I am currently designing a containment vessel that must withstand an impact of 290 mph. I am contemplating how to calculate the impact force to run simulations in Mechanica. The two methods being considered are energy and momentum.
For Energy, I would equate the kinetic energy (.5*m*v^2) to the force*distance, the distance being the shortest length from the outer edge of the vessel to the critical point being examined in the vessel.
For momentum, I would equate the momentum (m*v) to the impulse (F*t), where t is the time it would take to travel the previously defined distance at 290 mph.
After I get either number, I would apply a certain safety factor to keep everything conservative.
I have yet to crunch any numbers. I am simply trying to get some perspective from others, hopefully someone who may have experience with these kind of calculations.
I just want some feedback on these methods or suggestions of other methods I should consider.
I agree with Fred, to expand a bit
Equate the kinetic energy just prior to impact to the internal strain energy stored at the maximum displacement, when the kinetic energy is 0.
The elastic strain energy stored is equal to the work done, 1/2 times the force times the maximum displacement
You could apply a load to get the stiffness, and then solve for the dispacement using the above.
Include the potential energy if required.
I don't now about tearing and plastic deformations, that would be a huge undertaking, but you indicated using a factor of safety, one buy product of the safety factor is that you can normally use linear elastic analysis.
As I indicated, the elastic strain energy stored is equal to the external work done, which is much easier.
Internal strain energy stored = 1/2*Force*displacement, which is 1/2*K*d^2 where K is the elastic stiffness corresponding to the location and direction of the force F.
So, do a model, apply a load F, determine the displacement and then the stiffness. Then euqate to the Kinetic energy and solve for the displacement, then the force F=K*d (a dyanmicallly amplified equivanlent force) and solve for the resulting stresses.
You might be able to find classical solution (like from Roark), or and conservative simplification, but if not, you may need to use an analysis program to get the stiffness. (Or possibly do the entire problem)
The equation that Fred referenced can (and probable was) be derived using the above.
As a simple first step, calculate the deflections and stresses due to the static weight of the projectile at the impact point. Then the ratio of deflection and stress at 290 mph to static is sqrt((290mph)^2/(g*static deflection)).