General Introduction to Structural Crashworthiness
The term ‘structural crashworthiness’ is used to describe the impact performance of a structure when it collides with another object. A study into the structural crashworthiness characteristics of a system is required in order to calculate the forces duri
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Structural Impact
5. GENERAL INTRODUCTION TO STRUCTURAL CRASHWORTHINESS 5.1
Introduction
The term 'structural crashworthiness' is used to describe the impact performance of a structure when it collides with another object. A study into the structural crashworthiness characteristics of a system is required in order to calculate the forces during a collision which are needed to assess the darnage to structures and the survivability of passengers in vehicles, for example. This topic embraces the collision protection of aircraft, buses, cars, trains, ships and offshore platforms, etc. [5.1-5.7] and even spacecraft [5.8]. No attempt is made to review the entire field and only that part which is related to dynamic progressive buckling introduced in the previous chapter is discussed briefly.
5.2
Elementary aspects of inelastic impact
Consider a stationary mass M1 which is struck by a mass M2 travelling with an initial velocity V2, as shown in figure 5.l(a). Conservation of linear momentum demands that (5.1) where V3 is the common velocity of both masses immediately after an inelastic impact. 1 The loss ofkinetic energy is, therefore, K, = M2V/!2- (MI+ M2JV/!2, The cocfficient ofrestitution is taken as zero (e = 0). J. A. C. Ambrosio (ed.), Crashworthiness © Springer-Verlag Wien 2001
(5.2)
N. Jones
68
- - - M,
a.- -
+---
(a)
nPm -----:.111
(b) Figure 5.1
(a) A mass M 2 travelling with a velocity V2 towards a stationary mass M 1. (b) Horizontal forces acting on mass M 2 during the impact event.
which, when using equation ( 5. 1) for V3, may be recast into the form
K,
=
(M2V/12) I (J+M2/ MI),
(5.3)
where M2V/12 is the initial kinetic energy ofthe mass M2. Equation ( 5.3) gives the energy which must be absorbed by an energyabsorbing system which is interposed between the two masses MI and M2, in figure 5.l(a). If the striking mass M2 is much larger than the struck mass MI (i.e., M2/MI >> 1), then Kz 0, and no kinetic energy is lost during the impact event. In the other extreme case of a striking mass M2 which is much smaller than the struck mass MI (i.e., M2/MI < < 1), then K, M2 V/ /2 and all of the initial kinetic energy of the mass M2 must be absorbed during the impact. The loss ofkinetic energy for an impact between two equal masses is K1 = M2 V/14, which is one-half of the initial kinetic energy of the striking mass M2. The variation of the dimensionless kinetic energy loss K/(M2V2 2!2) with the mass ratio M/MI is shown in figure 5.2.
=
=
Frequently, the struck mass MI in figure 5.l(a) is constrained to remain stationary throughout a practical impact event. In other words, M/M2 > > 1 and equation (5.3) gives K1 = M2 V/12, as expected.
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Structural Impact
1.0
M2VV2 0.75
ol0 --------~1 o~::::::~2~o========~3o~======~~~ M2/M1
Figure 5.2
Variation of the dimensionless kinetic energy loss given by equation (5.3) with the mass ratio M2/M1.
Now, it is evident from figure 4.3(a) that Da = PmL1 is the energy which is absorbed in an axially crushed circular tube and indeed is the energy absorbed
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