Impact force calculation

[Student BE]

Hi,

I would like to learn how to calculate impact force for use as a static load in FEA simulation. Let’s say you model car crash or some falling object impact and don’t want to use explicit dynamics analysis in which objects will actually crash. I’ve found some examples of such calculations in FEA applications but they can be divided into 2 groups:

- very basic method (and results seem to be incorrect as it’s hard to assume the impact duration time) : F=m*a, a=v/t

- very complicated methods used in car crash mechanics, I don’t want to go so far with this

So I began searching and found 2 interesting articles. The problem is that they have different equation for the same thing:

1)

https://www.engineeringtoolbox.com/impact-force-d_1780.html

2)

https://sciencing.com/calculate-force-impact-7617983.html

As you can see in the first one they assume that W=(1/2)*F*s and in the second one it is W=F*d (d is the same as s before). Which one is correct ?

Another method I’ve found:
s=v0*t-((a*t^2)/2)
a=(v0-vk)/t
And here you assume that vk=0, s - displacement of the center of the mass after the crash. Then you can solve this equation system to get t and a needed for the last part of calculations: F=m*a.

And also this article suggests another way:

https://www.wired.com/2014/07/how-do-you-estimate-impact-force/

So which method would you choose to calculate impact force approximately ? Or maybe you know about any better way to do it ?

Thanks in advance for reply

 

[IceBreakerSours]

Impact is a transient event so inertial effects (mass/density) play a critical role in determining the forces (analytically in simple elastic impact sort of situations; numerically, otherwise). It does not seem like you are interested in impact. Instead, it seems you are interested in contact forces; not sure. Anyway, analytical solutions of simple problems have been around since Hertz first solved a problem so I bet some time on Google/Wikipedia will be sufficient for some quick introduction to the topic.

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[Student BE]

I realise that it should be transient analysis but I would like to simplify it and use static analysis. Unfortunately the best example I've found is in Polish but I would like to do something like that:

https://www.arcjournals.org/pdfs/ijmsme/v3-i1/1.pdf

in steady state. So I want to calculate force like in these articles and then apply it in simulation.

And apart from simulations - why there is difference between these 2 articles ? Which equation is correct ? W=(1/2)*F*s or W=F*s ? And which method would you recommend for hand calculations ?

 

[IceBreakerSours]

I cannot spend time figuring out what others have written but the basic ideas are simple. In case of impact, you want to use conservation of momentum as your guiding principle. Khan Academy has a nice grade school level introduction on this subject, if you are new to mechanics. Otherwise, try this link for an undergraduate mechanics level introduction.

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[rb1957]

I'm voting for 1) in that it is the area under a linear increasing force. 2) seems to me to be saying that the impact force is effective at t=0, being applied continuously over the deformation distance, s (or d or x).

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