By Gabi Ben-Dor
The monograph relies at the result of the authors got over the past decade and purely in part released in medical periodicals. half I provides a few universal equipment of engineering penetration modeling. specific realization is given to 2 heavily similar ways: the localized interplay and hollow space enlargement approximations which are primary within the monograph. during this half for the 1st time seems to be a accomplished description of the localized interplay technique and the instruments for its program to penetration mechanics. half II is dedicated, generally, to form optimization of impactors utilized to diversified media (metal, concrete, FRP laminate) and utilizing diversified impactor-shield interplay versions. 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 safeguard 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 supposing 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 purely simple wisdom of sturdy mechanics and arithmetic. The short exposition of the required additional info is gifted within the e-book.
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Additional resources for Applied High-Speed Plate Penetration Dynamics (Solid Mechanics and Its Applications)
20) into Eq. 5 kh + k0 ) . 27) Using Eqs. 27), we can rewrite Eq. 28) where ⎧ L [ 6 A0 ( 1 )σ ( 0 ) + C0 L ( kL + 3k0 )] β ⎫ vimp 0 = ⎨ ⎬ 6m ⎩ ⎭ 1β . 28) allow us to calculate the DOP of 3-D conical impactor into a SIS. In the case of a sharp impactor, k0 = 0 , σ ( 0 ) = 0 , and Eqs. 30) if vimp ≥ vimp 0 where vimp 0 ⎛ C kL3 β = ⎜⎜ 0 ⎝ 6m ⎞ ⎟ ⎟ ⎠ 1β . 3 Impactor of revolution In the case of an impactor of revolution penetrating a SIS, Eqs. 19) for calculating H and Eq. 33) h ~ Dinit ( h ) = π [ A0 ( 1 )Φ 2 ( 0 ) + 2 B0 ( x )dx ] .
The equation of its lateral surface is: Φ ( x ,ϑ ) = k0 + kx. 5) If an impactor has a flat bluntness then: σ ( 0 ) = k0 = r = 0 . 6) Formulas for u ,U , σ ( x) and σ ( 0 ) in. Table 2-2 are derived using the corresponding formulas in Table 2-1 and taking into account the equations describing the surface of the impactor. The following formulas for the drag force D of impactors having different shapes are obtained from Eq. 3). Table 2-2. Description of LIM with arbitrary Ω n for impactors of different shapes Function 3-D cone Body of revolution Cone of revolution Φ ( k 0 + k x )η ( ϑ ) Φ( x ) k 0 + kx u kη 2 Φ′ k U ( k0 + kx )u~( ϑ ) u~ kη 2 + µ fr η 2 + η ′ 2 σ( x ) 1 ( k 0 + kx ) 2 η 2 ( ϑ )dϑ 2 η 2 ( k 2η 2 + 1 ) + η ′ 2 Φ ′2 + 1 Φ ( Φ ′ + µ fr ) k2 +1 ( k 0 + kx )u~ k + µ fr 2π ∫ πΦ 2 ( x ) π ( k 0 + kx ) 2 πr 2 πk 02 Eq.
25) Sharp cone: k 0 = 0 Chapter 2 50 Function/variable 3-D impactor 3-D conical impactor Q Eq. 9) Eq. 9) Eq. 9) vbl Eq. 11) Eq. 11) v res Eq. 12) T Eq. 13) Eq. 11) Sharp cone: Eq. 22) Eq. 12) Sharp cone: Eq. 24) Eq. 13) Sharp cone: Eq. 21) Eq. 16) Cone of revolution: Eq. 17) C0 , C 2 8. 3 Impactor of revolution Eq. 12) Eq. 13) Generalized “Newton’s model” The most widely used model of the type determined by Eq. 26) A0 ( u ) = a0 vα , A2 ( u ) = a2 u 2 . 27) i. , Although commonly used values of the constants are α = 0 and β = 2 − α = 2 , we still consider the case with 0 ≤ α < 2 , since it does not complicate the obtained formulas or the exposition.