. half II is dedicated, more often than not, to form optimization of impactors utilized to assorted media (metal, concrete, FRP laminate) and utilizing various impactor-shield interplay types. half III bargains with research and optimization of multi-layered shields opposed to ballistic effect. during this a part of the monograph the impact of the order of the plates within the defend and of the spacing among the plates at the ballistic parameters are studied. This half contains the research of the optimal constitution of metal/ceramic shields. even though the emphasis within the booklet is at the analytical equipment, rigorous mathematical proofs and numerical simulations supplement one another within the e-book, and the consequences are provided in an illustrative demeanour. The monograph is self-contained and assumes merely simple wisdom of strong mechanics and arithmetic. The short exposition of the required more information is gifted within the publication.

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**Sample text**

The latter definition implies that θ ( h ) = Θ ( h ) = L for h > b + L . An identity similar to Eq. 3) is valid for some function Ξ ( x ) ≥ 0 applied to a SFT (Figure 2-7a-b): b+ L Θ( h ) L h = x +b L (h) 0 h= x 0 ∫ dh θ ∫ Ξ ( x )dx = ∫ Ξ ( x )dx ∫ dh = b∫ Ξ ( x )dx . 7) Thus Eq. 5) can be used as a unified description of the area of impactor-shield interaction, taking into account that h ≥ 0 and θ = 0 for a semi-infinite shield and 0 ≤ h ≤ b + L and θ ( h ) is defined by Eq. 6) for a SFT. The model can be simplified if we do not take into account the stage at which penetrator is only partially immersed in the shield.

Differentiating, after this substitution, both sides of this equation with respect to vimp , we obtain: mvimp 1 ∂Hˆ ( = Θ 2 Hˆ ( υ , vimp ) . 14) ( Substitution of D from Eq. 11) yields: Ω n (sinυ ,vimp ) −1 ⎡ 2 ∂Hˆ ⎤ = ⎢Θ Hˆ ( υ ,vimp ) ⎥ . 15) After the change of variables, υ = sin −1 u , vimp = v , we obtain an expression for function Ω n (u ,v ) that determines the LIM: Ω n (u ,v ) = −1 ⎡ 2 ˆ ∂Hˆ ⎤ −1 ⎢Θ H (sin υ ,v ) ⎥ . 16) A similar approach can be used for a SFT, provided that the function vˆbl ( υ ,b ) , which determines the dependence of the BLV of a straight circular conical impactor vs.

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 4. CONSIDERED SHAPES OF THE IMPACTOR Formulas for calculations using the general model determined by Eq. 1) and for different shapes of the impactor are summarized in Table 2-2.