The problem comes up as part of a final master's project in FEM analysis. The project consists in calculating the oscilation response of the World Trade Center towers after the plane impacts. The particular problem I'm having trouble is that I need to transform the plane impact of wich mass and speed is known, to data the FEM software can use: force in a period of time. The software allows you to define a table of points of F and t. The data I have is: Plane speed: 166.67 m/s Mass: 170 metric tonnes. Length= 50m The plane penetrates 30 m inside the building before it stops. I've tried two suggested solutions. - Aceleration is constant. I use the classic equations: F=m*a a=a_0 (constant) v=a_0*t+v_0 (v_0=166.67 m/s) s=.5*a_0*t^2+166.66*t+s_0 (s_0=0 as I use the very moment of impact as reference for t=0) Solving with the data: v_final^2-v_0^2=2*a_0*s; a_0=(0-166.67^2)/2*30=-462.98 m/s^2 From velocity equation: 0=-462.98*t+166.67; Solving for t gives t=0.36 s (this is the impact time) Equivalent Force: F=170000*462.98=7870660 N So the plane impact is equivalent to a Force of 7870660 applied during 0.36s. Using the software, it's equivalent to a "pulse": A horizontal line during .36 seconds. Is this correct?. After running the FEM sim, maximum deflection at top of tower gives 0.4 m, that I assume as correct, as the real tower swinged 0.6 m and after all simplifications of my model I think is close enough. - Second solution: deceleration is linear (not constant). 0 at the moment of impact and maximum when the plane stops. Our acceleration will be: a=a_plane*t;(Assuming a=0 at t=0) Integrating the expression we can obtain velocity and distance: v=a_plane*t^2/2+v_0 s=a_plane*t^3/6+v_0*t We know that at s=30→v=0. We also know that v_0=166.67 m⁄s . We obtain a non-linear two equation system. Solving it we obtain than a_plane=-4572.4188 m⁄s^2 and t=0.27 s. The plane stops at 0.27 s from impact. The force we need to define in is: F=m∙a=170000∙-4572.4188∙t=-7.773∙10^8∙t N, applied during 0.27s, gives a triangular shape in the software F-t graphic. This solution gives a deflection of several meters, so it's not correct, but I don't see where I made a mistake. The area of the graphics for both assumptions should be the same, but it isn't. Any ideas? Thank you very much.