By Gabi Ben-Dor

ISBN-10: 1402034520

ISBN-13: 9781402034527

ISBN-10: 1402042396

ISBN-13: 9781402042393

The monograph is predicated at the result of the authors acquired over the last decade and basically partly released in medical periodicals. half I offers a few universal tools of engineering penetration modeling. specific recognition is given to 2 heavily comparable methods: the localized interplay and hollow space growth approximations which are commonly used within the monograph. during this half for the 1st time looks a entire description of the localized interplay process and the instruments for its software to penetration mechanics. half II is dedicated, more often than not, to form optimization of impactors utilized to diversified media (metal, concrete, FRP laminate) and utilizing varied impactor-shield interplay versions. half III offers with research and optimization of multi-layered shields opposed to ballistic influence. during this a part of the monograph the impression of the order of the plates within the protect 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 e-book is at the analytical equipment, rigorous mathematical proofs and numerical simulations supplement one another within the booklet, and the consequences are provided in an illustrative demeanour. The monograph is self-contained and assumes in basic terms easy wisdom of stable mechanics and arithmetic. The short exposition of the required additional info is gifted within the publication.

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**Extra resources for Applied High-Speed Plate Penetration Dynamics (Solid Mechanics and Its Applications)**

**Sample text**

3) for function Ω n ( u ,v ) , which is defined by Eq. 3) 0 B0 ( x ,ϑ ) = A0 (u( x ,ϑ ))U ( x ,ϑ ) . 4) The equation of motion (Eq. 20) can be written as: mv dv + D( h ) = 0 . 5) The solution of this differential equation with the initial conditions given by Eq. 7) 0 β = 2 −α . 15) are valid in the case of a 3-D impactor penetrating a SIS, and Eq. 9) where h 2π 0 0 ~ Dinit ( h ) = A0 ( 1 )σ ( 0 ) + dx B0 ( x ,ϑ ) dϑ . 10) Then, the equation for determination of DOP, H , can be obtained by substituting h = H and v = 0 into Eq.

4) ∫ Eq. 3) can be rewritten, after substituting σ ( 0 ) from Eq. 4), in the following form, which is more convenient when optimization problems are investigated: D0 ( v ) = Ω n ( 1,v )σ ( L ) 2π L ∫ ∫ + dx {[ Ω n ( u ,v ) − Ω n ( 1,v )]ΦΦ x + µ fr Ω n ( u ,v ) Φ 2 + Φϑ2 }dϑ . 5) 0 The equation of impactor motion (Eq. 20) can be simplified: mv dv b + D0 ( v ) = 0 .

1) where µ fr is a friction coefficient. 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.

### Applied High-Speed Plate Penetration Dynamics (Solid Mechanics and Its Applications) by Gabi Ben-Dor

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