By Gabi Ben-Dor
The monograph is predicated at the result of the authors bought over the past decade and merely in part released in medical periodicals. half I offers a few universal equipment of engineering penetration modeling. specific awareness is given to 2 heavily similar techniques: the localized interplay and hollow space enlargement approximations which are common within the monograph. during this half for the 1st time seems to be a complete description of the localized interplay strategy and the instruments for its software to penetration mechanics. half II is dedicated, typically, 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 effect. during this a part of the monograph the impact of the order of the plates within the guard and of the spacing among the plates at the ballistic parameters are studied. This half comprises the research of the optimal constitution of metal/ceramic shields. even if the emphasis within the publication is at the analytical tools, rigorous mathematical proofs and numerical simulations supplement one another within the ebook, and the consequences are provided in an illustrative demeanour. The monograph is self-contained and assumes in basic terms uncomplicated wisdom of strong mechanics and arithmetic. The short exposition of the mandatory additional info is gifted within the booklet.
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Additional resources for Applied High-Speed Plate Penetration Dynamics (Solid Mechanics and Its Applications)
9) 0 2π σ(0 ) 1 2 k 0 η 2 ( ϑ )dϑ 2 ∫ 0 D Eqs. 11) v bl , sharp impactor Eqs. 11) Eqs. 12) H , sharp impactor Eqs. 11) Eqs. 8) ⎝ k +1 ⎠ ) = π r 2 Ω n ( 1, v ) δ ( h ) + 2πΩ n (sin υ , v )(tan υ + µ fr )D( h ), where υ is a half-angle of the apex of the cone and Θ( h ) ) k D( h ) = ( k0 + kx )dx = k0 [ Θ ( h ) − θ ( h )] + [ Θ 2 ( h ) − θ 2 ( h )] . 10) ) where D( h ) is defined by Eq. 9) and 2π ( D( v ) = Ω n (u( ϑ ),v )u~( ϑ )dϑ . 11) 0 For a cone of revolution, Eq. 11) can be simplified as: ( D( v ) = 2πΩ n (sinυ ,v)(tanυ + µ fr ) .
8) where ⎛β h Q( h ) = exp⎜ f ( ζ ) dζ ⎜m 2 0 ⎝ ∫ ⎞ ⎟. 9) Localized interaction approach 47 In the case of a SIS, Eq. 10) 0 where Eq. 15) must be taken into account. 8. 2 Shield with a finite thickness. General model 8. 1 3-D impactor In the case of a SFT, the BLV, vbl , can be calculated from Eq. 8) by substituting h = b + L , v( h ) = 0 and vimp = vbl : vblβ = β m b+ L ∫ f ( h ) Q( h ) dh . 11) 0 This case will be considered below in more detail. Assuming that vimp ≥ vbl , we can write Eq. 12) where T = Q( b + L ) .
3) but they subsequently decided that the dependence of a0 on the impactor velocity can be neglected because 0 < α << 1 . Although the development of a LIM describing the interaction between the medium and the impactor’s surface was not the direct goal of the study of Vitman and Stepanov (1959), their formula is often referred as a LIM. Let us now show that under several assumptions Eq. 2) implies Eq. 1) with Ωτ = 0 . Consider the penetration of a sharp straight conical impactor into a SIS without friction for h ≥ L .
Applied High-Speed Plate Penetration Dynamics (Solid Mechanics and Its Applications) by Gabi Ben-Dor