By Gabi Ben-Dor
High-speed effect dynamics is of curiosity within the primary sciences, e.g., astrophysics and area sciences, and has a few vital 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 valuable effects. in spite of the fact that, whilst profitable, analytical ways let us make certain normal legislation that aren't basically vital in themselves but in addition function benchmarks for next numerical simulations and experiments. the most objective of this monograph is to illustrate the capability and effectiveness of analytical equipment in utilized high-speed penetration mechanics for 2 sessions of challenge. the 1st category of challenge is form optimization of impactors penetrating into ductile, concrete and a few composite media. the second one type of challenge contains research of ballistic homes and optimization of multi-layered shields, together with spaced and two-component ceramic shields. regardless of the large use of mathematical ideas, the acquired effects have a transparent engineering that means and are awarded in an easy-to-use shape. one of many chapters is dedicated exclusively to a few universal approximate versions, and this is often the 1st time finished description of the localized impactor/medium interplay procedure is given. within the monograph the authors current systematically their theoretical leads to the sphere of high-speed effect dynamics acquired over the last decade which in basic terms partly seemed in clinical journals and meetings lawsuits.
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Extra resources for Applied High-Speed Plate Penetration Dynamics (Solid Mechanics and Its Applications)
11) Localized interaction approach 33 where u = u( x ) = Φ ′ / Φ ′2 + 1 = sinυ~ , and υ~ = υ~( x ) is the angle between the tangent to the generator and the axis of the impactor. The integral in Eq. 12) ∑ σ (υ~ ,v )⋅δσ ( x ) . n i i i Here, as shown in Figure 2-9, the impactor’s surface that interacts with the shield is divided into sub-areas using the planes x = x i , where θ ( h ) = x1 < x2 < ... < xi < xi + 1 < ... < x N = Θ ( h ) , and σ ( xi ) is the cross-sectional area of the impactor in the plane x = xi , δσ ( xi ) = σ ( xi + 1 ) − σ ( xi ) , υ~i = υ~ ( xi ).
10). 40) also remains valid in the cases of 3-D conical impactors and ~ impactors having the shape of a body of revolution, where function Dinit ( h ) is determined by Eq. 27) and Eq. 34), respectively. 8. TWO-TERM LOCALIZED INTERACTION MODELS In this section, we consider the following model: Ω n ( u , v ) = A2 ( u )v 2 + A0 ( u )vα , 0 ≤ α < 2 . 1) The derived final expressions are summarized in Table 2-4 and Table 2-5. 1 General solution for a tree-dimensional impactor Taking into account Eq.
27) Eq. 34) Eq. 27) e0 ÷ e 5 Eqs. 26) C0 Eq. 22) vbl Eq. 40) Eq. 40) Eqs. 26) Eq. 35) Eq. 40) Eq. 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 2π h ~ Dinit ( h ) = A0 ( 1 )σ ( 0 ) + dx B0 ( x ,ϑ ) dϑ .